Gravity Gradient Boom Design

Gravity Gradient Boom Design MIM 702

The Capstone Design Course Report Format Project #9 Second-Quarter Report

Design Advisor: Prof. Gregory Kowalski Design Team Jason Stricker, Arthur Inglot, Gene Rossov, Jack Rafalowski, Steve Souza

Department of Mechanical, Industrial and Manufacturing Engineering College of Engineering, Northeastern University Boston, MA 02115

Gravity Gradient Boom Design

Design Team Art Inglot, Jack Rafalowski, Gene Rossov, Steve Souza, Jason Stricker

Design Advisor

Sponsor

Prof. Gregory Kowalski

NASA, Ames Research Center John Hines

Abstract Attitude control systems are a very important aspect in satellite design. The Northeastern design team’s goal is to develop a passive gravity gradient boom design that can be used on the ONYX satellite or be adaptable to other micro satellites. The ONYX, designed by Santa Clara University in collaboration with NASA, is a micro satellite in an Earth reconnaissance and research mission. During its intended 45 day mission, the ONYX will operationally test autonomous computer control techniques while conducting an Earth observing mission, providing educational services as well. Attitude control for an imaging satellite is vital. The objective of the design team is to develop a gravity gradient boom (GGB) for passive attitude control, while following specified design parameters set forth by NASA and Santa Clara University’s ONYX satellite team. These design parameters are: the GGB system must not exceed a physical volume of 12cm x 12cm x 15cm, the system must stabilize the satellite to +/- 5° with respect to the Earth pointing Nadir vector, it must be under a 10kg weight, must not hinder physical properties of the overall satellite (ONYX), must be inexpensive, and strong enough to withstand launch vibrations. The key design features of this system consist of space qualified materials, a tip mass, a single bolt release mechanism, a non motorized mass launch, and a spool of specifically chosen wire.

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TABLE OF CONTENTS Error! Bookmark not defined. 1.0.0 PROBLEM STATEMENT.................................................................................................................... 5 2.0.0 PROJECT RESEARCH ........................................................................................................................ 6 2.1.0 Micro Satellites.................................................................................................................................. 6 2.2.0 ONYX ............................................................................................................................................... 6 2.3.0 Orbital Study ..................................................................................................................................... 7 2.3.1 Orbital Paths................................................................................................................................... 8 2.3.2 Polar Orbit ...................................................................................................................................... 8 2.3.3 Sun synchronous............................................................................................................................. 8 2.3.4 Low Earth Orbit (LEO) .................................................................................................................. 9 2.4.0 Attitude Sensors and Control Devises ............................................................................................ 9 2.4.1 Sensors............................................................................................................................................. 10 Sun Sensors ........................................................................................................................................... 10 Horizon sensors..................................................................................................................................... 10 Magnetometers ...................................................................................................................................... 10 Star Sensors........................................................................................................................................... 11 2.4.2 Attitude Control Devises ................................................................................................................. 11 Active Attitude Control ............................................................................................................................ 12 Reaction Wheel...................................................................................................................................... 13 Momentum Wheel.................................................................................................................................. 13 Torquer Coils ........................................................................................................................................ 14 Controlled Momentum Gyro ................................................................................................................. 14 Gas Actuators........................................................................................................................................ 14 Passive Attitude Control........................................................................................................................... 15 Radiation Pressure................................................................................................................................ 15 Hysteresis Rods ..................................................................................................................................... 15 Gravity Gradient devices........................................................................ Error! Bookmark not defined. 2.5.0 Gravity Gradient Boom Physics ........................................................... Error! Bookmark not defined. 2.6.0 Deployment Devices ........................................................................................................................... 29 2.6.1 Importance to the ONYX ................................................................................................................ 29 2.6.2 Types of Deployment Devices......................................................................................................... 30 Tethers................................................................................................................................................... 30 Wire Drum Deployer............................................................................................................................. 34 Tubular Booms...................................................................................................................................... 35 Telescoping Booms................................................................................................................................ 36

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Coilable Booms ..................................................................................................................................... 37 2.7.0 Launch Vehicles ............................................................................... Error! Bookmark not defined. 2.8.0 Thermal Concerns ................................................................................ Error! Bookmark not defined. 2.9.0 Electrical System .................................................................................. Error! Bookmark not defined. 2.10.0 Space Collisions ................................................................................. Error! Bookmark not defined. 3.0.0 Final Deployment Device..................................................................... Error! Bookmark not defined. 3.1.0 Telescoping Booms ............................................................................................................................. 39 3.2.0 Wire-Drum Deployers ..................................................................................................................... 40 Size........................................................................................................................................................ 40 Weight ................................................................................................................................................... 40 Mechanical Complexity ........................................................................................................................ 41 Retractability ......................................................................................................................................... 41 Thermal Characteristics......................................................................................................................... 41 Length of Boom .................................................................................................................................... 41 Adaptability to other missions/small satellites ...................................................................................... 42 Structural Predictability......................................................................................................................... 42 4.0.0 The design ........................................................................................................................................... 42 4.1.0 Final Design ........................................................................................................................................ 42 5.0 Final Conclusion...................................................................................... Error! Bookmark not defined. REFERENCES...........................................................................................................................................6160 Appendix……………………………………………………………………………………………………62

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PHASE I 1.0.0 PROBLEM STATEMENT The main objective of this project was to develop an attitude stabilization system for a small satellite. The ONYX satellite was development by Santa Clara University with the aid of NASA’s Ames Research Center. The ONYX is classified as a micro satellite, having a mass of 30 kilograms. It will travel in a Low Earth Orbit (LEO) at an altitude between 500-700 kilometers taking multi-spectral images of Earth. It will operate with the use of autonomous control techniques, through an advanced microprocessor analysis and control system. Northeastern University’s role in this project is to create a passive attitude control system that will be tested on the ONYX and possibly other small satellites flying similar missions.

The Northeastern team goal was to design a gravity gradient boom for passive stabilization to integrate with the ONYX. Image capturing satellites, such as ONYX, have additional stabilization needs as well. As a satellite orbits an image can only be taken when the target is in view. A proper stabilization device will reduce the movements in the X, Y, and Z axis to a minimum, allowing the satellite’s camera to focus and take clear, undisturbed pictures. There are several design classifications of deployment mechanisms for gravity gradient booms. The Northeastern design team will strive to build a passive control system that will be precise in its orientation over long periods of time. The goal is to implement a successful stabilization system that directly interfaces with the Emerald Protocol Suite, conforming to the specifications of NASA and needs of Santa Clara University.

The constraints that the designed gravity gradient boom must follow consist of mass, volume/size, and power consumption. The final design must have a mass less than 10kg. Dimensions of the completed system are limited to the available area inside the ONYX or the cylindrical launch envelope on the outside. The final size of the GGB system must not exceed a 12cm x 12cm x 15cm volume. The power is limited to 30 watts. However, power consumption could be zero if system would be completely passive. Additional requirements that the system must adhere to is to generate a pointing accuracy of +/-5 degrees with respect to the earth pointing Nadir vector. It also must not hinder the satellites physical properties, be inexpensive, and extremely adaptable to other satellites. The system must be small and lightweight.

The gravity gradient boom design was appealing for several reasons. A well designed device can provide accurate control and stabilization, without the constant use of power. In addition, a correctly chosen deployment mechanism can be compact and cost efficient. The concept behind the gravity gradient boom has been around for several decades, and initial studies and research have shown that it is effective on small satellites similar to the ONYX.

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Similar to all space/flight components, a prototype must be physically tested to meet space flight requirements. This is usually done on a three dimension vibration table to simulate launch conditions. However, similar tests regarding vibration and physics principles do to time constraints have been obtained. Vibration tests can be obtained through CAD drawings and ANSYS simulations. Physics equations can be calculated using excel and MATLAB.

2.0.0 PROJECT RESEARCH AND BACKGROUND As stated previously the Northeastern team will be responsible for the stabilization and attitude control of the satellite over the course of its 45 day mission. However, before the team can design an attitude system, certain other areas of satellite flight and operation must be researched. These areas of research include orbital studies, launch vehicle vibration profile, and thermal effects.

2.1.0 Micro Satellites The micro satellite is a classification of small satellites more than 10kg and less then 100kg. The micro satellite is the most common researched satellite used in the small satellite category. The main reason engineers try to keep the satellite mass low is due to the high cost launching to reach a low earth orbit (LEO). A launch costs an estimated $10,000 for every kilogram that is sent into space. [ ] Micro satellites in the past decades have provide images of Earth and Space, as well as preformed numerous tests. Since mass is such an issue when designing a satellite, every aspect that goes into the satellite must follow strict design considerations.

2.2.0 ONYX The ONYX satellite is an ongoing project of Santa Clara University, headed by Chris Kitts. ONYX is designed in collaboration with multiple departments of the United State’s government including; the Air Force Research Lab (AFOSR), Defense Advanced Research Projects Agency (DARPA), and the NASAAmes Research Lab. The purpose of ONYX, short for ONboard autonomY eXperiment, is to monitor anomalies in orbital motion and resolve them using two autonomous processing systems. The output of this system provides two simultaneous solutions. The optimal solution is then acted upon and recorded. This system is the first of its kind, and one of the interests the defense agencies and the AFSOR have in this

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project. The ONYX satellite is also equipped with a camera cable of capturing images in multiple ranges of visual and non visual light. During the duration of its 45 day mission ONYX will take images of Earth in multiple spectrums. The images captured are used for educational and research purposes. The 30kg hexagonal ONYX has dimensions of 21cm per hexagonal side and 42cm tall. This satellite is capable of different orbits depending on its desired mission or the mission of the launch platform it piggy backs on. One focus of the ONYX project is to be adaptable to change its configuration for different research purposes. These multiple trials and launches will ensure continued research and development of and in time a more successful satellite. See Figure 1 for a CAD model of the hexagonal ONYX.

Figure 1: ONYX Satellite

2.3.0 Orbital Study

When designing a free-flying satellite one of the most important aspects is the orbit of the satellite. The orbit of a satellite will affect the radiation and thermal control of the system. A satellite’s orbit is determined by a combination of two forces: the earth’s gravitational pull and the satellite’s horizontal velocity. Basic physics demonstrates that gravitational pull is the attraction of two massive objects, in this

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case the mass of the earth and the mass of the satellite. Gravitational pull prevents the satellites’ velocity from propelling it off into deep space; the velocity of the satellite prevents the gravitational pull from bringing the satellite crashing down to earth [5].

2.3.1 Orbital Paths

Many different types of satellite orbits may be chosen depending on the specific function of the satellite. These different orbits depend on the path it passes over and the altitude. The three aspects that should be explained are polar and sun synchronous orbit and low Earth orbit (LEO).

2.3.2 Polar Orbit

A polar orbit is an orbit with an inclination of 90° from the equator. A satellite with a polar orbit circles around the earths’ poles. Polar orbits are very useful for satellites that carry out mapping, surveying, or surveillance functions due to the fact that the rotation of the earth grants the satellite access to almost any point on the earth [5]. A polar orbit may be used; however the satellite’s attitude and orientation would constantly change as it orbits around the North Pole, equator, and South Pole. When over the North Pole the satellites imaging face will be pointing towards earth. Over the equator the front face will be parallel to the plane of the equator and over the South Pole the front face will be pointing away from earth. The use of sensors and careful deployment of the gravity gradient boom would have to be used due to the constant shift in satellite attitude and orientation.

2.3.3 Sun synchronous

Overexposure to the heat of the sun may be a big concern when designing a satellite. Particular instruments and equipment may not be able to withstand the higher temperatures when the satellite is orbiting in sunlight. This will decrease performance and hinder the mission of the satellite. A sun synchronous orbit has an orbital plane with the same period as the planets’ solar orbit period [5]. With this type of orbit the satellite will have a period of shade as well as sunlight. Due to extreme temperature changes the satellite can endure thermal shock. Thermal shock will be further analyzed in the course of the project.

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2.3.4 Low Earth Orbit (LEO)

The majority of free-flying satellites are launched into a low earth orbit (LEO). A low earth orbit generally falls into an altitude range of 100-1500km above earth. Low earth orbits are often used for free flying small satellites that are not supposed to remain in space indefinitely. A satellite whose orbit path crosses through earth’s magnetic gravity gradient will gradually be pulled down to earth. The satellite will then decay due to aerodynamic frictional forces created by the earth’s atmosphere [6]. Depending on the starting altitude, the length of time that the satellite remains in orbit can be determined. Most of the experiments performed on free-flying small satellites are designed to last from 96 hours to a couple weeks. The ONYX may have a LEO path.

2.4.0 Attitude Sensors and Control Devices

Figure 2: Orientation

Attitude, or orientation, is determined by the satellite’s position relative to a set location. Its orbit is portrayed by a coordinate in the three axes: X, Y, Z. There are different levels of orientation control for satellites. Figure 2 above shows these three axis and there term of rotation in a given axis. A satellite will rotate in these axes randomly as it freely spins in orbit with out control. In the fifty years of space travel multiple control systems have been successfully designed and used. The selection of attitude control devices and systems are chosen according to the satellite’s mission and project constraints.

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2.4.1 Sensors

A satellite must use a sensor to provide a frame of reference for the satellite giving it a location as well as attitude in the X, Y, and Z plane. With this data gathered the attitude adjustment devices can be controlled. Five sensors that are readily used in satellites and other spacecrafts are; sun sensors, horizon sensors, magnetometers, and star sensors. These sensors all have different methods of gathering information regarding the satellites position and behavior.

Sun Sensors

Figure 3: Sun Sensor Sun sensors use the suns power to determine orientation. This sensor determines this by analyzing the solar energy gathered by the solar panels. The sun sensor can determine the angle the sun is hitting the solar panel as well as the distance from then sun. [1] Sun sensors are the most common attitude sensor. [3]

Horizon sensors

Figure 4: Horizon Sensor Only effective in LEO, horizon sensors measure the difference in brightness of earth compared to the darkness of space using the infrared spectrum view. With this it can measure the satellites distance from Earth and provides a reference point for judging attitude. [4]

Magnetometers

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Figure 5: Magnetometer This sensor measures Earth’s magnetic field. This is another popular device due to its output in vector components, low weight, and operating power. Once again this switch is only accurate under 1000 Km. [4]

Star Sensors

Figure 6: Star Sensor The star sensor is known for its very high accuracy; however it is heavy and expensive. They are mainly used for higher Earth orbits. Its accuracy works by setting up a coordinate system between cataloged starts. [4]

2.4.2 Attitude Control Devices There are three primary reasons to control the orientation or attitude of orbiting satellites. The first is for communication needs. Satellites must have a connection or link to ground stations through its antennas. If spinning and motion is uncontrolled the connection will be difficult to obtain for any period of time. The second is in regards to positioning with respect to the Sun. A satellite must collect energy from solar panels to recharge its batteries. However, if there is no spin and a section is in direct sunlight to long thermal shock and deformation can occur. The third and most relevant in ONYX case is for image capturing. Satellites equipped with camera must have some form of attitude control to obtain a deseed image. If a satellite’s orientation in orbit is not controlled; all of these essential processes would not be possible.

Attitude control devices are classified in two main subcategories, active and passive. Active design systems use energy in pulses or continuously from a stored power source such as batteries. The batteries in a satellite can be recharged through energy collected by solar panels. Active control devices that are currently in use include reaction wheels, momentum wheels, torquer coils, controlled momentum gyros, and gas actuators. All have their benefits and draw backs and are carefully selected to optimize the mission of a satellite. Passive design systems do not use internal energy. Instead of using energy from a stored source, they use physics properties and theories for attitude control. The three main passive controls each use

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different principals to achieve attitude control. In many instances devices can be combined to form a system that fits the project’s requirements. Located on the next page is the device matrix based on the summation of this research.

Table 1: Attitude Control Device Matrix ATTITUDE

Active (A)

CONTROL

or

DEVICES

Passive(P)

Power Needs L 1

Controlled momentum gyro

A

Gas actuators

A

Gravity gradient

P

Hysteresis Rods Momentum Wheel Radiation Pressure

P

A

P

Reaction Wheel

A

Torquer Coils

A

2

Cost

H

L

4

1

3

2

Has it been found in

Weight H

L

3

1

30kg > satellite H

2

4 when needed

3

3

(see sec )

(see sec )

(see sec )

4 Limited supply

2

3

(see sec )

(see sec )

(see sec )

1 Deployment

1

1

(see sec )

(see sec )

(see sec )

0 no power needed

1

1

(see sec )

(see sec )

(see sec )

3 Contrant draw

3

3

(see sec )

(see sec )

(see sec )

0 no power needed

3

1

(see sec )

(see sec )

(see sec )

4 when needed

3

3

(see sec )

(see sec )

(see sec )

3 when needed

2

2

(see sec )

(see sec )

(see sec )

2.4.3 Active Attitude Control

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3

YES or NO

NO

YES

YES

YES

YES

YES

YES

YES

Reaction Wheel

Figure 7: Reaction wheels use a motor to spin a mass, creating a torque. This torque provides a moment when needed, which controls the satellite’s attitude in orbit. This device can be extremely accurate; however, it has two drawbacks for an active device: cost and weight. One reaction wheel can cost several thousand dollars. For a complete control system three must be used, one for each axis of rotation. Adding to this cost is the software, sensors, and additional batteries needed to run the system. Each device consists of a motor and solid circular mass. This adds substantial weight to the design yet is very efficient. However because of its high stabilization precision, the use of a reaction wheel may be justified. With this control a satellite can point to multiple locations in space and on Earth. [1]

Momentum Wheel

Figure 8: Momentum Wheel Momentum wheels are similar to reaction wheels, but with one difference. Momentum wheels are continuously working as opposed to reaction wheels which only work in short bursts. This gives a constant rotational velocity stabilizing the satellite. Since only one momentum wheel is needed and it does not require the same computing software as the reaction wheel, the cost and weight are less. However, it does not achieve the same precision and attitude adjustment abilities as a reaction wheel that you can choose. Momentum wheels are used more as stabilization then axial motion. [1]

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Torquer Coils

Figure 9: Torquer Coils This system uses the Earths magnetic field for attitude control. Torquer coils are loops of wire that current runs through to create an adjustable magnet field. This device responds to changes of attitude and corrects its orientation. This device is only effective in low Earth orbit, and most efficient in an equatorial orbital trajectory. The reason for this is that Earth’s magnetic gradients are projected from its poles and at more elevated orbits the magnetic force can not be used effectively due to weaker forces when further away from the Earth.

Controlled Momentum Gyro

Figure 10: Momentum Gyro The momentum gyro works by spinning on mass in multiple axes, and operates when needed, as determined by a processor. One gyro can do the same work as three reaction wheels. Although this is a benefit, it has a higher cost and mass than the momentum wheel system and rarely used in small satellites. [1]

Gas Actuators Gas actuators release pressurized gas that is stored in the satellite for control. Although the force it creates has the capability to be significantly higher then the other active control devices, its energy source is limited. While batteries can be recharged by solar energy, propellant is limited in quantity. Gas actuators

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are classified in as either hot or cold. Hot gas actuators undergo a chemical reaction where as cold gas actuators do not. [1]

2.4.4 Passive Attitude Control Radiation Pressure Radiation pressure uses the energy from the sun as a passive a control device. Solar radiation pressure exerts a force by harnessing the photons on a defined area. An effective surface must be of significant size and directed towards the sun. This proves that solar radiation pressure can not be a stand alone passive device. This system needs a complex active system, such as reaction wheels or a momentum gyro to insure that its normal vector is constantly pointing towards the sun.

Hysteresis Rods Hysteresis rods use the same magnetic principle as Torquer coils, yet are completely passive. This system aligns a desired face towards the Earth’s magnetic field. Common materials used in this system are magnetized nickel, iron, and cobalt. The system is designed to dampen the rotation velocity. Complete stabilization of a satellite using hysteresis rods would create a heavy control system. This attitude control system is determined by the strength of the rod’s flux and the number used. Many satellites use this system as a primary means of attitude control because it is passive, light, and inexpensive. Multiple satellites will use hysteresis rods as a secondary control device along with a primary active system.

2.5.0 Gravity Gradient Boom Physics Gravity gradient booms were first used by NASA in LEO satellites in the late 1960’s with minimal success due to they’re complexity. Further testing in and more advance computing capabilities in the 90’s gave rise to more accurate means of solving ordinary differential equations. This proved them to be a valuable means of passive attitude control for one main reason. They use little or no electrical power relying mostly on stored energy in springs for deployment and once deployed require no means of power, as they rely heavily on astrophysics and orbital mechanics. Many small satellites have employed the use of these booms in LEO.

The structure of a gravity gradient boom consists of a base which is attached to the satellite. This base unit contains a deployment system which, once the satellite is in space, deploys the boom structure which holds the tip mass. The boom can either be a rigid structure like a truss or it can be made out of wire. Boom lengths vary from hundreds of centimeters to hundreds of meters depending on the orbit, mass of the

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satellite, and mass of the weight at the end of the boom. The mass at the tip of the boom is the last major piece to this system. This mass can vary but is generally only a small percentage of the satellites total mass, approximately 5 to 10 percent. [7]

A gravity gradient boom works on the basis of Newton’s Law of Universal Gravitation, equation 1, which states that the force of gravity is inversely proportional to the distance between the two objects. Also the satellite is in an orbit giving rise to an orbital velocity.

1)

FG = G

m 1m 2 R2

The gravity gradient boom is sent into space as part of the overall satellite structure. As the satellite is deployed from the launch vehicle the force of gravity acts on the gravity gradient boom and the satellite equally because the boom is stowed inside the satellite during take off. The satellite and boom now have a characteristic orbital path; it has a specific altitude, orbital velocity, and eccentricity. Next the gravity gradient boom is deployed from the satellite toward earth.

Conservation of momentum holds true in the case of the satellite/tip mass system. A force is needed to give the mass a velocity away from the satellite. In turn the satellite is given a resultant velocity in the opposite direction. Equation 2 shows this relationship. 2) m sat v sat = − mtip v tip As the two masses, the satellite and tip mass, respectively, move away from each other the systems center of mass changes as well. Now because the masses are so far away from the center of mass of the system the center of mass is no longer the point where the system orbits the earth. Instead because the gravitational field is not uniform over the entire system the center of gravity is actually slightly closer to the Earth than the center of mass and it is the new point of orbit for the system. Figure 11 depicts the difference between the two. It also shows the different types of forces this system experiences.

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Figure 11: Gravitational Force When the mass deploys the satellite experiences an equal and opposite reaction and moves above its orbital plane while the mass moves below it. The two are still connected and this connection causes the tip mass and the satellite to continue to act as one system. The tip mass now has a lower elevation than the satellite; it experiences a higher gravitational force than the satellite. The satellite on the other hand experiences a higher centrifugal force, similar to that of a bucket of water being spun around by the handle. The water continues to stay in the bottom of the bucket whether it is spun horizontally or vertically. The reason the satellite has a greater centrifugal force is due to the fact that the two masses, the satellite and the tip mass, are traveling in the same vertical plane although the satellite is farther away from the Earth. This force, although an artificial force, gives a good representation of how the angular momentum will cause a tension on the connection between the satellite and the tip mass. This centrifugal force is caused by the angular momentum.

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The system shown in figure 11 is in equilibrium, thus it is not oscillating. This is because the center of mass of the satellite, tip mass, and Earth are all in line with each other. The gravity gradient is acting on the satellite and the tip mass is in line. There are no horizontal vectors of the gravitational gradient in this figure. This is almost never the case especially when the system is first deployed. When the boom is deployed there are dynamic, vibrating, and atmospheric forces acting on the satellite, therefore it will never be in total equilibrium. Certain sensors and other monitoring devices will show how the satellite behaves when the boom is deployed.

Sensors on the satellite relay information on the position of the satellite relative to certain celestial bodies such as the Sun, the Moon, or the Earth. These sensors are linked to the electronics which then make the decision whether or not to deploy the boom. The boom must be deployed in such a way that it travels towards the Earth if the satellite is to be oriented in that direction. If it was deployed in the direction of the orbital path the system would be horizontal and the there would be no difference between the force of gravity acting on satellite or the tip mass. It is crucial for the mass to be deployed when it is in the same vertical plane as the satellite but in a lower orbit. This would allow the force of gravity to be stronger on the tip mass, stabilizing the satellite.

Once the mass is deployed, the whole system will have similar tendencies to a pendulum. This is due to vibration and atmospheric forces and the tip mass not being precisely aligned with the satellite and earth’s gravitational field. In a pendulum the tip mass stops swinging once the force of gravity aligns the center of mass with earth’s gravitational field.

The stability or tolerance of the system once it is in relative equilibrium is also a main concern. The system will never be totally damped without oscillation due to disturbances found in space. This will be a crucial part in case study research because the gravity gradient boom needs to develop a torque that will over come all environment and atmospheric torques combined. When this is achieved the stabilization of the satellite body is a maximized.

Small satellites have many different functions ranging from communications, observation, or scientific research missions. It is vital for them to overcome any disturbances that can disrupt their mission. One such disturbance as mentioned previously is oscillation due to the satellites angular momentum as it orbits the earth. This oscillation can throw off the stabilization tolerance which is +/- 5 degrees along the nadir vector pointing straight toward earth. MATLAB was used to model these oscillatory motions and select boom length and tip mass.

The Coriolis Effect

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Figure 12: Coriolis Effect

Figure 13 : Coriolis Effect

An additional disturbance that has to be taken into consideration is the Coriolis Effect. This is defined as the effect whereby a body moving in a rotating frame of reference experiences the Coriolis force acting perpendicular to the direction of motion. [8] Figure 6 and 7 shows the Coriolis Effect taking place on a disk with reference points A and B. The disk can be thought of as a merry go round. The ball is centered at point A and moves to an outer edge, point B while the disk is uniformly spinning. For someone standing at a reference point outside the spinning disk the ball appears to be traveling in a straight line from point A to point B. However, standing in the reference points A and B, the ball moves in a curvilinear path as seen in Figure 8. The Coriolis Effect may happen in space when the satellites orbit is thought of as a uniformly spinning disk. As the satellite spins along its orbit the gravity gradient boom is deployed towards earth. The system may appear to be deploying straight but in reality it is actually twisting and curving around itself. The severity of the Coriolis Effect will be determined once the orbit and orbital speeds are known.

3.0.0 ADDITIONAL DESIGN CONCERNS There are several important design concerns that must be taken into consideration when building a gravity gradient boom and especially when designing a satellite.

3.1.0 Launch Vehicles

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The Northeastern team along with the Santa Clara team has not yet received information on a launch provider and specific launch vehicle. Launch vehicle information is critical for vibration and cyclic stress load analysis. The gravity gradient should be able to withstand vibrations of any launch vehicle. These vehicles are the Falcon 1, Minotaur I and IV, Dnepr-1, and the Delta IV. The gravity gradient boom will be designed to withstand the harsh vibrations of these rockets during take off as well as immense g-loads during flight.

To insure that the gravity gradient boom does not negatively affect the structural stability of the ONYX it will be designed to the same specifications as the ONYX. The gravity gradient boom will be designed to withstand +/- 20 G’s and a maximum vibration of 500 Hz. Conforming to these values will safely allow the ONYX to be launched on any available launch provider.

3.2.0 Thermal Concerns A great concern when designing a gravity gradient boom for the ONYX is the thermal effects of solar radiation. Solar energy absorbed by a satellite in space is much greater than on earth because of the lack of atmosphere in space. Getting rid of that solar energy also proves to be a much harder task because convection is not present as a form of heat transfer in outer space. A satellite has three methods to get rid of solar energy: radiation, conduction, and reflection. Solar energy will also effect the satellite and gravity gradient boom with regards to thermal shock and thermal distortion.

Thermal shock occurs when the object transitions rapidly from a shaded configuration to a sunlit one [9]. In the case of gravity gradient boom, when this happens the temperature differential is so sudden and large, that rapid thermal expansion causes the boom to oscillate transversely. Temperature can change from extremes as high as 40-50 degrees Celsius to as low as -20 degree Celsius. Oscillations are detrimental to a satellite’s mission especially when the attitude tolerance is within a few degrees, as it is on the ONYX. Thermal shock can be completely ignored if the satellite has an independent damping device to counter oscillations [9]. Thermal shock can also be unfavorable for the boom deployer.

A deployer mounted externally on the satellite will be directly affected by the effects of solar radiation. A deployer mechanism can either be a DC motor or a simple release system. The more moving parts in the deployer mechanism the more thermal conditions have to be taken under consideration. A DC motor can be most affected by thermal shock as it has more moving parts than a simple release system.

Thermal distortion is the outcome of slow heating of an element in space. An object that is partially in a sunlit configuration and partially in a shaded configuration with little change for extended periods of time

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will experience distortion due to non-uniform thermal expansion. In the case of a gravity gradient boom, thermal distortion will cause twisting and curvature in the boom [9]. Deformation of a boom is not as detrimental to the satellite mission as oscillations would be, but should still be considered in the design process. In the case of a telescoping boom thermal distortion can be countered by using a reflective thermal coating or paint that reflects the suns energy back into space [9]. Perforating the boom could also be done so that the front and back of the boom receive an even amount of heat [9].

A deployer mounted on the inside of the satellite will be protected by the thermal control system of the satellite. Solar cells on the outside of the satellite will be absorbing a large flux of the solar energy as well as reflecting a small percentage back into space. Mounting the deployer on the inside of the satellite would be the preferable configuration as it would eliminate the requirement for an independent thermal control system for the deployer.

Figure 18: Satellite Heat Balance

The gravity gradient boom system will be stored inside the satellite for an indefinite amount of time. The gravity gradient boom will deploy when all the passive stabilization devices have slowed down the spin rate (also known as tumbling) to .3 meters per second. During the time that the boom is in inside satellite, the satellites thermal control system will insulate and protect the boom from outer space. Figure 18 shows a typical heat balance for a satellite. A brief overview is provided on how small satellites use passive and active thermal control systems to maintain a proper heat balance.

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Passive control systems use thermal coatings, metalized tapes, special paints, MLI (Multi Layered Insulation) blankets, and radiating surfaces. Active systems use heaters, coolers, thermostats, temperature controllers, and coolant loops that are incorporated into the satellites structure. The thermal control system for small satellites is always built around a passive design first and an active system may be incorporated if necessary.

3.3.0 Electrical System Integration The ONYX micro satellite utilizes the Emerald Protocol Suite developed by students at Santa Clara University. The Emerald Protocol Suite is a modular system with multiple spacecraft bus support nodes. The system was designed to be used as a standardized method of satellite communication and power for micro satellites. Two separate buses are used, one for power and telemetry (EPTP) and one for data transfer (EDP). Standard 9-pin serial port connectors are used to tap into the system for both the data and power buses. A standardized hardware interface eliminates the need for complex wiring systems and harnesses. The design of the gravity gradient boom deployment device will directly interface with the Emerald Protocol Suite. The figure below illustrates the various subsystems and how they are linked across the two buses, EPTP and EDP. The PIC Mechanical board is the subsystem that the deployment device will have to interface with. Two DC motor controls and two release mechanism control are included in the Mechanical subsystem. In the case of the example in the figure below the DC motor controls are being used to drive two drag panel linear actuators. One release mechanism is used for the VLF antenna release and the other is used for inter-satellite separation. Utilizing the data bus (EDP) will provide the capability of using potentiometers to determine length of deployment of the boom. The design team will be workingin conjunction with Santa Clara University to interface the deployment device with the mechanical board.

22

Figure 19: Emeral Protocol Suite Layout

3.4.0 Space Collisions

Another aspect that must be considered when designing a gravity gradient boom is possible collisions with other satellites and space debris. Collisions with other satellites can be avoided by selecting a clear orbital path for the launch profile of the satellite and selecting a boom design with a reasonable length. Designing to account for random collisions with space debris can be a difficult and expensive task. A retractable boom design could be an effective solution, for example if a collision occurred and threw the boom out of sync, retracting the boom and redeploying it could save the attitude control system.

4.0.0 PRELIMINARY GRAVITY GRADIENT AND CENTER OF MASS STUDY

23

The purpose of this study was to determine the amount of force needed to align a wooden block in such a way that the desired face was parallel to the ground, as shown in figures 14. Initially the block is suspended from one of the larger faces while the other large face is parallel to the ground as shown in figure 14. This leaves the desired side perpendicular, the undesired orientation.

Figure 14: Preliminary CAD drawing of wooden block This problem was first modeled in Solidworks. The reason for this was to determine the center of mass of the system when it was off set with a large bolt. When this point was determined the eye bolt was then added to the system but in line with the face of the desired side which would be perpendicular with the ground and this center of mass (C.M) of the system. The system’s center of mass now shifts but only in two axes. The system is suspended from this point (center of mass) and the two large faces are parallel to the ground. Since this is system is not moving it is in static equilibrium and equation 3 applies. T is the tension in the wire secured from the C.M. to the ceiling.

∑F =T −m

Tot

3)

g =0

mTot = mbolt + meyebolt + mblock g = 9.8

m s2

The next step was to determine the correct weight in our “tip mass” to give a desired torque to orient the desired side parallel to the ground. This was done by taking the sum of torques about the C.M. and using the “tip mass” as the intended variable to solve.

24

Figure 15: Force diagram on wooden block

∑F =T − F

CG

− FGG

FGG = (nwasher )(mwasher )( g ) FCG = (mTot )( g )

∑M

o

= FGG (.07 m) − (T )(.0175m) = 0

mbolt = 0.011kg meyebolt = 0.018kg mblock = 0.048kg mwasher = 0.0019kg

nwasher = 6

25

Figure 16: Force diagram on wooden block

Figures 15 and 16 show the different forces on the block. The distances are as follows: x1=0.07m, x2=0.0175. Because Solidworks solved the C.M. for us the forces from the mass of the bolt and eyebolt were not needed. The required amount of weight was determined to be approximately 0.0114, the amount of 6 washers. The washers were attached to the eyebolt via a string. The length of this string was irrelevant, as opposed to our GGB design which incorporated boom length.

The 6 washers were held manually. The block was oriented as pictured in figure 14. The washers were then let down and the system oriented itself in the direction shown Figure 15 and 16.

The correlation to the GGB is as follows. The tension in the top of the wood block is relative to the centripetal force exerted on the satellite while the washers at the end pulling down is relative to the force exerted on the tip mass from the GGB. In the case of the GGB the forces seen in orbit will be much greater, on the order of 300 Newtons for the centripetal force and around 16 Newtons for the gravitational force on the tip mass. These values will be shown more in depth later.

4.1.0 Gravity Gradient Boom Design Our gravity gradient design was modeled as a ridged body system. Using the equation: 4) Jα = .5 sin(θ ) Ftension Lcmtosat + .5 sin(θ ) Ftension Lcmtotip J was determined from the parallel axis theorem between the tip mass and the mass of the satellite to the position of the center of mass. The force of tension was determined using Newton’s Law of Gravitation and the centripetal force exerted by the rotational velocity. The gravitational force depended highly on the

26

value of theta as this changed our effective boom length. This boom length was coupled with cosine of theta to give an effective boom length and an accurate distance between the satellite and the tip mass. These forces for different altitudes are tabulated in appendix E. The force of tension of this system is also shown in a graphical representation from the offset angle in table 2.

Table 2: Force Tension 5

4

3

2

y = -2E-05x - 6E-16x + 0.0002x + 3E-15x - 0.0003x - 2E-15 2 R =1 Note: Alt=500km Tip mass=1kg, Lboom=10m

FRestore vs. Θ

0.00020

0.00015

0.00010

Newtons

0.00005

0.00000 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-0.00005

-0.00010

-0.00015

-0.00020 Radians

The distances from the center of mass were determined from the following equations: 5) Lcmtotip =

Lboom M tip / M sat + 1

6) Lcmtosat = Lboom − Ltip The centripetal forces exerted on each are as follows: 7) Fcentonsat = m sat rsat ω 8) Fcentontip = mtip rtip ω

2

2

The r values in these two previous equations are the distances to each respective part of the system. This is the key to gaining this attitude control. The angular velocity for the system is constant and is determined by the equation:

27

9)

ω=

M earth G r3

Figure 17: Free Body Diagram of ONYX and Force calculations This angular velocity is the only part of the system that stays constant. G is equal to 6.67x10^-11, it is the gravitational constant. The mass of the Earth is 5.97x10^24. We chose this circular orbit at an altitude of 500 kilometers because it has the most frequent small satellites and it also is out of has minimal aerodynamic resistance. Here are two figures of our satellite and the tip mass configuration with the resultant forces. Below is a dampening graph from Matlabs Simulink.

Figure 18: Free Body

diagram of ONYX satellite

28

Figure 19: Dampening graph from MATLAB Simulink

.

5.0.0 DEPLOYMENT DEVICES The selection of a deployment device to release the boom and the tip mass is crucial. The deployment device must meet all design constraints and not interfere with the satellites mission as well as physical properties.

3.2.1 Importance to the ONYX In recent years deployment devices have become very important to small satellites. One of the main goals of a small satellite is to make it as compact as possible to reduce cost. Today a satellite is launched into space in its compact state and then deploys its attitude and communication devices to operate and complete its mission. Small satellites today use a wide variety of deployment devices for gravity gradient booms. These deployment devices are telescoping booms, tubular booms, coilable booms, tethers, and metallic wire-spool deployers.

There are three main reasons why the gravity gradient boom must be stowed and then deployed after the satellite is launched as opposed to just building it as a stationary feature. First, there is a given physical envelope that the ONYX must not exceed for the launch. Without the use of one of these deployment devices it would be impossible to create an effective gravity gradient boom that would fit in this physical envelope. Second, the ONYX’s center of mass must be as close to the actual center of the satellite as possible. This is essential to ensure a successful launch and to reduce the “tumbling” motions once the

29

satellite is released from the launch vehicle. Finally, there must be some control over when the gravity gradient boom when deployed. It is crucial for the boom to be deployed while the satellites imaging face is pointing towards earth. A deployment device minimizes the risk of failure because it allows for precise deployment of the boom.

3.2.2 Types of Deployment Devices There are many types of deployment devices that could be used on the ONYX satellite. Each device will have to be fully explored determine which deployer would be optimal for the ONYX. Size, weight, cost, and reliability will be some of the main deciding factors as to which deployment device is chosen for the ONYX. The gravity gradient boom system cannot exceed a physical volume of 10x10x15 cm. It also cannot weigh more than 20kg. More importantly it must not drastically alter the center of mass and inertia properties of the ONYX. Finally, because the ONYX is a University built satellite, the cost of the whole system needs to be minimal. Choosing the correct deployment system will be the key factor in the accurate passive stabilization of the ONYX satellite.

Tethers Satellite tether stabilization is a fairly new area of research. Tethers are essentially long lengths of composite rope that either connect two satellite bodies in different orbits or use an electromagnetic force to stabilize the satellite.

Mechanical tethers simply work by connecting a sub-satellite body to the main satellite body. The lower satellite body will slow down and fall to a lower orbit because the force of gravity on it is stronger. The upper satellite is further away from earth, at the same time it will tend to speed up and move to a higher orbit. Eventually the tether will develop opposing tension on the two satellites and the system will become stabilized. For such a system to work, lengths of 2 kilometers or more are required.

Tethers can also stabilize a satellite by intersecting earth’s magnetic gradient field inducing an electromotive force along the tether. This force can be as powerful as several hundred volts per kilometer. [10] The tether will then start collecting electrons from earth’s ionospheric plasma field and the electromotive force will drive them up the tether. The current that is now flowing up the tether will begin to cause a Lorentz force that will oppose the motion of the tether and begin to lower the orbit of the satellite. Further stabilization can be had when a propulsive force from solar cells or batteries is generated opposing the original electromotive force. Figure 8 shows a rough sketch of how an electrodynamic tether works.

30

Figure 20: Electrodynamic tether stabilization The use of tethers is very appealing and has been widely researched with some successful missions dating back to 1996. However, there are still some major concerns which limit their performance. One major concern is the dampening of oscillatory motions after the tether is initially deployed. Due to the tether’s extremely long length and the difference in masses of the two satellites, there are several types of oscillations that can occur. These oscillations are detrimental to the tether and some instances to the satellite itself.

A tether system can be thought of as a ball connected to a string. The tether may compress initially which will cause longitudinal accelerations, as seen in Figure 21. If a current is applied to the tether and it reacts with earth’s magnetic field transverse oscillations and “skip-rope” oscillations can be experienced, as shown in Figure 22 and Figure 23. Figure 24 shows the pendulum motion which occurs at slower speeds. [11]

31

Figure 21:

Figure 22:

Longitudinal acceleration

Transverse Oscillation

Figure 23:

Figure 24:

Skip-Rope motion

Pendulum motion

32

These random oscillations have to be dampened, otherwise they will create forced vibrations that hinder satellite stabilization, overall system performance, and in the most extreme cases drastically reduce mission life.

Aside from oscillatory vibrations, tethers suffer from short mission life because they are highly vulnerable to multiple collisions with orbital space debris. Space debris collisions can limit the mission life of a space tether to just several days. Orbital debris may include other satellites, random pieces from previous satellite collisions, and small meteorites.

There are over 8000 satellites in low earth orbit today, and countless smaller pieces generated by space craft collisions and explosions. These smaller pieces pose a greater risk to tether life than larger whole satellites because they travel at a velocity of 7-10 kilometers per second. [10]

NASA has used space debris modeling software along with physical tests that have shown a thermoplastic tether totally degraded from collisions with particles as small as 100 microns. [10] A tether made of multiple layers of Kevlar and aluminum wires had better results but also suffered serious damage over a slightly longer period of time. An alternative solution is to use thicker tether material and to coat it with protective insulation. Unfortunately this adversely affects the weight and size of such a system. If thicker tether material is used, the system needs to use a larger spool to wind tether up. As a result of this the overall storage size would increase as well as weight. The motor needed to unwind a larger diameter tether would need to be more powerful, drawing more power. Protective insulation coating adds weight and increases the coefficient of friction which hinders the unwinding of the tether. Figure 25 and Figure 26 show degradation of high strength Polyethylene and aluminum-Kevlar tether material, respectively.

33

Figure 25: Heavily Damaged

Figure 26: heavily damaged dual and

Polyethylene Tether

triple layered aluminumKevlar Tether

Satellite tethers still remain as an option for a gravity gradient boom stabilization device. They have been shown to work previously, especially on smaller satellites similar to size and weight of the ONYX.

Wire Drum Deployer The wire drum deployment system is similar to a tether device. The tether is spun around a spool which is connected to a DC motor. The DC motor then unwinds the tether into space. The tether goes through tensioners and pulleys before it is unwind into space. The wire deployer uses a thin copper-beryllium wire that is wound around a small drum and deployed out of the satellite. Several student designed and launched satellites have successfully used a copper-beryllium gravity gradient boom to stabilize their satellites. These satellites were designed and launched by Arizona State University, University of Missouri, University of Denmark, and several other Air Force back projects. A copper-beryllium gravity gradient boom can be much shorter and simpler than a tether system. The wire can be as thin as .008’’ in diameter. In addition a motor is not needed to deploy it and it has a much lower rate of space collisions because of its size and length. Typical boom lengths have ranged from 2.5 meters to 18 meters. This type of gravity gradient boom also employs a tip mass at the end of its length to help stabilize the satellite. The tip mass will be flying at a lower orbit having a greater gravitational pull exerted

34

on it. This pull will orient the main satellite in a perpendicular position with respect to earth. This type of position is optimal for the ONYX satellite and its multi-spectral digital camera, making this boom a very appealing consideration. [9]

Due to the use of a tip mass at the end of the wire, the copper beryllium boom is drastically shorter than the tethered boom. The chance of collisions with space debris is much lower. Reliability and longevity are important considerations that the copper-beryllium boom satisfies. The tip mass also allows boom to develop a torque of its own that can oppose all the disturbance torques that hinder attitude stabilization. These torques include aerodynamic torques in low earth orbit and gravitational torques.

Copper-Beryllium possesses excellent characteristics that make it an optimal choice for wire material. It has a very high tensile strength of 700MPA. In addition it is resistant to corrosion, can be as thin as .008”, and possesses very good thermal shock characteristics. It is also important to note that a metallic wire deployer is similar to a tethered system but it differs in adaptability, simplicity, and size. The oscillations it can experience would be much smaller than a tether system due to much shorter boom lengths and actual tip mass at the end of the boom.

Tubular Booms

A tubular boom is similar to the measuring tape device. A thin metal sheet is rolled flat on a reel but when deployed it forms a curved shape which enhances structural rigidity. To get the required stiffness of a boom the thin metal is curved more than 360 degrees as seen in Figure 15. As seen in this figure the material comes off the reel flat and then is sent through guide rollers to regain its curved shape. This type of tubular boom is called the overlapping thin-wall tube. Another type of tubular boom is a multi-element tube. This tube consists of two curved pieces of material from different reels that wrap around each other to form one interlocking tube. Adding the second curved piece increases the bending and torsion strength of the boom. A third type of tubular boom is called lenticular tube. This type consists of two curved sheets that are welded on both the top and the bottom seam and then rolled onto one reel. This helps increase the bending and torsion strength and also keeps the deployer simple with only one reel. [9]

35

Figure 27: Tubular Boom

Telescoping Booms Telescoping booms extend in a fashion similar to a radio antenna on an automobile. In its stowed position the boom consists of many tubes nested inside of each other. The boom extends tube by tube until it reaches its final deployed length. The tubes of a telescoping boom can fabricated from virtually any material, metal or composite, depending on the structural performance that is required. [9] One of the most common methods to extend the tubes is to use a lead screw to deploy each tube as seen in Figure 27. Another approach to deploying a telescoping boom is to inflate it with the use of air. Inflatable booms add to the complexity of the whole system because a small air pump is needed to pump the air through the inflatable bladder that will run inside the tubes. In addition the air pump will have to operate in a space vacuum environment which will add to its complexity in order to function properly.

Figure 27: Telescoping Boom

36

Coilable Booms A coilable boom most closely looks like a truss. To stow this boom, the flexible truss is twisted into a helical shape. Twisting the boom makes it possible to stow it at 2% of its deployed length. The deployable part of a coilable boom is made up of 3 main parts, the longerons, the battens, and the diagonals. Figure 17 shows these 3 parts: the longerons, battens, and diagonals. The longerons run along the full length of the boom. This is the part that gets twisted when the boom is in its stowed position. The battens are what hold the longerons together. The diagonals crisscross between each batten for the full length of the boom. They also provide support to the battens and the longeruns. A long rigid boom is erected when these three parts work together in stabilizing the structure.[9] These parts are all interlocked with each other, meaning the coilable boom will fail at the point that it is the weakest. Like other booms coilable booms must be thoroughly inspected and built with quality parts to make sure that the structural integrity is uniform through the whole boom. However, a minor defect may be more detrimental in a coilable boom than other booms because each part is interlocked with another.

Batten

Diagonal

Longeron

Figure 17: Coilable Boom

FINAL DEPLOYMENT DEVICE After initial trade studies have been done on the most common gravity gradient boom deployment devices, the group made a design matrix with weighting factors to help select the most optimal deployment option and gravity gradient boom. Each of the group members selected a ranking value for the deployers in each of the critical design categories. The values ranged from most optimal being 4 to least optimal, 1. These

37

values were than averaged out among the group members. Weighting factors were than applied to each of the design considerations. Some categories are more crucial for the proper design than others. It is important to note than initially, the “thermal characteristics” category had a weighting factor of 1x. Upon further research, thermal characteristics, structural response, and mission adaptability were important design parameters that weighed in heavily on the selection of the deployment device. A boom structure needs to possess very strong thermal characteristic. Weak thermal characteristic can cause unwanted disturbances which can lead to mission failure.

Table 2 shows the design matrix with tabulated values and scores. The final thought process between the wire-drum deployer and the telescoping boom will be described in detail below. Tethers and coilable booms will be mentioned, but not as thoroughly as the other two because they were clearly not optimal for the satellite.

Table 2: Design Matrix Weight Factor

3X

3X

Size/Volume

Weight

3.8

3.2

3.8

3.4

3

1.6

1.4

2.4

2.8

2.4

Tether

1.8

2.2

2

1.6

2

Coilable

2.8

3.4

1.8

1.8

2.6

2X

4X

2X

4X

1X

2X

Power

Cost

Multiplier Deployment Type/Boom Wire/Drum Telescoping Tubular

Weight Factor Multiplier

Deployment

Possible

Type/Boom

Length

Wire/Drum

3.8 2

Telescoping Tubular

Adaptability to

2X

Mechanical Complexity

2X

Retractability

1X

Thermal Characteristics

Structural

Damping/Dynamic

Predictability

Response

4

3.2

2.6

3

3.4

2.8

3.2

3.6

1.8

2

other missions/sats

Tether

2.2

1.8

1.4

1.6

1.6

2

Coilable

2

1.4

2.2

2.2

3.6

2.6

38

Deployment Type/Boom Wire/Drum

Totals 88.6

Telescoping Tubular

63.6

Tether

47.6

Coilable

60

Telescoping Booms The telescoping boom scored very high in the design matrix. However, some of the design parameters that held it back were size, mechanical complexity, thermal characteristics, and mission adaptability. The stored configuration of the telescoping boom does not represent a small compact system. The tubular telescoping boom is bulky and long. Telescoping booms do provide structural rigidity and good dynamic response characteristics however this is at the expense of the overall weight and size of the system. The tubing would need to be larger in diameter and thicker which would increase the weight of the whole system.

Another main concern was the thermal characteristics of the telescoping boom. The telescoping boom would be prone to thermal shock and thermal bending. Due to the telescoping booms larger cross section it will hold a larger temperature gradient. Thermal bending will deform and bend the boom due to slowly varying temperature gradients at different parts of the boom. [12] These deformations can result in change of inertia distributions on the satellite which correspondingly can change the gravity gradient torque and aerodynamic drag. This may hinder satellite performance and pointing accuracy.

Thermal shock is another thermal characteristic that limits the life of the telescoping boom. Thermal shock is a sudden impulsive torque generated because of rapid and extreme temperature changes. The disturbance torque produces thermal vibrations which result in oscillatory motions having a dynamic response. The telescoping boom usually deals very well with dynamic response oscillatory motion. However, it may have an adverse effect on the whole satellite structure itself. More importantly the telescoping boom is made of different materials, which have different coefficients of expansion. These parts expand at different rates when exposed to heat. This will increase friction and risk of jamming the boom during deployment. There are methods of countering this phenomenon with special coatings and proper material selection. This will add to the complexity, cost, and weight of the system. Correspondingly, these alterations hinder adaptability to other satellites with similar missions.

Adaptability is an important aspect to this project. The telescoping boom will not have many interchangeable parts. It will not be able to fit on other satellites due to its complex nature and final design.

39

Its size and weight is usually too large for micro satellites. Tether deployers also shared similar characteristics. Tethers were not optimal from research in initial case studies. Tethered satellite booms were shown to be excessively complicated and heavy. It requires large amounts of rope or tether material to be spooled and then unwound using an electrical motor. In addition the tether is not structurally predictable and has a very limited life span if collisions with space debris will occur.

Coilable booms are also affected by shadowing as well other mentioned thermal characteristics. Shadowing is when parts of the boom block the sunlight to the other parts of the boom causing varying temperature gradients. [12] When one part is getting hit with direct sunlight and the other part remains cold, the whole coilable boom may begin to exhibit a harmonic motion because every part of the coilable boom is interlocked with each other. In addition, the coilable boom has an elastic nature so these vibrations may also be amplified and upset the stabilization of the whole satellite.

Wire-Drum Deployers Through the design matrix and case studies the wire-drum deployer is chosen because it is the most optimal deployment system that meets the most important requirements of the design matrix. In addition it easily meets the requirements set forth by NASA and Santa Clara University. Below is a detailed analysis of the decision process behind the wire-drum deployer

Size

Because of the copper beryllium wire’s small thickness, relatively long amounts of wire can be spooled up on a drum and then unwound into space. The wire would be unwound along with a tip mass at the end. The size of the deployment system will be small. Only the drum/spool and motor assembly will take up space. The whole system along with the tip mass should fit into the 10x10x15 cm volume that was initially given to work with.

Weight

This is another strong feature of the wire deployer. Copper beryllium is very light; in this particular application it will be even lighter because the thickness of the wire will only be eight thousandths of an inch. Copper Beryllium has a density of 8.3x103Kg/m3. It is light and strong at the same time. The spools and electrical motor would be very light as well. Due to low weight, more weight on the tip mass can be

40

used to enhance ONYX’s stabilization. A larger tip mass will enable the gravity gradient boom to produce a larger torque than the combined disturbance torques.

Mechanical Complexity

The wire deployer can become more complex if needed but at this initial moment the system seems fairly simple. Complexities may arise from ONYX design team constraints and the active attitude control system interfering with the gravity gradient boom.

Retractability

Retractability may be an important concern when flying in space. If the system does not fully retract on the first time or if there is a collision with micro particles along the same orbit the boom may need to retracted and the redeployed again. With the use of an electrical motor this should be done easily.

Thermal Characteristics

Thermal properties are very important and will be studied more intensely as the research continues on. Thermal characteristics include thermal bending properties, thermal shock properties, thermally induced vibrations, and thermal flutter. Thermal characteristics will play a vital role in the satellites mission, structure, and stabilization. Due to Copper Beryllium’s very small diameter sizes, thermal consideration will not be as important because the area of the temperature gradient of the .008’’ thick wire will be very small.

Length of Boom

This category may also be changed. Initially, it appears that the wire deployer may accommodate a longer boom because the copper-beryllium wire is very thin, therefore long amounts of it can be spooled and released into space. Proper calculations of magnetic restoring forces, environmental space disturbance torques, and orbit will lead to a known boom length.

41

Adaptability to other missions/small satellites

It was advised by Professor Kitts of Santa Clara University to build a gravity gradient boom that will be adaptable to other satellites flying similar earth reconnaissance missions. The wire deployer will be an optimal choice for this. The ability of the wire deployer system to utilize many different tip masses as well as wire lengths allows it to adapt to almost any satellite mission. Adaptability will be greatly influenced by thermal characteristics, structural predictability, and pointing accuracy of the camera being used (if a reconnaissance mission is required).

Structural Predictability

Structural predictability is closely related to thermal characteristics because it must be known how the boom will respond to different disturbance torques and how it will react to different thermal loads. Copper Beryllium possess strong tensile strength (700 MPA) and it is not a shape memory metal.

PHASE II The design

7.1.0 Final Design The final system that the Northeastern team designed is in figure #.

Origen Z X -Y

Figure #

42

Mass :

3.761 kg

Dimensions=: (z-y-x) Center of mass:

Moment of Inertia

Moment of rotation

142 x 100 x 100mm X=

0.101 mm

Y=

-0.023 mm

Z=

115.4 mm

XX=

4022 kg mm2

YY=

4031 kg mm2

ZZ=

3789 kg mm2

X=

3.26˚

Y=

10.11˚

Z=

19.66˚

Figure The system designed is a non retractable Wire Deployer Gravity Gradient Device.

Components: 1) Mass, Tip:

Mass:

3.00 kg

Volume:

176.5 cm3

Material:

Tungsten Alloy (17g/mm3)

Design Features:

#8 tap along Z axis

- Mass precision is high to agree with calculations -Excel sheet derives the shape ( see Appendix # for Screen shots) - Inputs: Desired diameters, mass, density, height, angle - #8 tap to match securing bolt - The selection of 3kg will be shown later

43

- See appendix # for detailed drawing

2) Base Plate:

Mass:

g

Dimensions:

10cm x 10cm x 1/8”

Volume: Material:

Al 6061

Design Features:

- Hole location M5 through holes - Oversized wire opening smooth and polished with no sharp edges

- Hole Pattern has high precision to line up all -Launch assembly mount holes slotted lowering precision - See appendix # for detailed drawing

3) Deployment System Assembly

Mass:

74g

Components: a

Base

b

Lower Hinge

c

Upper Hinge

d

Torsion Springs

e

Bearings

f-g

M3 Dowel Pins

h

M3x.5 Nylon Screw

- See Appendix # for BOM - See appendix # for Individual drawings of machined parts

44

a) Launch Base:

Mass:

31.27g

Dimensions:

40mm x 40mm

Material:

Al 6061

Design Features:

-x4 M5 bolt holes -Chamfer to lock arms -M3 Drill holes for Dowel pins

b) Lower Hinge:

Mass:

6.5g (x4)

Dimensions:

7mm x 15mm x 41mm

Material:

Al 6061

Design Features:

-High precision or middle milling -Mount for torsion spring -Upper hinge pivots around top

c) Upper Hinge:

Mass:

1.3g (x4)

Dimensions:

5mm x 7mm x 25mm

Material:

Al 6061

Design Features:

-Thread for mounting bearing -Mount for torsion spring -High precision on 7mm max width

d) Torsion Spring:

Mass:

.05g

Dimensions:

ID Ø 3.25mm

rd

e) Bearings:

3 party part:

McMaster-Carr pt# 9287K62

Mass:

.3 g

Dimensions:

Ø6mm x Ø3mm x 2.5mm

rd

3 party part:

45

VXB.com pt# Kit7032

f) M3 Dowel Pin:

Mass:

1.0 g

Dimensions:

M3 x 16mm Lg

rd

g) M3 Dowel Pin:

h) Nylon Screw:

3 party part:

McMaster-Carr pt# 91585a065

Mass:

3.3 g

Dimensions:

M3 x 40mm Lg

3rd party part:

McMaster-Carr pt# 91585a076

Mass:

3.3 g

Dimensions:

M3 x .5

rd

3 party part:

4) Top Seal:

5mm Lg

McMaster-Carr pt# 95280A114

Mass:

263 g

Dimensions:

OD =Ø10cm

Material:

Al 6061

Design Features:

- 45˚ incline to lock on mass -Removed material to accommodate deployment system - x4 M5 Tap to mount to base plate

- See appendix # for detailed drawing

46

5) Mounting Ring:

Mass:

32 g (x4)

Material:

Delrin Plastic

Design Features:

-M5 Thread through to mount with satellite -Inner Diameter and hole pattern has high precision to align with other parts

- See appendix # for detailed drawing

6) Wire Guide/Bolt Mount:

Mass:

9.2 g

Material:

Al 6061

Design Features:

-Holds bolt in tension on plate - Ø2mm wire guide

- See appendix # for detailed drawing

7)

Frangibolt® Actuator

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Mass:

20 grams

Volume:

2.33 cm3

Power:

25 Watts

Material:

Titanium Nickel

-The Frangibolt a Titanium Nickel shape memory Vendor/Part #: actuator uses TiNi Aerospace/FC2-16-31SR2 alloy that when heated expands and breaks the fastener. -The TiNi Frangibolts have excellent flight heritage and have previous been used by NASA.

8)

Frangibolt® Fastener Mass:

10 grams

Bolt Size:

#8 X 1.75 in

Material:

Titanium

Vendor: TiNi Aerospace -The Frangibolt fastener is a titanium bolt with a notch cut in it where you want the bolt to break. -The fastener being used is a #8 bolt that can support up to 2200 N

9)

Spool Bracket Mass:

113.2 grams

Volume:

41.8 cm3

Material:

12 Gauge Aluminum 6061

Design Features

M5 Clearance Holes

-See appendix # for a detailed drawing

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10)

Spool

Mass:

14.7 grams

Volume:

5.42 cm3

Material:

Aluminum 6061

Design Features Holes for 6mm OD Bearings -See appendix # for a detailed drawing

11)

Spool Rod Mass:

0.931 grams

Volume:

0.34 cm3

Material:

3mm Rod Aluminum 6061

Design Features M2 Taps -See appendix # for a detailed drawing

12)

Wire

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Mass:

6.88 grams

Length:

10 meters

Material:

.008 inch Copper-Beryllium Wire

Vendor: Little Falls Alloys -Copper-Beryllium is flight proven and has been used on other wire deployers -Copper-Beryllium was selected because of its high tensile strength of 700 MPA

13)

Solenoid Mass:

24.8 grams

Volume:

3.45 cm3

Power:

4.5 Watts

Vendor/Part #:

Ledex/282340-0XX

-The Ledex® low profile linear solenoid was selected because of its small size and lower power usage -The solenoid can be powered by at power source or 12 volt battery

Design Concept All wire deployer systems contain a tip mass and wire with a set length. The mass, attached to the wire, is deployed from the system away from the satellite. As the distance increases, the mass, which is closer to earth, feels a greater force of gravity. After a period of time the full length of the wire is extended and the swaying of the satellite will decrease.

Below, Figure # is a diagram of the four phases that the NEU gravity gradient device will go through in detail.

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Figure #

Phase 1: Launch through Deploy During launch the gravity gradient device will be subjected to high frequency vibrations and forces nearly twenty times Earth’s gravity. During this stage the team designed against two possible failures. These failures would be not securing the tip mass and the wire spool.

The 3kg mass tip is secure on all sides except the top. Because of this, the bolt must secure the mass against the 20g force with a moderate factor of safety of 1.5:

m = 3kg Boltstrength = 2,200 N m a = 9.81 2 * 20 s

F1 = 3kg * 9.81 * 20 *1.5 F1 = 882.9 N Boltstrength > F1

F1 = m * a * FoS F1 < Boltstrength

As shown above the bolt will not yield or deform in the worst case scenario when a 1.5 factor of safety is applied.

The wire spool, during launch, was also an area of concern. During launch, vibrations will attempt to unravel the wire from the spool, know as blossoming. The design solution for this was adding a pulling solenoid. With a solenoid mounted securely to the frame, its tip can be inserted into an opening located on the spool. The addition of the solenoid did not surpass any constraints on size or power.

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Phase 2: Deployment stage 1 Stage two initiates when the satellite settles to its expected rotation and oscillation. At this time a signal will be sent to unfasten the spool by activating 4.5 watts and 12V to the solenoid. Once this is completed, and the satellite starts its rotation towards Earth, power will be diverted to the Frangibolt® Actuator. After an estimated 40 seconds at 25 watts the actuator will heat the bolt causing the bolt to snap, releasing the mass. The four arms with fully compressed torsion springs and ball bearing tips begin to propel and guide the mass out from the satellite.

Phase 3: Deployment stage 2 The four launch springs are of the lowest torque values. However in space, were only a fraction of the weight is felt, the four spring and their moment arms propel the mass at an initial 1.85N and .6m/s2. See Apendix # for full calculations. This initial force will be enough to start spinning the spool and align the wire.

Phase 4: Deployment Finished A design concern as the mass would be reaching its given length is whether a damper would be needed to halt acceleration. The solenoid that initial secures the spool during launch vibrations and protects it from blossoming will serve a second purpose. When the boom is about to reach its fully extended length the solenoid will press against the flange of the spool to slow the forward momentum of the boom and tip mass. This will ensure safe speed and limit vibrations in the boom as it reaches a safe stop. In addition, it will prevent the spool from spinning backwards.

THE PROTYPE

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The prototype, constructed from Northeaster’s SLA 3D printer, was assembles to better understand our design, and as a tangible scale replica. Below, Figure #, shows our assembly with machined parts as well as well as some purchased parts.

Tests preformed on the prototype:

Once the prototype was completed the design concepts were reestablished and tested. Two tests completed were to confirm the strength of the springs, and test force and velocity calculations. After the calculation for the springs were completed and checked, slight inconsistencies show from McMaster-Carr’s data. The next step taken was to find the holding force of the four springs. From this, a third comparison could be made on the torsion spring data. The results from this show that the actual spring’s tensional constant is lower then what was stated on McMaster- Carr and another vendor should be found for this part. Full results for this test can be found in the Appendix.

The next test was similar to the one with the wood block. The second test was to simulate deployment in near weightlessness. This was accomplished by the use of a low friction pulley that connected the prototype tip mass with the matching weight in bolts and washers. This test showed the functionality of two key features of the design; wire and spool bearings. In addition to this it showed the similarity between the centripetal forces of the satellite vs. the slightly stronger gravity gradient force. The test was set up as the following. The Northeaster’s gravity gradient boom devises prototype was set up on a stool under the pulley with the wire secured to the mass on both sides, one through the pulley the other unto the locked spool. When the mass was released from the spring deployer it raised with a low velocity.

:

CONCLUSION

Mission Adaptability and Integration

Adaptability and proper integration to other micro satellites was an important design constraint that was set forth by NASA and Santa Clara. The Northeastern design team designed a gravity gradient boom that is very compact and light but produces enough torque to overcome all outside disturbance torques, combined.

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The gravity gradient booms light weight and very compact size makes it adaptable to other small satellites. In addition, the only time the gravity gradient boom draws power is when a current is applied to the Frange bolt to let it detach the tip mass.

The Frange bolt is a space proven part with space heritage. It can withstand +/-20g of acceleration in all axes. The entire gravity gradient boom is built out of aluminum 6061 parts that are also space qualified with space heritage.

Optimized Design Constraint As mentioned earlier in the paper several strict constraints had to be followed in the design of the gravity gradient boom. The deployment system and the boom have to be small enough and compact enough to fit into the ONYX. More importantly the system cannot drastically change the satellite’s physical properties such as center of gravity and moments of inertia.

The gravity gradient boom system cannot exceed a 30kg mass. Other constraints were that it cannot draw more than 30 Watts of power and that it has to fit into a volume of 12cmx12cmx15cm which is extremely small. The gravity gradient boom that was designed maximizes all of these constraints and actually saves room in the satellite. Finally, a pointing accuracy of 5 degrees within the earth pointed Nadir vector must be achieved.

The systems weight mostly comes from the tip mass that is used. The tip mass is the most essential part in generating a torque that will be strong enough to overcome all other disturbance torques that will hinder satellite stabilization. The overall mass of the system is 3.761kg which falls under the 5-10kg maximum mass constraint. For space applications, every pound that is sent into space over the target weight will cost an estimated $10,000. [ ] Such a light weight gravity gradient boom system allows for extra development of other vital subsystems of a micro satellite without having to worry about mass budget concerns.

The gravity gradient boom also meets and exceeds size and volume constraints. The whole system, including the tip mass can be mounted inside the satellite that takes up a volume of 10cm x 10cm x 14.2cm. For ease of design and very tight time constraints the Northeastern design team chose to work around the targeted volume. A smaller system can be made. However, additional space can be made to incorporate extra sensors inside the gravity gradient boom if needed. The booms inertia properties are very small due to its compact nature and very low weight. This means that the satellites inertia properties will be not be changed and no extra modifications need to be done to the active attitude control system to initial stabilization as it is tumbling. A detailed design table shows all physical properties of the gravity gradient boom system.

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Since the ONYX is an image capturing satellite it needs to have a high degree of stabilization so the camera can take clear and precise images of the earth. The initial pointing accuracy specified by Santa Clara University was +/- 5 degrees of the Nadir vector pointing towards earth. Northeastern’s gravity gradient boom can achieve a stabilization angle of +/- 2 degrees within the Nadir vector. With the given length of boom and given mass of the tip it will take 5 days for the satellite to stabilize to such a tight tolerance. However, this is under the assumption that the active attitude control system will “de-tumble” the satellite to 30 degrees with respect to the Nadir. If the active control system will de-tumble the satellite closer to the Nadir it will take less time for the gravity gradient boom to further stabilize the satellite to a high degree of accuracy. In addition, a longer boom and heavier tip mass can be used to ensure faster stabilization. Due to the gravity gradient boom’s design, interchanging longer booms and heavier tip masses is simple and cost effective.

To achieve such a high degree of pointing accuracy the gravity gradient boom has to develop a torque great enough to overcome all other disturbance torques. These disturbance torques arise from the gravity gradient, solar radiation pressure, magnetic field, and aerodynamic drag. The table below shows the worst case disturbance torques experienced in low earth orbit. [ ]

Aero dynamic Torque

1.1 x 10^-8 N-m

Gravity Gradient Torque

5.1 x 10^-8 N-m

Table # 3 Solar Radiation Torque

2.6 x 10^-6

Magnetic Field Torque

8.6 x 10^-4 N-m

Torque Developed by GGB

3.2 x 10^-3 N-m

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The total combined disturbance torque is 8.6 x 10-4 N-m which is smaller than the torque developed by the gravity gradient boom. Theoretically, once the gravity gradient boom is deployed in low earth orbit it will stabilize the satellite for the duration of the mission.

8.30 Adaptability to Electronic Subsystems

The gravity gradient boom that has been developed is also adaptable to electronic devices via the Emerald Protocol Suite. There is enough available volume to mount a motor a have it unwind the spool, deploying the tip mass. Sun sensors and magnetometer connections can also be fit in but the gravity gradient boom was designed as a complete stand alone system with the assumption that all sensors will be on the satellite already.

The initial design incorporated a DC motor that had the spool attached to its output shaft. Santa Clara University and NASA had never given a direct requirement for retract ability so the design team concentrated on building a small light weight system that can use a motor if needed.

The motor allows for a more controlled manner of deployment and it also allows the boom to retract in increments if needed. Proper motor selection is essential for a gravity gradient boom that is meant to use an electric unwinding device.

The motor has to be able to withstand strong dynamic loads of +/- 20g in all axes. It also has to withstand the harsh vibrations of the launch. Proper calculations and design concentrates have to be made to select a motor that will work well with the gravity gradient boom. The inertial properties of the spool have to be known, tension in the boom wire, and optimal deployment speed. From those initial design parameters the motor selection process can start.

The tension in the boom wire is a very small .0003N. A motor was selected based on a .003N tension to overcome any error in power requirements. Most miniature DC motors spin at a rate of several thousand rotations per minute. Speed and torque is a function of voltage that is applied to the motor. For the gravity gradient boom application the motor catalogue that was used contained the slowest spinning motors with optional gear heads and encoders to produce a desired rotation of the output shaft. Micromo Electronics was selected as the vendor for miniature DC motors. Micromo has produced numerous DC motors that have been on past and present space flights. Many motors have space heritage in addition to their already small size and light weight.

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The slowest motor from Micromo can spin at 9900RPM under a 24 volt power supply. The motor would run in a 24 volt winding using a 12 Volt connection. The desired speed is roughly 5000RPM. When coupled to a gear head it will produce the desired output shaft speed to safely deploy the boom. The power and speed required for the motor are given in the equations below

W = no x Torque/ 1350 Where no is the desired rotational speed of the motor, T is the torque in oz-in, 1350 is a constant, and W is power in Watts. The motor would need to produce .425 oz-in of torque to over come a tension of .003N in the boom wire. With a desired speed of 5000RPM, the equation above indicates that 1.57W of power is required for the motor to overcome the tension. The power needed is well under the maximum 30W that can be used. In a 12 Volt setting the motor will spin approximately 5000RPM, the voltage ratio is shown below

n12volts 12 x 9900RPM = 4950RPM 24

Through the help of the engineers at Micromo, a series 1524SR motor was selected with a 24 Volt winding help monitor and maintain deployment speed. The mass of the motor is only 21 grams with dimensions of 24mm in length and 15mm in diameter. It is robust and light weight with very strong thermal properties. Total cost of the motor with supporting gear head and encoder is $180 from Micromo electronics.

The designed prototype does not use a motor. Due to the mounting system and the optimization of size, a motor can be placed in the spool bracket with minimal changes to physical and inertial properties. The gravity gradient boom is versatile enough to incorporate a motor if the application strictly requires the use of one. All materials are space qualified with large amounts of space heritage. Micromo even supplies the right fluids that will allow the motor to work properly in a space environment.

Cost Analysis

The initial cost analysis may be higher than the actual expected cost analysis due to rushed machining costs and overall preliminary design considerations. The machining of precise aluminum parts and the Frangibolt® are the most expensive design pieces. It is important to note that both of these parts and materials are space qualified, therefore costs are expected to be higher. Below is an estimated cost analysis of all the parts making the up the gravity gradient boom.

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Part

Cost Aluminum 6061 and machining costs

FrangBolt from TiNi Aerospace, Inc. * Part # FC2-16-31SR2 # 8

$1000 $2,550

#8 FrangiBolt Fastener TBD configuration *

$85

Part# W2-32-Ti #8 FrangiBolt Washers

$10

Ledex Low Profile Solenoid

$80

24’ of Beryllium Copper Wire

$63

Torsion springs

$14

3mm x 6mm x 2.5mm Bearings

$15

Dowel Pin

$10

M2, M3, M5 and Alloy Metric Rod

$31

Optional – Series 1524SR motor with encoder and 16/7 Gear Head

$180

Total Cost

$4,038*

* Prices from several vendors can be significantly discounted for University Projects

The cost for a final design is estimated due to several vendors offering discounts on University projects. The prototype was built using plastic parts from a 3D printer due to time constraints with the machine shop for aluminum 6061.

8.4.0 Future Considerations and Improvements The Northeastern design team was able to meet many of the constraints that were set forth. The gravity gradient boom is a very light weight and compact design, which can be highly adaptable to other micro satellites. Future improvements should consider proper CAD modeling to ensure accurate meshing in ANSYS finite element software. This will yield accurate results for modal vibration analysis. Other design considerations would be to improve metal on metal contact and simplifying the system even more to reduce estimated costs.

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REFERENCES [1] Singh, Sahjendra N., and Woosoon Yim. "Nonlinear Adaptive Spacecraft Attitude Control Using Solar Radiation Pressure." (2005). 19 June 2006. [2] Bong, Wie, comp. Dynamic Modeling and Attitude Control Of. 10 Jan. 2002. Arizona State University. 23 Jan. 2007 . [3] Makovec, Kristin L. A Nonlinear Magnetic Controller for Three-Axis Stability of Nano-Satellites. Virginia Polytechnic Institute and State University. Blacksburg, Virginia, 2001. [4] "Sensors for Spacecraft Applications." 19 June 2006 <www.tsgcoutexas.edu>. [5] Braeunig, Robert A., comp. "Orbital Mechanics." Ed. Robert A. Braeunig. 2005. 16 June 2006 . [6] Darling, David. "Orbit." The Encyclopedia of Astrobiology Astronomy and Spaceflight. 2006. 16 June 2006 . [7] "Mechanical Components." Computing and System Sciences Department. Taylor University. 20 Jan. 2007 . [8] Giancoli, Douglas C. Physics for Scientistst & Engineers with Modern Physics. 3rd ed. Upper Saddle River, New Jersey: Prentice Hall, 2000. 114-149. [9] Conley, Peter L., ed. Space Vehicle Mechanisms: Elements of Successful Design. New York: John Wiley & Sons, Inc., 1998. 495-542. [10] 22 Jan. 2007 . [11] Penson, James S., and Dr. Mark Burchell. HYPERVELOCITY IMPACT STUDIES ON SPACE TETHERS. 1-10. 23 Jan. 2007 . [12] Baturkin, Volodymyr. Micro-Satellites Thermal Control-Concepts and Components. National Technical University of Ukraine. Kyiv, Ukraine, 1997. [13] "Spacecraft Thermal Control Coating Design and Application." Preferred Reliability Practices (1995).

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