Unit-3 The Solar System.docx

UNIT-3 SOLAR SYSTEM Nebular theory of formation of our Solar System. Sun-its origin and fate, Source of Energy and Solar wind. Brief description of Planets about shape, size, period of rotation about axis and period of revolution, distance of planets from sun. Bode’s law, Keplar’s Laws of planetary motion, Newton’s deductions from Kepler’s Laws, Newton’s Law of gravitation, correction of Kepler’s third law. Determination of mass of Earth, Determination of mass of planets with respect to earth. Brief description of Asteroids, Satellites and Comets. The Solar System Our solar system consists of an average star we call the Sun, the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. It includes: the satellites of the planets; numerous comets, asteroids, and meteoroids; and the interplanetary medium. The Sun is the richest source of electromagnetic energy (mostly in the form of heat and light) in the solar system. The Sun's nearest known stellar neighbor is a red dwarf star called Proxima Centauri, at a distance of 4.3 light years away. The whole solar system, together with the local stars visible on a clear night, orbits the center of our home galaxy, a spiral disk of 200 billion stars we call the Milky Way. The Milky Way has two small galaxies orbiting it nearby, which are visible from the southern hemisphere. They are called the Large Magellanic Cloud and the Small Magellanic Cloud. The nearest large galaxy is the Andromeda Galaxy. It is a spiral galaxy like the Milky Way but is 4 times as massive and is 2 million light years away. Our galaxy, one of billions of galaxies known, is traveling through intergalactic space. The planets, most of the satellites of the planets and the asteroids revolve around the Sun in the same direction, in nearly circular orbits. When looking down from above the Sun's north pole, the planets orbit in a counter-clockwise direction. The planets orbit the Sun in or near the same plane, called the ecliptic. Pluto is a special case in that its orbit is the most highly inclined (18 degrees) and the most highly elliptical of all the planets. Because of this, for part of its orbit, Pluto is closer to the Sun than is Neptune. The axis of rotation for most of the planets is nearly perpendicular to the ecliptic. The exceptions are Uranus and Pluto, which are tipped on their sides. Composition Of The Solar System The Sun contains 99.85% of all the matter in the Solar System. The planets, which condensed out of the same disk of material that formed the Sun, contain only 0.135% of the mass of the solar system. Jupiter contains more than twice the matter of all the other planets combined. Satellites of the planets, comets, asteroids, meteoroids, and the interplanetary medium constitute the remaining 0.015%. The following table is a list of the mass distribution within our Solar System.       

Sun: 99.85% Planets: 0.135% Comets: 0.01% ? Satellites: 0.00005% Minor Planets: 0.0000002% ? Meteoroids: 0.0000001% ? Interplanetary Medium: 0.0000001% ?

Interplanetary Space Nearly all the solar system by volume appears to be an empty void. Far from being nothingness, this vacuum of "space" comprises the interplanetary medium. It includes various forms of energy and at least two material components: interplanetary dust and interplanetary gas. Interplanetary dust consists of microscopic solid particles. Interplanetary gas is a tenuous flow of gas and charged particles, mostly protons and electrons -- plasma -- which stream from the Sun, called the solar wind.

The solar wind can be measured by spacecraft, and it has a large effect on comet tails. It also has a measurable effect on the motion of spacecraft. The speed of the solar wind is about 400 kilometers (250 miles) per second in the vicinity of Earth's orbit. The point at which the solar wind meets the interstellar medium, which is the "solar" wind from other stars, is called the heliopause. It is a boundary theorized to be roughly circular or teardrop-shaped, marking the edge of the Sun's influence perhaps 100 AU from the Sun. The space within the boundary of the heliopause, containing the Sun and solar system, is referred to as the heliosphere. The solar magnetic field extends outward into interplanetary space; it can be measured on Earth and by spacecraft. The solar magnetic field is the dominating magnetic field throughout the interplanetary regions of the solar system, except in the immediate environment of planets which have their own magnetic fields.

The Terrestrial Planets The terrestrial planets are the four innermost planets in the solar system, Mercury, Venus, Earth and Mars. They are called terrestrial because they have a compact, rocky surface like the Earth's. The planets, Venus, Earth, and Mars have significant atmospheres while Mercury has almost none. The following diagram shows the approximate distance of the terrestrial planets to the Sun.

The Jovian Planets Jupiter, Saturn, Uranus, and Neptune are known as the Jovian (Jupiter-like) planets, because they are all gigantic compared with Earth, and they have a gaseous nature like Jupiter's. The Jovian planets are also referred to as the gas giants, although some or all of them might have small solid cores. The following diagram shows the approximate distance of the Jovian planets to the Sun.

The Nebular Theory of the origin of the Solar System

Any model of Solar System formation must explain the following facts: 1. All the orbits of the planets are prograde (i.e. if seen from above the North pole of the Sun they all revolve in a counter-clockwise direction).

2. All the planets (except Pluto) have orbital planes that are inclined by less than 6 degrees with respect to each other (i.e. all in the same plane). 3. Terrestrial planets are dense, rocky and small, while jovian planets are gaseous and large.

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I. Contraction of insterstellar cloud Solar system formed about 4.6 billion year ago, when gravity pulled together low-density cloud of interstellar gas and dust (called a nebula).

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The Orion Nebula, an interstellar cloud in which star systems and possibly planets are forming. Initially the cloud was about several light years across. A small over density in the cloud caused the contraction to begin and the over density to grow, thus producing a faster contraction --> run away or collapse process Initially, most of the motions of the cloud particles were random, yet the nebula had a net rotation. As collapse proceeded, the rotation speed of the cloud was gradually increasing due to conservation of angular momentum.

Going, going, gone Gravitational collapse was much more efficient along the spin axis, so the rotating ball collapsed into thin disk with a diameter of 200 AU (0.003 light years) (twice Pluto's orbit), aka solar nebula with most of the mass concentrated near the center.

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As the cloud contracted, its gravitational potential energy was converted into kinetic energy of the individual gas particles. Collisions between particles converted this energy into heat (random motions). The solar nebula became hottest near the center where much of the mass was collected to form the protosun(the cloud of gas that became Sun). At some point the central temperature rose to 10 million K. The collisions among the atoms were so violent that nuclear reactions began, at which point the Sun was born as a star, containing 99.8% of the total mass. What prevented further collapse? As the temperature and density increased toward the center, so did the pressure causing a net force pointing outward. The Sun reached a a balance between the gravitational force and the internal pressure, aka as hydrostatic equilibrium, after 50 million years.

Around the Sun a thin disk gives birth to the planets, moons, asteroids and comets. Over recent years we have gathered evidence in support of this theory.

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Close-up of the Orion Nebula obtained with HST, revealing what seem to be disks of dust and gas surrounding newly formed stars. These protoplanetary disks span about 0.14 light years and are probably similar to the Solar Nebula. II. The structure of the disk The disk contained only 0.2% of the mass of the solar nebula with particles moving in circular orbits. The rotation of the disk prevented further collapse of the disk. Uniform composition: 75% of the mass in the form of hydrogen, 25% as helium, and all other elements comprising only 2% of the total. The material reached several thousand degrees near the center due to the release of gravitational energy -> it was vaporized. Farther out the material was primarily gaseous because H and He remain gaseous even at very low T. The disk was so spread out that gravity was not strong enough to pull material and form planets. Where did solid seeds for planet formation come from? As the disk radiated away its internal heat in the form of infrared radiation (Wien's law) the temperature dropped and the heaviest molecules began to form tiny solid or liquid droplets, a process called condensation. There is a clear relation between the temperature and the mass of the particles that become solid (Why?). Near the Sun, where the T was higher, only the heaviest compounds condensed forming heavy solid grains, including compunds of aluminum, titanium, iron, nickel, and, at somewhat cooler temperatures, the silicates. In the outskirts of the disk the T was low enough that hydrogen-rich molecules condensed into lighter ices, including water ice, frozen methane, and frozen ammonia. The ingredients of the solar system fell into four categories: o Metals: iron, nickel, aluminum. They condense at T~1,600 K and comprise only 0.2% of the disk. o Rocks: silicon-based minerals that condense at T=500-1,300 K (0.4% of the nebula). o Ices: hydrogen compounds like methane (CH4), ammonia (NH3), water (H2O) that condense at T~150 K and make up 1.4% of the mass. o Light gases: hydrogen and helium that never condensed in the disk (98% of the disk).

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The great temperature differences between the hot inner regions and the cool outer regions of the disk determined what of condensates were available for planet formation at each location from the center. The inner nebula was rich in heavy solid grains and deficient in ices and gases. The outskirts are rich in ice, H, and He. Meteorites provide evidence for this theory.

A piece of Allende meteorite showing white inclusions. The inclusions are aluminum-rich minerals that formed first in the solar nebula. The inclusions are surrounded by material with lower condensation temperatures which aggregated later. III. Formation of the planets  The first solid particles were microscopic in size. They orbited the Sun in nearly circular orbits right next to each other, as the gas from which they condensed. Gently collisions allowed the flakes to stick together and make larger particles which, in turn, attracted more solid particles. This process is called accretion.  The objects formed by accretion are called planetesimals (small planets): they act as seeds for planet formation. At first, planetesimals were closely packed. They coalesced into larger objects, forming clumps of up to a few kilometers across in a few million years, a small time compared to the age of the solar system.  Once planetesimals had grown to these sizes, collisions became destructive, making further growth more difficult. Only the biggest planetesimals survived this fragmentation process and continued to slowly grow into protoplanets by accretion of planetesimals of similar composition.  After protoplanet formed, accumulation of heat from radioactive decay of short-lived elements melted planet, allowing materials to differentiate (to separate according to their density).

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Inner structure of the Earth Formation of terrestrial planets: o In the warmer inner solar system, planetesimals formed from rock and metal, materials cooked billions of years ago in cores of massive stars. o These elements made up only 0.6% of the material in the solar nebula (and the faster collisions among particles close to the Sun were more destructive on average), so the planets could not grow very large and could not exert large pull on hydrogen and helium gas. o Even if terrestrial planets had hydrogen and helium, proximity to Sun would heat gases and cause them to escape. o Hence, terrestrial planets (Mercury, Venus, Earth, and Mars) are dense small worlds composed mostly from 2% of heavier elements contained in solar nebula.

Formation of jovian planets: o In the outer solar nebula, planetesimals formed from ice flakes in addition to rocky and metal flakes. o Since ices were more abundant the planetesimals could grow to much larger sizes, becoming the cores of the four jovian (Jupiter, Saturn, Uranus, and Neptune) planets.

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The cores were sufficiently large (at least 15 times Earth's mass) that they were able to capture hydrogen and helium gas from the surroundings (nebular capture) and form a thick atmosphere. They became the large, gaseous, low-density worlds rich in hydrogen and helium, with dense solid cores.

Far from Sun (beyond Neptune), in coldest regions of the nebula, icy planetesimals survived. However, the density of the disk was so low that the icy/dusty planetesimals could only grow to the size of a few kilometers. They could not accrete the surrounding gas so they remained like small dirty snowballs. They constitute the family of Kuiper belt comets, a prediction of the theory of the formation of the solar system which was confirmed in 1990.

Pluto does not fit the category of terrestrial or jovian planet -- it is small, like terrestrial planets, but lies far away from Sun and has low density just like jovian planets. In fact, some astronomers believe that Pluto belongs to the family of comets (probably the largest member).  Asteroid belt -- located between Mars and Jupiter -- is made of thousand of rocky planetesimals from 1,000 km to a few meters across. These are thought to be debris of the formation of the solar system that could not form a planet due to Jupiter's gravity. When asteroids collide they produce small fragments that occasionally fall on Earth. These rocks are called meteorites and provide valuable information about the primordial solar nebula. Most of these fragments have the size of sand grains. They burn up in the Earth's atmosphere, causing them to glow like meteors (or shooting stars). IV. Formation of moon systems  As the early jovian planets captured large amounts of gas, the same process that formed the solar nebula -contraction, spinning, flattening and heating -- formed similar but smaller disks of material around these planets. Condensation and accretion took place within the jovian nebulae, creating a miniature solar system around each jovian planet (Jupiter has well over a dozen moons!).  ``Double planet hypothesis'': the planet and its moon assembled independently at same time from the same rocks and dust.

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The moons formed elsewhere and then captured (``capture hypothesis''). Mars, for example. Other examples of likely captures -- Pluto and Charon, perhaps some of the jovian moons and moonlets (movie).

Mars' moons: Phobos and Deimos

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Pluto and Charon Giant impact of large body with young Earth explains Moon's composition.

V. Evolution of Solar System  The Sun, planets, moons, comets, asteroids are believed to form within 50-100 million years.  Once nuclear burning began in the Sun, it became a luminous object and cleared nebula as pressure from its light and solar wind pushed material out of Solar System.  Planets helped to clean up by absorbing some planetesimals and ejecting others. o Some of the planetesimals collided with the planets, causing craters or major effects. Uranus' axis tilt may have been caused by a large impact. The Earth was probably hit by a Mars-size object,

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ejecting debris that coalesced to form the Moon. The vast majority of the impacts occurred in the first few hundred million years. o Gravitational encounters with the planets ejected other planetesimals to remote parts of Solar System. Once Solar System was mostly clear of debris, planet building ended. Today, all solid surfaces scarred by craters from meteorite impacts (movie). The scars can be seen on the Moon, but erosion and geological processes on Earth have been erasing the craters.

Impacts still occur at a lower rate (65 million years ago, an asteroid or comet impact is thought to have caused the extinction of 90% of the species on Earth). Venus, Earth and Mars acquired their atmospheres at later stages in formation of Solar System: o The early bombardment brought some of the materials from which atmospheres and oceans formed in the terrestrial planets. These compounds arrived in the inner planets after their initial formation, most likely brought by impacts of planetesimals formed in the outskirts of the solar system (Q: What was Jupiter's role in bringing water to Earth?). o Outgassing (from gas blown out of volcanos) is another likely source for atmosphere's formation. o On Earth, oxygen, essential to animals, was produced by plants breaking down CO2. Rings around giant planets, such as Saturn's, are probably result of stray planetesimals being torn apart by gravity when they ventured too close to planet.

To learn about the planets than just their position and name, the following paragraphs give detailed information about each planet. You may wish to share some of these key characteristics with students. Constantly repeating and questioning students will help them retain planetary information.

Mercury is the closest planet to the Sun. It orbits the Sun quickly, once every 88 days. It rotates slowly, however, only once every 59 days. Mercury is small, about 4850 kilometers (~3000 miles) in diameter. Because Mercury is so close to the Sun, the side of its surface that faces the Sun is very hot, ~800oK. The surface of Mercury is gray to orange in color, and is covered with craters. Mercury is named for a mythical god who ran very fast. Venus, the second planet away from the Sun, is Earth’s closest neighbor. It is about the same size as the Earth, a little over 12,000 kilometers (7300 miles) in diameter. Venus has a very thick atmosphere, composed largely of sulphuric acid and CO2. We could not breathe on Venus, because the atmosphere would be very toxic to humans. This atmosphere gives Venus a brownish-yellow color. It also traps heat (the greenhouse effect) making the surface of Venus the hottest in the Solar System, about 900oK. Venus rotates very slowly, taking 243 days to complete one turn. It is named for the Roman goddess of love. Earth is a little more than 12,000 kilometers in diameter. It differs from the other planets because it has liquid water on its surface, maintains life, and has active plate movement. It rotates on its axis every 24 hours (a day) and revolves around the Sun every 365 days (a year). The Earth has one moon. Mars is a little more than half the size of the Earth, having a diameter of 6,790 kilometers. It takes Mars 687 days to revolve once around the Sun. It rotates at about the same speed as the Earth, taking 24.6 hours. Mars has a very thin atmosphere which is composed largely of CO2. Its surface is very cold, and is covered with craters, volcanoes, and large canyons. Mars is reddish in color. Mars has two small moons. It is named for the Roman god of war. Jupiter is the largest planet in the Solar System, with a diameter of 142,980 kilometers, more than 11 times wider than the Earth. Jupiter orbits the Sun once every 12 years. It rotates very fast, in 9 hours and 19 minutes.. Its surface is made up of gas (mostly hydrogen), so that if you landed on the surface you would sink into it. Jupiter probably has a core of metallic hydrogen and rock, although evidence for this is theoretical. The outer gaseous part of Jupiter is broken into bands of white, yellow, red, and brown clouds. Jupiter has 4 rings mainly composed of dust. Huge oval-shaped storms also occur on the surface. Jupiter has 67 known satellites (as of 2016) including the four large Galilean moons (Io, Europa, Callisto, and Ganymede) plus many more small ones some of which have not yet been named. Jupiter is named for the Roman supreme god of heaven. Saturn is well known for its system of three rings. It is a large planet: at 120,536 kilometers it is only a little smaller than Jupiter. It revolves around the Sun in 12 years, and rotates a little more than 10 hours. Like Jupiter, Saturn is composed of mostly gas, and has a core composed of rock and metallic hydrogen. The surface of Saturn looks banded, and has a brown-yellow, butterscotch color. Saturn’s rings are probably composed of small particles of ice and rock. Saturn has 62 moons (as of 2016). It is named for the Roman god of agriculture. Uranus is 51,118 kilometers in diameter, about 4.4 times the size of the Earth. It revolves around the Sun slowly, taking 84 years to complete one orbit. It rotates in about 17 hours. It is covered by a thick layer of gas, and has a fairly uniform blue-green color. Uranus has 27 moons (as of 2016) and is surrounded by a system of nine rings. It is named for another Roman god, the grandfather of Jupiter Neptune is slightly smaller than Uranus, with a diameter of 49,500 kilometers. It circles the Sun once every 165 years, and rotates in 16 hours. Its atmosphere appears blue , and is marked by large dark blue storm systems. It is surrounded by a system of five rings and at least 14 moons. Neptune is named for the Roman god of the ocean. Pluto in 2006 was renamed as a dwarf planet. It has an eccentric, oval-shaped orbit, which is tilted with respect to the rest of the Solar System. Pluto revolves around the Sun in 248 years, and rotates in a period of 6.4 days. Pluto is probably composed of rock. Its surface and color are unknown. It has one large moon that is almost like a twin with 2 smaller moons. Pluto is named for the Roman god of outer darkness.

Bode's Law The Titius-Bode Law is rough rule that predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was formulated as a mathematical expression by J.E. Bode in 1778. It lead Bode to predict the existence of another planet between Mars and Jupiter in what we now recognize as the asteroid belt. The law relates the mean distances of the planets from the sun to a simple mathematic progression of numbers. To find the mean distances of the planets, beginning with the following simple sequence of numbers: 0 3 6 12 24 48 96 192 384 With the exception of the first two, the others are simple twice the value of the preceding number. Add 4 to each number: 4 7 10 16 28 52 100 196 388 Then divide by 10: 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 The resulting sequence is very close to the distribution of mean distances of the planets from the Sun: Body Actual distance (A.U.) Bode's Law Mercury 0.39 0.4 Venus 0.72 0.7 Earth 1.00 1.0 Mars 1.52 1.6 2.8 Jupiter 5.20 5.2 Saturn 9.54 10.0 Uranus 19.19 19.6

Kepler's laws of planetary motion

Elliptical path of planet orbiting the Sun First Law Kepler was a sophisticated mathematician, and so the advance that he made in the study of the motion of the planets was to introduce a mathematical foundation for the heliocentric model of the solar system. Where Ptolemy and Copernicus relied on assumptions, such as that the circle is a “perfect” shape and all orbits must be circular, Kepler showed that mathematically a circular orbit could not match the data for Mars, but that an elliptical orbit did match the data! We now refer to the following statement as Kepler’s First Law: 

The planets orbit the Sun in ellipses with the Sun at one focus (the other focus is empty).

Here is a demonstration of the classic method for drawing an ellipse:

The classic method for drawing an ellipse using a loop of string around two tacks separated by a small distance. The two thumbtacks in the image represent the two foci of the ellipse, and the string ensures that the sum of the distances from the two foci (the tacks) to the pencil is a constant. Below is another image of an ellipse with the major axis and minor axis defined:

Diagram of a drawing of an ellipse, showing definition of major and minor axes and foci. We know that in a circle, all lines that pass through the center (diameters) are exactly equal in length. However, in an ellipse, lines that you draw through the center vary in length. The line that passes from one end to the other and includes both foci is called the major axis, and this is the longest distance between two points on the ellipse. The line that is perpendicular to the major axis at its center is called the minor axis, and it is the shortest distance between two points on the ellipse. In the image above, the green dots are the foci (equivalent to the tacks in the photo above). The larger the distance between the foci, the larger the eccentricity of the ellipse. In the limiting case where the foci are on top of each other (an eccentricity of 0), the figure is actually a circle. So you can think of a circle as an ellipse of eccentricity 0. Studies have shown that astronomy textbooks introduce a misconception by showing the planets' orbits as highly eccentric in an effort to be sure to drive home the point that they are ellipses and not circles. In reality the orbits of most planets in our Solar System are very close to circular, with eccentricities of near 0 (e.g., the eccentricity of Earth's orbit is 0.0167). For an animation showing orbits with varying eccentricities, see the eccentricity diagram at "Windows to the Universe." Note that the orbit with an eccentricity of 0.2, which appears nearly circular, is similar to Mercury's, which has the largest eccentricity of any planet in the Solar System. The elliptical orbits diagram at "Windows to the Universe" includes an image with a direct comparison of the eccentricities of several planets, an asteroid, and a comet. Note that if you follow the Starry Night instructions on the previous page to observe the orbits of Earth and Mars from above, you can also see the shapes of these orbits and how circular they appear. Kepler’s first law has several implications. These are:  

The distance between a planet and the Sun changes as the planet moves along its orbit. The Sun is offset from the center of the planet’s orbit.

Second Law In their models of the Solar System, the Greeks held to the Aristotelian belief that objects in the sky moved at a constant speed in circles because that is their “natural motion.” However, Kepler’s second law (sometimes referred to as the Law of Equal Areas), can be used to show that the velocity of a planet changes as it moves along its orbit! Kepler’s second law is: 

The line joining the Sun and a planet sweeps through equal areas in an equal amount of time.

The image below links to an animation that demonstrates that when a planet is near aphelion (the point furthest from the Sun, labeled with a B on the screen grab below) the line drawn between the Sun and the planet traces out a long, skinny sector between points A and B. When the planet is close to perihelion (the point closest to the Sun, labeled with a C on the screen grab below), the line drawn between the Sun and the planet traces out a shorter, fatter sector between points C and D. These slices that alternate gray and blue were drawn in such a way that the area inside each sector is the same. That is, the sector between C and D on the right contains the same amount of area as the sector between A and B on the left.

Click on this image to launch the animation in Windows Media Player. It shows a planet sweeping out equal areas in equal times. Kepler's 2nd Law Since the areas of these two sectors are identical, then Kepler's second law says that the time it takes the planet to travel between A and B and also between C and D must be the same. If you look at the distance along the ellipse between A and B, it is shorter than the distance between C and D. Since velocity is distance divided by time, and since the distance between A and B is shorter than the distance between C and D, when you divide those distances by the same amount of time you find that: 

A planet is moving faster near perihelion and slower near aphelion.

The orbits of most planets are almost circular, with eccentricities near 0. In this case, the changes in their speed are not too large over the course of their orbit. For those of you who teach physics, you might note that really, Kepler's second law is just another way of stating that angular momentum is conserved. That is, when the planet is near perihelion, the distance between the Sun and the planet is smaller, so it must increase its tangential velocity to conserve angular momentum, and similarly, when it is near aphelion when their separation is larger, its tangential velocity must decrease so that the total orbital angular momentum is the same as it was at perihelion. Third Law Kepler had all of Tycho’s data on the planets, so he was able to determine how long each planet took to complete one orbit around the Sun. This is usually referred to as the period of an orbit. Kepler noted that the closer a planet was to the Sun, the faster it orbited the Sun. He was the first scientist to study the planets from the perspective that the Sun influenced their orbits. That is, unlike Ptolemy and Copernicus, who both assumed that the planet's “natural motion” was to move at constant speeds along circular paths, Kepler believed that the Sun exerted some kind of force on the planets to push them along their orbits, and because of this, the closer they are to the Sun, the faster they should move. Kepler studied the periods of the planets and their distance from the Sun, and proved the following mathematical relationship, which is Kepler’s Third Law: 

The square of the period of a planet’s orbit (P) is directly proportional to the cube of the semimajor axis (a) of its elliptical path.

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P2∝a3

What this means mathematically is that if the square of the period of an object doubles, then the cube of its semi major axis must also double. The proportionality sign in the above equation means that: 

P2=ka3

where k is a constant number. If we divide both sides of the equation by a3 , we see that: 

P2/a3=k

This means that for every planet in our solar system, the ratio of their period squared to their semimajor axis cubed is the same constant value, so this means that: 

(P2 / a3) Earth = (P2 / a3) Mars = (P2 / a3) Jupiter

We know that the period of the Earth is 1 year. At the time of Kepler, they did not know the distances to the planets, but we can just assign the semimajor axis of the Earth to a unit we call the Astronomical Unit (AU). That is, without knowing how big an AU is, we just set aEarth = 1 AU . If you plug 1 year and 1 AU into the equation above, you see that: 

(P2 / a3) Earth = (P2 / a3) Mars = (P2 / a3) Jupiter

So for every planet, P2 / a3 = 1 if P is expressed in years and a is expressed in AU. So if you want to calculate how far Saturn is from the Sun in AU, all you need to know is its period. For Saturn, this is approximately 29 years. So: (P2 / a3) Saturn = (29 years)2 / (a AU)3 = 1 (a AU)3 = 841 (a AU) = 3√ 841 = 9.4 AU So Saturn is 9.4 times further from the Sun than the Earth is from the Sun! Summary of Kepler's Laws Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky. 1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus. 2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times. 3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well. Newton’s deductions from Kepler’s Laws (Derivation of Kepler’s Laws from Newton’s Laws) Kepler’s Laws 1. A planet orbits the sun in an elliptical path with the sun at one of the foci. 2. The area swept out by a planet radially from the sun over a fixed period of time is constant. (Hence the planets vary their speed as orbit the sun; planets travel faster when they are closer to the sun.)

3. The square of the orbital period is proportional to the cube of the semimajor axis of the orbit.

Newton’s Laws 1. F = ma 2. Suppose a point mass M is located at the origin (0, 0) and a point mass m is located at ( x, y ) . If we let r denote the vector ( x, y ) and r denote the length of this vector (i.e., r 

x 2  y 2 ), then the gravitation force that M exerts on

m is given by Mm r r3 where G is a universal constant, independent of M , m , and r. F  G

Angular Momentum of planet about the origin is conserved Suppose a point mass M is located at the origin (0, 0) and a point mass m is located at ( x, y ) . Suppose that at all times, there is a central force acting on m (i.e., a force always in the direction of r = ( x, y ) . Note r is the position of mass m relative to M. By Newton’s law of universal gravitation, gravity is such a force. Let v = r  = ( x, y) be the velocity vector of m . Define the angular momentum of m2 to be L = r × mv . Then

L  0 Proof. A corollary of this result is that the motion of m2 must lie in a single plane determined by the normal vector L . Areas swept out are constant (Kepler’s Second Law) The key challenge here is express the area swept out in a given amount of time. The most convincing way I know is to express it in polar coordinates based at the origin. Define r = r (cos  i  sin  j ) . NOTE: r and  are functions of time.  is relative to some (arbitrary) fixed ray. Now the area swept out by m2 from time 0 to time t is given by

A

 (t )

r d

1 2

 (0) 2

Taking the derivative with respect to time we get

A  12 r 2  Now taking the derivative of r = r (cos  i  sin  j ) , we find

v = r (cos  i  sin  j )  r ( sin  i  cos  j ) So

L = v = r × mv = r (cos  i  sin  j ) × m  r (cos  i  sin  j )  r ( sin  i  cos  j )   mr 2 k Hence

A  12 r 2  

L  constant 2m

where L denotes the magnitude of the constant angular momentum vector. Another way of approaching this is to think about the incremental area swept out as one half of the area of the parallelogram formed by r and Δr , i.e.,

ΔA  12 | r  r | Then

A 1 r  2 r t t In the limit,

dA 1 L  2 r v  dt 2m Differentiate the unit radius vector One way to derive the first law is to differentiate the vector

r . r

 r  v r      2r r r r 1 = 3 (r 2 v  rr r ) r 1  3 ((r  r )v  (r  v )r ) r r  (r  v )  3 r L a   m GM 1  ( a  L) GMm 1  (v  L) GMm Hence,

1 r (v  L)     e = a constant vector GMm r Note that e is in the plane of motion; the plane of motion is the plane whose normal is L and e  L = 0 . Taking the dot product with r,

1 r r r  (v  L)    r e GMm r

L2  r  re cos  GMm2 or

L2  r  re cos  GMm2 where  is the angle between e and r now.

Kepler’s First Law Case 1. e = 0. Then

r

L2 GMm2

The orbit is a circle. Now let

L2  ed GMm 2 Then

ed  r (1  e cos  ) Convert to Cartesian coordinates:

ed  er cos   r ed  ex  x 2  y 2 e 2 (d  x) 2  x 2  y 2 e 2 d 2  2de 2 x  e 2 x 2  x 2  y 2 e 2 d 2  x 2 (1  e 2 )  2de 2 x  y 2 We now obtain Case 2: If e = 1, the orbit is a parabola. Also if e > 1, then we get Case 3: If e > 1, the orbit is a hyperbola. Now assume e  1 . Complete the square to get 2

 e2 d  y2 e2 d 2  x   1  e 2  1  e 2 (1  e 2 ) 2  2

 e2 d  x    1  e2  y2   1 e2 d 2 e2 d 2 (1  e 2 ) 2 (1  e 2 ) Let a 2 

e2 d 2 e2 d 2 2 , . Then distance from the center to the ellipse to the focus is c where c 2  a 2  b 2 . b  (1  e2 )2 (1  e2 )

c2  a 2  b2 

e2 d 2 e2 d 2  (1  e 2 ) 2 (1  e 2 )



e4 d 2 (1  e 2 ) 2

 e2 d   2   1 e  So c 

2

e2 d . So (0,0) is a focus of the ellipse. Note that the eccentricity of the ellipse is 1  e2

e2 d c 1  e2  e. ed a 1  e2 Kepler’s Third Law Assume The derivative of the area is a constant

L . Thus over an entire closed orbit of time T 2m

L T   ab 2m Therefore

T

2m  ab L

2 m  ed   ed     L  1  e2   1  e2  2 m (ed ) 2  L (1  e2 )3/2



But

L2  ed or L  edGM m GMm 2

So

T

2 m (ed ) 2 2 3/2 edGM m (1  e )

2 (ed )3/2 2 3/2 GM (1  e ) 2  a 3/2 GM



Or

T2 

4 2 3 a GM

Newton’s Correction Newton realized that mass m will pull on M as well. A more complete analysis goes as follows. m

r2 − r1 r2 M

r1

Mr1 G

Mm (r2  r1 ) | r2  r1 |3

mr2  G

Mm (r2  r1 ) | r2  r1 |3

Or

r1 G

m (r2  r1 ) | r2  r1 |3

r2  G

M (r2  r1 ) | r2  r1 |3

Subtract the first equation from the second:

r2  r1 G

M m (r2  r1 ) | r2  r1 |3

Or

(r2  r1 )  G

M m (r2  r1 ) | r2  r1 |3

Therefore, taking into account that the larger mass is also affected by the smaller mass, we see that the distance between bodies actually satisfies the same equation as above with M replaced by m + M. The corrected analysis is essentially identical as the one above. M is replaced by M + m. Kepler’s Third Law becomes

4 2 T  a3 G(M  m) 2

Further analysis (which is essentially the same analysis as above) shows for an outside observer both M and m orbit the center of mass of the system in ellipses with the same period. Newton's Law of Gravitation Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joing the objects (See Fig.). The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them. For the two objects in Figure: Figure: Gravitational Force Between Two Masses



m1 exerts a force

 

m2 exerts a force on m1 . By Newton's third law:

on m2 .

=

.

The magnitude of the gravitational force is: (22)

F12 = G

.



G is Newton's constant: G = 6.67 x 10- 11 N m 2 /kg 2. Newton's Modification of Kepler's Third Law Because for every action there is an equal and opposite reaction, Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun. Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system. He then modified Kepler's 3rd Law to read,

where P is the planetary orbital period and the other quantities have the meanings described above, with the Sun as one mass and the planet as the other mass. Notice the symmetry of this equation: since the masses are added on the left side and the distances are added on the right side, it doesn't matter whether the Sun is labeled with 1 and the planet with 2, or vice-versa. One obtains the same result in either case. Now notice what happens in Newton's new equation if one of the masses (either 1 or 2; remember the symmetry) is very large compared with the other. In particular, suppose the Sun is labeled as mass 1, and its mass is much larger than the mass for any of the planets. Then the sum of the two masses is always approximately equal to the mass of the Sun, and if we take ratios of Kepler's 3rd Law for two different planets the masses cancel from the ratio and we are left with the original form of Kepler's 3rd Law:

Thus Kepler's 3rd Law is approximately valid because the Sun is much more massive than any of the planets and therefore Newton's correction is small. The data Kepler had access to were not good enough to show this small effect. However, detailed observations made after Kepler show that Newton's modified form of Kepler's 3rd Law is in better accord with the data than Kepler's original form. Determination of mass of Earth Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. It is the only planet in our solar system that sustains life and it is the planet that we can call our own. In approximately 230 BC, the Greek mathematian, Eratosthenes calulated the radius of the Earth. He compared the shadows in the wells during the summer solstice and obtained the value 6.38 × 106 M. In the 16th century, Galileo determined the acceleration due to the force of gravity near the surface of the Earth and obtained 9.8 m/sec2.

Sir Isaac Newton greatly contributed to the study of physics and therefore, his efforts determined the mass of the Earth. His law of gravity and second law of motion are used together to obtain a value for the mass of our planet. Newton's law of gravity formulates the gravitational force that two masses exert on each other and is given by F = GmM/r2 M an m are the two masses, r is the separation between them, and G is the universal gravitational constant which was calculated by Henry Cavendish in 1798, which has a value of 6.67 × 10−11 m3/(kg sec2). If we assumed that M is the mass of the Earth, and m is the mass of an object on the surface of the Earth, we can solve for M by equating Newton's Law of Gravity with his second law of motion F = ma We have: F = GmM/r2 = ma → GM/r2 = a Solving for M, the mass of the Earth, and using Where a = 9.8 m/s2, r = 6.38 × 106 G = 6.67 × 10−11 m3/(kg sec2)

m,

and

we obtain: M = ar2/G = 5.98 × 1024 kg. Determination of mass of Plants with respect to Earth We start by determining the mass of the Earth. Issac Newton's Law of Universal Gravitation tells us that the force of attraction between two objects is proportional the product of their masses divided by the square of the distance between their centers of mass. To obtain a reasonable approximation, we assume their geographical centers are their centers of mass. Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extemely small force of 6.67 x 10-11 Newton’s between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."

Calculating the Sun's Mass Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun. The centripetal force = the Earth's mass times the square of its speed / its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass. Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass. Brief Description of Asteroids Asteroids are rocky worlds revolving around the sun that are too small to be called planets. They are also known as planetoids or minor planets. There are millions of asteroids, ranging in size from hundreds of miles to several feet across. In total, the mass of all the asteroids is less than that of Earth's moon. Despite their size, asteroids can be dangerous. Many have hit Earth in the past, and more will crash into our planet in the future. That's one reason scientists study asteroids and are eager to learn more about their numbers, orbits and physical characteristics. If an asteroid is headed our way, we want to know that. Formation Asteroids are leftovers from the formation of our solar system about 4.6 billion years ago. Early on, the birth of Jupiter prevented any planetary bodies from forming in the gap between Mars and Jupiter, causing the small objects that were there to collide with each other and fragment into the asteroids seen today. Understanding of how the solar system evolved is constantly expanding. Two fairly recent theories, the Nice model and the Grand Tack, suggest that the gas giants moved around before settling into their modern orbits. This movement could have sent asteroids from the main belt raining down on the terrestrial planets, emptying and refilling the original belt. Physical characteristics Asteroids can reach as large as Ceres, which is 940 kilometers (about 583 miles) across. On the other end of the scale, the smallest asteroid ever studied is the 6-foot-wide (2 meters) space rock 2015 TC25, which was observed when it made a close flyby of Earth in October 2015. The chances of it hitting Earth in the foreseeable future are small, Vishnu Reddy of the University of Arizona's Lunar and Planetary Laboratory said in a statement.

"You can think of [an asteroid] as a meteorite floating in space that hasn't hit the atmosphere and made it to the ground — yet," Reddy added. Nearly all asteroids are irregularly shaped, although a few of the largest are nearly spherical, such as Ceres. They are often pitted or cratered — for instance, Vesta has a giant crater some 285 miles (460 km) in diameter. The surfaces of most asteroids are thought to be covered in dust. As asteroids revolve around the sun in elliptical orbits, they rotate, sometimes tumbling quite erratically. More than 150 asteroids are also known to have a small companion moon, with some having two moons. Binary or double asteroids also exist, in which two asteroids of roughly equal size orbit each other, and triple asteroid systems are known as well. Many asteroids seemingly have been captured by a planet's gravity and become moons — likely candidates include Mars' moons, Phobos and Deimos, and most of the outer moons of Jupiter, Saturn, Uranus and Neptune. The average temperature of the surface of a typical asteroid is minus 100 degrees Fahrenheit (minus 73 degrees Celsius). Asteroids have stayed mostly unchanged for billions of years — as such, research into them could reveal a great deal about the early solar system. Asteroids come in a variety of shapes and sizes. Some are solid bodies, while others are smaller piles of rubble bound together by gravity. One, which orbits the sun between Neptune and Uranus, comes with its own set of rings. Another has not one but six tails. Classification Asteroids lie within three regions of the solar system. Most asteroids lie in a vast ring between the orbits of Mars and Jupiter. This main asteroid belt holds more than 200 asteroids larger than 60 miles (100 km) in diameter. Scientists estimate the asteroid belt also contains between 1.1 million and 1.9 million asteroids larger than 1 km (3,281 feet) in diameter and millions of smaller ones. Not everything in the main belt is an asteroid — Ceres, once thought of only as an asteroid, is now also considered a dwarf planet. In the past decade, scientists have also identified a class of objects known as "main belt asteroids," small rocky objects with tails. While some of the tails form when objects crash into an asteroid, or by disintegrating asteroids, others may be comets in disguise. Many asteroids lie outside the main belt. Trojan asteroids orbit a larger planet in two special places, known as Lagrange points, where the gravitational pull of the sun and the planet are balanced. Jupiter Trojans are the most numerous, boasting nearly as high a population as the main asteroid belt. Neptune, Mars and Earth also have Trojan asteroids. Near-Earth asteroids (NEAs) circle closer to Earth than the sun. Amor asteroids have close orbits that approach but no not cross Earth's path, according to NASA. Apollo asteroids have Earth-crossing orbits but spend most of their time outside the planet's path. Aten asteroids also cross Earth's orbit but spend most of their time inside Earth's orbit. Atira asteroids are near-Earth asteroids whose orbits are contained within Earth's orbit. According to the European Space Agency, roughly 10,000 of the known asteroids are NEAs. In addition to classifications of asteroids based on their orbits, most asteroids fall into three classes based on composition: The C-type or carbonaceous asteroids are grayish in color and are the most common, including more than 75 percent of known asteroids. They probably consist of clay and stony silicate rocks, and inhabit the main belt's outer regions. The S-type or silicaceous asteroids are greenish to reddish in color, account for about 17 percent of known asteroids, and dominate the inner asteroid belt. They appear to be made of silicate materials and nickel-iron. The M-type or metallic asteroids are reddish in color, make up most of the rest of the asteroids, and dwell in the middle region of the main belt. They seem to be made up of nickle-iron.

There are many other rare types based on composition as well — for instance, V-type asteroids typified by Vesta have a basaltic, volcanic crust. Earth impacts Ever since Earth formed about 4.5 billion years ago, asteroids and comets have routinely slammed into the planet. The most dangerous asteroids are extremely rare, according to NASA. An asteroid capable of global disaster would have to be more than a quarter-mile wide. Researchers have estimated that such an impact would raise enough dust into the atmosphere to effectively create a "nuclear winter," severely disrupting agriculture around the world. Asteroids that large strike Earth only once every 1,000 centuries on average, NASA officials say. Smaller asteroids that are believed to strike Earth every 1,000 to 10,000 years could destroy a city or cause devastating tsunamis. According to NASA, space rocks smaller than 82 feet (25 m) will most likely burn up as they enter Earth's atmosphere, which means that even if 2015 TC25 hit Earth, it probably wouldn't make it to the ground. On Feb. 15, 2013, an asteroid slammed into the atmosphere over the Russian city of Chelyabinsk, creating a shock wave that injured 1,200 people. The space rock is thought to have measured about 65 feet (20 m) wide when it entered Earth's atmosphere. When an asteroid, or a part of it, crashes into Earth, it's called a meteorite. Here are typical compositions: Iron meteorites  Iron: 91 percent  Nickel: 8.5 percent  Cobalt: 0.6 percent Stony meteorites  Oxygen: 6 percent  Iron: 26 percent  Silicon: 18 percent  Magnesium: 14 percent  Aluminum: 1.5 percent  Nickel: 1.4 percent  Calcium: 1.3 percent Asteroid defense Dozens of asteroids have been classified as "potentially hazardous" by the scientists who track them. Some of these, whose orbits come close enough to Earth, could potentially be perturbed in the distant future and sent on a collision course with our planet. Scientists point out that if an asteroid is found to be on a collision course with Earth 30 or 40 years down the road, there is time to react. Though the technology would have to be developed, possibilities include exploding the object or diverting it. [Image Gallery: Potentially Dangerous Asteroids] For every known asteroid, however, there are many that have not been spotted, and shorter reaction times could prove more threatening. When asteroids do close flybys of Earth, one of the most effective ways to observe them is by using radar, such as the system at NASA's Goldstone Deep Space Communications Complex in California. In September 2017, the near-Earth asteroid 3122 Florence cruised by Earth at 4.4 million miles (7 million km), or 18 times the distance to the moon. The flyby confirmed its size (2.8 miles or 4.5 km) and rotation period (2.4 hours). Radar also revealed new information such as its shape, the presence of at least one big crater, and two moons. In a NASA broadcast from earlier in 2017, Marina Brozovic, a physicist at NASA's Jet Propulsion Laboratory, said radar can reveal details such as its size, its shape, and whether the asteroid is actually two objects (a binary system, where a

smaller object orbits a larger object.) "Radar is a little bit like a Swiss army knife," she said. "It reveals so much about asteroids all at once." In the unlikely event that the asteroid is deemed a threat, NASA has a Planetary Defense Coordination Office that has scenarios for defusing the situation. In the same broadcast, PDCO planetary defense officer Lindley Johnson said the agency has two technologies at the least that could be used: a kinetic impactor (meaning, a spacecraft that slams into the asteroid to move its orbit) or a gravity tractor (meaning, a spacecraft that remains near an asteroid for a long period of time, using its own gravity to gradually alter the asteroid's path.) PDCO would also consult with the White House and the Federal Emergency Management Agency (FEMA) and likely other space agencies, to determine what to do. However, there is no known asteroid (or comet) threat to Earth and NASA carefully tracks all known objects through a network of partner telescopes. Water delivery? Ironically, the collisions that could mean death for humans may be the reason we are alive today. When Earth formed, it was dry and barren. Asteroid and comet collisions may have delivered the water-ice and other carbon-based molecules to the planet that allowed life to evolve. At the same time, the frequent collisions kept life from surviving until the solar system calmed down. Later collisions shaped which species evolved and which were wiped out. According to NASA's Center for Near Earth Object Studies CNEOS), "It seems possible that the origin of life on the Earth's surface could have been first prevented by an enormous flux of impacting comets and asteroids, then a much less intense rain of comets may have deposited the very materials that allowed life to form some 3.5 - 3.8 billion years ago." Discovery & naming In 1801, while making a star map, Italian priest and astronomer Giuseppe Piazzi accidentally discovered the first and largest asteroid, Ceres, orbiting between Mars and Jupiter. Although Ceres is classified today as a dwarf planet, it accounts for a quarter of all the mass of all the known asteroids in or near the main asteroid belt. Over the first half of the 19th century, several asteroids were discovered and classified as planets. William Herschel coined the phrase "asteroid" in 1802, but other scientists referred to the newfound objects as minor planets. By 1851, there were 15 new asteroids, and the naming process shifted to include numbers, with Ceres being designated as (1) Ceres. Today, Ceres shares dual designation as both an asteroid and a dwarf planet, while the rest remain asteroids. Since the International Astronomical Union is less strict on how asteroids are named when compared to other bodies, there are asteroids named after Mr. Spock of "Star Trek" and rock musician Frank Zappa, as well as more solemn tributes, such as the seven asteroids named for the crew of the Space Shuttle Columbia killed in 2003. Naming asteroids after pets is no longer allowed. Asteroids are also given numbers — for example, 99942 Apophis. Exploration The first spacecraft to take close-up images of asteroids was NASA's Galileo in 1991, which also discovered the first moon to orbit an asteroid in 1994. In 2001, after NASA's NEAR spacecraft intensely studied the near-earth asteroid Eros for more than a year from orbit, mission controllers decided to try and land the spacecraft. Although it wasn't designed for landing, NEAR successfully touched down, setting the record as the first to successfully land on an asteroid. In 2006, Japan's Hayabusa became the first spacecraft to land on and take off from an asteroid. It returned to Earth in June 2010, and the samples it recovered are currently under study.

NASA's Dawn mission, launched in 2007, began exploring Vesta in 2011. After a year, it left the asteroid for a trip to Ceres, arriving in 2015. Dawn was the first spacecraft to visit Vesta and Ceres. As of 2017, the spacecraft still orbits the extraordinary asteroid. In September 2016, NASA launched the Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx), which will explore the asteroid Bennu before grabbing a sample to return to Earth. "Sample return is really at the forefront of scientific exploration," OSIRIS-REx principal investigator Dante Lauretta said at a press conference. In January 2017, NASA selected two projects, Lucy and Psyche, via its Discovery Program. Planned to launch in October 2021, Lucy will visit an object in the asteroid belt before going on to study six Trojan asteroids. Psyche will travel to 16 Psyche, an enormous metallic asteroid that may be the core of an ancient Mars-size planet, stripped of its crust through violent collisions. In 2012, a company called Planetary Resources, Inc. announced plans to eventually send a mission to a space rock to extract water and mine the asteroid for precious metals. Since then, NASA has begun to work on plans for its own asteroid-capture mission. According to CNEOS, "It has been estimated that the mineral wealth resident in the belt of asteroids between the orbits of Mars and Jupiter would be equivalent to about 100 billion dollars for every person on Earth today." Brief Description of Comet What is a Comet? A comet is a very small solar system body made mostly of ices mixed with smaller amounts of dust and rock. Most comets are no larger than a few kilometres across. The main body of the comet is called the nucleus, and it can contain water, methane, nitrogen and other ices. When a comet is heated by the Sun, its ices begin to sublimate (similar to the way dry ice “fizzes” when you leave it in sunlight). The mixture of ice crystals and dust blows away from the comet nucleus in the solar wind, creating a pair of tails. The dust tail is what we normally see when we view comets from Earth. A plasma tail also forms when molecules of gas are “excited” by interaction with the solar wind. The plasma tail is not normally seen with the naked eye, but can be imaged. Comets normally orbit the Sun, and have their origins in the Oort Cloud and Kuiper Belt regions of the outer solar system. Facts about Comets There are many misconceptions about comets, which are simply pieces of solar system ices travelling in orbit around the Sun. Here are some fascinating and true facts about comets.   

 

The nucleus of a comet is made of ice and can be as small as a few meters across to giant boulders a few kilometres across. The closest point in a comet’s orbit to the Sun is called “perihelion”. The most distant point is called “aphelion”. As a comet gets closer to the Sun, it begins to experience heat. That causes some of its ices to sublimate (similar to dry ice sizzling in sunlight). If the ice is close to the comet’s surface, it may form a small “jet” of material spewing out from the comet like a mini-geyser. Material streams from comets and populates the comet’s orbit. If Earth (or another planet) happens to move through that stream, those particles fall to Earth as meteor showers. As a comet gets close to the Sun, it loses some of its mass due to the sublimation. If a comet goes around enough times, it will eventually break up. Comets also break up if they come TOO close to the Sun or another planet in their orbits.

    

Comets are usually made of frozen water and supercold methane, ammonia and carbon dioxide ices. Those are mixed with rock, dust, and other metallic bits of solar system debris. Comets have two tails: a dust tail (which you can see with the naked eye) and a plasma tail, which is easily photographed but difficult to see with your eyes. Comet orbits are usually elliptical. Many comets formed in the Oort Cloud and Kuiper Belts, two of the outermost regions of the solar system. Comets are not spaceships or alien bases. They are fascinating bits of solar system material that date back to the formation of the Sun and planets.

Brief Description of Satellites In general, a satellite is anything that orbits something else, as, for example, the moon orbits the earth. In a communications context, a satellite is a specialized wireless receiver/transmitter that is launched by a rocket and placed in orbit around the earth. There are hundreds of satellites currently in operation. They are used for such diverse purposes as weather forecasting, television broadcast, amateur radio communications, Internet communications, and the Global Positioning System, (GPS). The first artificial satellite, launched by Russia (then known as the Soviet Union) in the late 1950s, was about the size of a basketball. It did nothing but transmit a simple Morse code signal over and over. In contrast, modern satellites can receive and re-transmit thousands of signals simultaneously, from simple digital data to the most complex television programming. There are three types of communications satellite systems. They are categorized according to the type of orbit they follow. A geostationary satellite orbits the earth directly over the equator, approximately 22,000 miles up. At this altitude, one complete trip around the earth (relative to the sun) takes 24 hours. Thus, the satellite remains over the same spot on the earth's surface at all times, and stays fixed in the sky from any point on the surface from which it can be "seen." So-called weather satellites are usually of this type. You can view images from some of these satellites on the Internet via the Purdue Weather Processor. A single geostationary satellite can "see" approximately 40 percent of the earth's surface. Three such satellites, spaced at equal intervals (120 angular degrees apart), can provide coverage of the entire civilized world. A geostationary satellite can be accessed using a dish antenna aimed at the spot in the sky where the satellite hovers. A low-earth-orbit (LEO) satellite system employs a large fleet of "birds," each in a circular orbit at a constant altitude of a few hundred miles. The orbits take the satellites over, or nearly over, the geographic poles. Each revolution takes approximately 90 minutes to a few hours. The fleet is arranged in such a way that, from any point on the surface at any time, at least one satellite is on a line of sight. The entire system operates in a manner similar to the way a cellular telephone functions. The main difference is that the transponders, or wireless receiver/transmitters, are moving rather than fixed, and are in space rather than on the earth. A well-designed LEO system makes it possible for anyone to access the Internet via wireless from any point on the planet, using an antenna no more sophisticated than old-fashioned television "rabbit ears." Some satellites revolve around the earth in elliptical orbits. These satellites move rapidly when they are near perigee, or their lowest altitude; they move slowly when they are near apogee, or their highest altitude. Such "birds" are used by amateur radio operators, and by some commercial and government services. They require directional antennas whose orientation must be constantly adjusted to follow the satellite's path across the sky. Types of Satellites and Applications  Communications Satellite.  Remote Sensing Satellite.  Navigation Satellite.  Geocentric Orbit type staellies - LEO, MEO, HEO.  Global Positioning System (GPS)  Geostationary Satellites (GEOs)