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Sheila Panyam Honors 392A 04/11/18 Reading Assignment 5 Pg.
Question
Answer
166- Redraw one half of Figure 32 and use it to 167 explain the apparent retrograde motion of Mars.
The Earth moves faster around the sun than Mars does, so at certain points, it ‘laps’ Mars. It is during this ‘lapping’ that retrograde motion appears to occur (in the case of inferior planets -- ones closer to the sun, they lap the Earth). The planet appears to be moving backwards because of the angle at which it is being viewed on Earth. This apparent westward motion only occurs when the Earth is closest to Mars, which is why it is brightest during this time. 167- Are planets’ cycles around the ecliptic regular?
This question has a two part answer. First, yes, on average, a planet’s orbit will take the same amount of time as circling the ecliptic. However, individual trips can vary greatly. In the case of the superior planets, the Earth completes its orbit faster, so it’s further along its second orbit by the time Mars, for example, finishes its first. That places Mars at a different apparent position on the ecliptic (not quite at one full cycle). The next time, however, the Earth shifts down the orbit again, and Mars appears to overcompensate, making over a full ecliptic cycle.
169 170
Kuhn argues that most of the Copernican system, while efficient, was not as accurate as Ptolemy’s epicycle/deferent system. It cannot describe the position of the planets as quantitatively as Ptolemy did, and ultimately used so many eccentrics and minor epicycles that wasn’t much less complicated than Ptolemy. Once these epicycles and eccentrics were added, Copernicus’ results weren’t any more a ccurate than Ptolemy’s, either. In that regard,
Describe how Copernicus’ theory explains why or why not.
What was the “propaganda victory” that Copernicus’ followers emphasized, and why is the victory only apparent according to Kuhn?
Kuhn asserts that Copernicus did not solve the problem of the planets. 172- In no more than two sentences, explain why 173 Mercury and Venus never appear very far from the ecliptic in the Copernican system. Then explain, in no more than two sentences, why this explanation was thought to be a reason favoring Copernicus’ rather than Ptolemy’s system.
Unlike in the Ptolemaic system, where the movement of Mercury and Venus are restricted because their epicycles must always lie between the Earth and the sun, the Copernican system simply locks them into the Earth’s orbit. When the inferior planet is visible, it cannot be too far from the sun, and the maximum elongation angle describes how far away the planet can possibly get from the sun. This explanation was favored because it seemed more natural (and straightforward) than Ptolemy’s; the latter requires additional aligned epicycles that locks the inferior planets with the sun. Copernicus did not have to use the additional epicycles and resorted to simple geometry.
174
In no more than a paragraph, explain (in rough detail) how Copernicus’ system can be used to calculate the number of days it takes Mercury to orbit the sun. Your explanation need not employ calculations unless you’d like to do so; just try to give the general idea. Then briefly explain how the lengths of the planets’ orbits was used to order the inferior planets in distance from the sun.
Since Mercury retrogresses every 116 days, that must be the amount of time it requires to ‘lap’ the Earth (because retrograde motion only happens when the planet is visible to us). Given this number, astronomers can find how many orbits the Earth has completed in that time, and then, how many orbits Mercury has travelled. Then, given the number of orbits it has travelled in 116 days, astronomers can find the length (in days) of an orbit (which, for Mercury, is 88). The planets with the smallest orbits were placed closer to the sun, as they required less time to complete an orbit. In that way, Mercury was placed closest with an orbit of 88 days, and Venus between it and the Earth with an orbit of 225 days. The superior planets were all distanced similarly, with the Earth in between Venus and Mars.
175- Recall that, in Ptolemaic models, the inferior 176 planets could be ordered (by distance from the
In the Ptolemaic model, observing planetary positions consistent with models did not always depend on the order or size of the planetary orbits. However, in the Copernican model, both of these factors were consequential. An example of this is in finding the maximum elongation angle of a planet between the Earth and the sun. This angle is found by drawing in a right angle triangle with the Earth, the inferior planet, and the sun as its vertices. One of the acute angles, the one that branches from the Earth, can determine the ratio between the inferior planet’s orbit and the Earth’s orbit. Knowledge of the ratio is vital to determining the length of an unknown orbit. If these distances were to be changed, then the angles (and consequently the orbit lengths) would all be disastrously erroneous.
179
Copernicus is often attributed with endorsing a form of Ockham’s razor when he writes, “We thus rather follow Nature, who producing nothing vain or superfluous often prefers to endow one cause with many effects.” What “one cause” is Copernicus discussing in this passage and which “many effects” does the cause explain? Hint: You may wish to consider reading until the next page to identify what Copernicus thinks the cause is.
Copernicus believes that the cause leading to all the various effects he describes is that the Earth is in constant motion. One effect is the illusion of retrograde motion -- and why planets differ in the amount of time they are ‘regressing.’ Another effect is that the Earth laps more distant planets (like Jupiter and Saturn) more frequently than Mars because they move a lot slower. The Earth’s motion explains why certain planets appear closer and brighter than others (and at different parts of their orbits).
183
With what was the Copernican Revolution “completed” according to Kuhn?
With the completion of his book, Copernicus turned the world away from a geocentric model of the universe in favor of a heliocentric one. With this new model came lots of new unanswered questions and problems, which he promptly directed towards the new generation of astronomers. These new problem-solvers looked to Copernicus’ research in the same way he had looked to Ptolemy, thus
Earth) in different ways, and the resulting predictions would be consistent with observation. In contrast, the superior planets’ order was fixed. However, the relative sizes of all planetary orbits – even those of the superior planets – could be changed in a way that would not render the model inconsistent with observation. Is the same true of planetary orbits in Copernicus’ model?
ending the revolution and beginning a new era of astronomy.
86, On page 86, Kuhn claims that, “[For 180- Aristotle], astronomy and terrestrial 184 physics are not independent sciences.” In no more than a paragraph, assess whether Copernicus would agree.
I think that Copernicus would agree with Aristotle indirectly. His work was not just about astronomy itself. It was about scientific principles (like utilizing Ockham’s razor) that I believe are applicable across all disciplines. Like William Harvey overthrowing Galen’s theory of blood circulation, Copernicus cleared the way for fresh astronomical thinking, which in turn, increased reception towards the likes of Newton. However, at the same time, Copernicus kept his work narrowly focused on the stars and ignored any discrepancies between a cosmology and the math that he was directly working with, so perhaps he wasn’t consciously trying to link the world together the way Aristotle did. Ultimately, though, given that the words “symmetry” and “harmony” are repeated throughout his book, I would assert that he saw some sort of connection between all the entities of the universe, and like Aristotle, found some satisfaction in it.
Question
Answer
166- Redraw one half of Figure 32 and use it to 167 explain the apparent retrograde motion of Mars.
The Earth moves faster around the sun than Mars does, so at certain points, it ‘laps’ Mars. It is during this ‘lapping’ that retrograde motion appears to occur (in the case of inferior planets -- ones closer to the sun, they lap the Earth). The planet appears to be moving backwards because of the angle at which it is being viewed on Earth. This apparent westward motion only occurs when the Earth is closest to Mars, which is why it is brightest during this time. 167- Are planets’ cycles around the ecliptic regular?
This question has a two part answer. First, yes, on average, a planet’s orbit will take the same amount of time as circling the ecliptic. However, individual trips can vary greatly. In the case of the superior planets, the Earth completes its orbit faster, so it’s further along its second orbit by the time Mars, for example, finishes its first. That places Mars at a different apparent position on the ecliptic (not quite at one full cycle). The next time, however, the Earth shifts down the orbit again, and Mars appears to overcompensate, making over a full ecliptic cycle.
169 170
Kuhn argues that most of the Copernican system, while efficient, was not as accurate as Ptolemy’s epicycle/deferent system. It cannot describe the position of the planets as quantitatively as Ptolemy did, and ultimately used so many eccentrics and minor epicycles that wasn’t much less complicated than Ptolemy. Once these epicycles and eccentrics were added, Copernicus’ results weren’t any more a ccurate than Ptolemy’s, either. In that regard,
Describe how Copernicus’ theory explains why or why not.
What was the “propaganda victory” that Copernicus’ followers emphasized, and why is the victory only apparent according to Kuhn?
Kuhn asserts that Copernicus did not solve the problem of the planets. 172- In no more than two sentences, explain why 173 Mercury and Venus never appear very far from the ecliptic in the Copernican system. Then explain, in no more than two sentences, why this explanation was thought to be a reason favoring Copernicus’ rather than Ptolemy’s system.
Unlike in the Ptolemaic system, where the movement of Mercury and Venus are restricted because their epicycles must always lie between the Earth and the sun, the Copernican system simply locks them into the Earth’s orbit. When the inferior planet is visible, it cannot be too far from the sun, and the maximum elongation angle describes how far away the planet can possibly get from the sun. This explanation was favored because it seemed more natural (and straightforward) than Ptolemy’s; the latter requires additional aligned epicycles that locks the inferior planets with the sun. Copernicus did not have to use the additional epicycles and resorted to simple geometry.
174
In no more than a paragraph, explain (in rough detail) how Copernicus’ system can be used to calculate the number of days it takes Mercury to orbit the sun. Your explanation need not employ calculations unless you’d like to do so; just try to give the general idea. Then briefly explain how the lengths of the planets’ orbits was used to order the inferior planets in distance from the sun.
Since Mercury retrogresses every 116 days, that must be the amount of time it requires to ‘lap’ the Earth (because retrograde motion only happens when the planet is visible to us). Given this number, astronomers can find how many orbits the Earth has completed in that time, and then, how many orbits Mercury has travelled. Then, given the number of orbits it has travelled in 116 days, astronomers can find the length (in days) of an orbit (which, for Mercury, is 88). The planets with the smallest orbits were placed closer to the sun, as they required less time to complete an orbit. In that way, Mercury was placed closest with an orbit of 88 days, and Venus between it and the Earth with an orbit of 225 days. The superior planets were all distanced similarly, with the Earth in between Venus and Mars.
175- Recall that, in Ptolemaic models, the inferior 176 planets could be ordered (by distance from the
In the Ptolemaic model, observing planetary positions consistent with models did not always depend on the order or size of the planetary orbits. However, in the Copernican model, both of these factors were consequential. An example of this is in finding the maximum elongation angle of a planet between the Earth and the sun. This angle is found by drawing in a right angle triangle with the Earth, the inferior planet, and the sun as its vertices. One of the acute angles, the one that branches from the Earth, can determine the ratio between the inferior planet’s orbit and the Earth’s orbit. Knowledge of the ratio is vital to determining the length of an unknown orbit. If these distances were to be changed, then the angles (and consequently the orbit lengths) would all be disastrously erroneous.
179
Copernicus is often attributed with endorsing a form of Ockham’s razor when he writes, “We thus rather follow Nature, who producing nothing vain or superfluous often prefers to endow one cause with many effects.” What “one cause” is Copernicus discussing in this passage and which “many effects” does the cause explain? Hint: You may wish to consider reading until the next page to identify what Copernicus thinks the cause is.
Copernicus believes that the cause leading to all the various effects he describes is that the Earth is in constant motion. One effect is the illusion of retrograde motion -- and why planets differ in the amount of time they are ‘regressing.’ Another effect is that the Earth laps more distant planets (like Jupiter and Saturn) more frequently than Mars because they move a lot slower. The Earth’s motion explains why certain planets appear closer and brighter than others (and at different parts of their orbits).
183
With what was the Copernican Revolution “completed” according to Kuhn?
With the completion of his book, Copernicus turned the world away from a geocentric model of the universe in favor of a heliocentric one. With this new model came lots of new unanswered questions and problems, which he promptly directed towards the new generation of astronomers. These new problem-solvers looked to Copernicus’ research in the same way he had looked to Ptolemy, thus
Earth) in different ways, and the resulting predictions would be consistent with observation. In contrast, the superior planets’ order was fixed. However, the relative sizes of all planetary orbits – even those of the superior planets – could be changed in a way that would not render the model inconsistent with observation. Is the same true of planetary orbits in Copernicus’ model?
ending the revolution and beginning a new era of astronomy.
86, On page 86, Kuhn claims that, “[For 180- Aristotle], astronomy and terrestrial 184 physics are not independent sciences.” In no more than a paragraph, assess whether Copernicus would agree.
I think that Copernicus would agree with Aristotle indirectly. His work was not just about astronomy itself. It was about scientific principles (like utilizing Ockham’s razor) that I believe are applicable across all disciplines. Like William Harvey overthrowing Galen’s theory of blood circulation, Copernicus cleared the way for fresh astronomical thinking, which in turn, increased reception towards the likes of Newton. However, at the same time, Copernicus kept his work narrowly focused on the stars and ignored any discrepancies between a cosmology and the math that he was directly working with, so perhaps he wasn’t consciously trying to link the world together the way Aristotle did. Ultimately, though, given that the words “symmetry” and “harmony” are repeated throughout his book, I would assert that he saw some sort of connection between all the entities of the universe, and like Aristotle, found some satisfaction in it.
