Mastering Astronomy Assignment 3

__Suppose you want to observe the apparent retrograde motion of Mars. How long will you need to see it?__

* A few days
* About an hour
* Many months
* One night

Many months

* Explanation 
* As you can see in Figure 2.3 in your textbook, Mars's period of apparent retrograde motion lasts a few months. Moreover, because it occurs only about every 26 months, you'd need to be watching during the correct period of time to notice it.

Which of the following paths could not be a real orbit for a planet around the Sun?

4th one

Explanation

* Kepler’s first law tells us that the orbit of a planet must be an ellipse with the Sun at one focus. Therefore, the path that shows the Sun in the center of the ellipse, rather than at a focus, cannot be the real orbital path of a planet. (Note that the circular path is allowed because a circle is an ellipse in which both foci are at the center.)

Which of the following orbits has the largest semimajor axis?

4th one

* __Explanation__
* The semimajor axis is half of the distance across the ellipse in its longest direction (which means half of the major axis), which is also the planet’s average distance from the Sun. Therefore, the ellipse that measures the longest across is the one with the largest semimajor axis

Which of the following orbits is the most eccentric?

3rd one

* __Explanation__
* Eccentricity is a measure of how “stretched out” an ellipse is. A perfect circle has zero eccentricity, and the most stretched-out ellipse has the largest eccentricity.

Which of the following orbits shows the planet at aphelion?

2nd one

* __Explanation__
* Aphelion is the point in a planet’s orbit that is farthest from the Sun.

__Suppose you drive from home to your child’s school, pick her up, and drive back home, covering a total distance of 25 miles in 1 hour. Which of the following statements are true?__

* You must accelerate when you reach the school.
* Your average speed for the trip is zero. 
* Your average speed for the trip is 25 miles per hour.
* Your velocity is different on the return home than it is on the way to school. 
* Your average velocity for the trip is 25 miles per hour.

You must accelerate when you reach the school.

Your average speed for the trip is 25 miles per hour.

Your velocity is different on the return home than it is on the way to school. 

* __Explanation__
* Your average speed is 25 miles per hour because you travel a total distance of 25 miles in one hour.  Your velocity is different on the way home than on the way to school because you are going in a different direction, and velocity includes direction. You must accelerate when you reach the school because you must slow down to stop there, then turn around (which is a change in direction), and then speed up to start on your way home; all three of these (slowing, change of direction, speeding up) represent changes in velocity and therefore are examples of acceleration

__Combine:__ net force, weight, velocity, angular momentum, mass, acceleration of gravity, momentum __with:__

* If your momentum is changing, then a(n) ___ must be acting on you
* If you stand on a scale on the Moon, your __ will be different than it is on Earth but your __ will be the same
* If you are in free-fall, then your ___ will be zero
* An object's __ is its mass times its velocity, and we say that it has __ if it is rotating or turning on a curved path.
* On Earth, the __ tells us that the __ of a falling object increases by about 10 m/s for each second it falls.

* If your momentum is changing, then a(n) **net force** must be acting on you
* If you stand on a scale on the Moon, your **weight** will be different than it is on Earth but your  **mass** will be the same
* If you are in free-fall, then your **weight** will be zero
* An object's **momentum** is its mass times its velocity, and we say that it has **angular momentum** if it is rotating or turning on a curved path.
* On Earth, the **acceleration of gravity** tells us that the **velocity** of a falling object increases by about 10 m/s for each second it falls

__Why are astronauts (and other objects) weightless inside the International Space Station as it orbits Earth?__

* they are in free-fall 


* the space station's engines fire to balance gravity
* there’s no gravity in space
* there is no net force acting on the space station

* they are in free-fall
* __Explanation__ 
* Note that this question is nearly identical to the one answered within the video. 

__Earth is slightly closer to the Sun in January than in July. How does the area swept out by Earth’s orbit around the Sun during the 31 days of January compare to the area swept out during the 31 days of July?__

* The area swept out in January is larger.
* Both areas are the same.
* The area swept out in July is larger.

* Both areas are the same.
* __Explanation__
* Kepler’s second law tells us that a planet always sweeps out equal areas in equal times. Therefore, Earth sweeps out the same area in any 31-day period, no matter what month it is.

__All of the following statements are true. Which one can be explained by Kepler’s second law?__

* Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.
* Earth is slightly closer to the Sun in January than in July.


* All the planets orbit the Sun in nearly the same plane.
* The Sun is not in the precise center of Saturn’s orbit.
* Venus orbits the Sun at a faster orbital speed than Earth.

* Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.
* __Explanation__
* Kepler’s second law tells us that a planet moves faster in its orbit when it is closer to the Sun (near perihelion) than when it is farther (near aphelion). This law applies to all planets and therefore explains the statement about Mars.

__When Copernicus first created his Sun-centered model of the universe, his model did not lead to substantially better predictions of planetary positions than the Ptolemaic model. Why not?__

* Copernicus misjudged the distances between the planets.
* Copernicus placed the planets in the wrong order going outward from the Sun.
* Copernicus used perfect circles for the orbits of the planets.
* Copernicus placed the Sun at the center but did not realize that the Moon orbits the Earth.

* Copernicus used perfect circles for the orbits of the planets.
* __Explanation__
* Because orbits are actually elliptical, his model did not make particularly accurate predictions.

__Match each statement to the scientist (Kepler or Newton) associated with it.__

* An object moves at constant velocity if there is no net force acting upon it
* A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times
* For any force, there is an equal and opposite reaction force
* The orbit of each planet about the Sun is an ellipse with the Sun at one focus
* More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p`^2` =a`^3`
* Force = mass x acceleration

* **newton:** An object moves at constant velocity if there is no net force acting upon it
* **kepler:** A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times
* **newton**: For any force, there is an equal and opposite reaction force
* **kepler**: The orbit of each planet about the Sun is an ellipse with the Sun at one focus
* **kepler**: More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p2 =a3
* **newton**: Force = mass x acceleration

__Match the correct laws to the examples in which they apply. Use each law only once.__ 

* **The orbit of each planet is an ellipse, with the sun at one focus**
* **Force equals mass times acceleration**
* **An object moves at constant velocity if there is no net force acting on it**
* **For planets orbiting the sun, period (p) and orbital distance (a) obey the relation p^2 = a^3**
* **For any force, there is an equal and opposite reaction force**
*  **A line between a planet and its sun sweeps out equal areas in equal times**
* explains why Earth's distance from the Sun varies over the course of each year.
* explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand.target 
* explains why a spaceship with no forces acting on it will continue moving even if it has no fuel.
* tells us that, when you are pushing on a table, the table is pushing up on you with a force that precisely balances the force of your push.
* explains why Earth's orbital speed varies over the course of each year.target 5 of 6
* explains why Earth orbits the Sun at a faster average speed than Mars.

* **The orbit of each planet is an ellipse, with the sun at one focus** explains why Earth's distance from the Sun varies over the course of each year.
* **Force equals mass times acceleration** explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand.target 
* **An object moves at constant velocityif there is no net force acting on it** explains why a spaceship with no forces acting on it will continue moving even if it has no fuel.
* **For any force, there is an equal and opposite reaction force** tells us that, when you are pushing on a table, the table is pushing up on you with a force that precisely balances the force of your push.
*  **A line between a planet and its sun sweeps out equal areas in equal times** explains why Earth's orbital speed varies over the course of each year.target 5 of 6
* **For planets orbiting the sun, period (p) and orbital distance (a) obey the relation p^2 = a^3** explains why Earth orbits the Sun at a faster average speed than Mars.

__Place each statement in the correct bin corresponding to when it first occurred in human history.__

* Ancient greece through ptolemy (about 150 A.D.); Early copernican revolution (1543-1600) ; Later copernican revolution (1609-1630) ; Newton and beyond (post 1687)
* Suggestion that earth might orbit the sun
* Recognition that sun-centered model should lead to stellar parallax
* Ability to predict planetary positions within a few deprees of arc
* Copernicus proposes sun-centered model
* Planetary observations accurate within 1 min of arc
* Ability to predict planetary positions within 1 min of arc
* Observation of phoases of venus
* Sun centered model with elliptical orbits
* Observations of stellar parallax
* Mathematical description of how gravity determines planetary orbits

* \
* __Ancient greece through ptolemy (about 150 A.D.)__ 
* Suggestion that earth might orbit the sun 
* Recognition that sun-centered model should lead to stellar parallax 
* Ability to predict planetary positions within a few deprees of arc 
* __Early copernican revolution (1543-1600)__ 
* Copernicus proposes sun-centered model 
* Planetary observations accurate within 1 min of arc
* __Later copernican revolution (1609-1630)__ 
* Ability to predict planetary positions within 1 min of arc 
* Observation of phoases of venus 
* Sun centered model with elliptical orbits 
* __Newton and beyond (post 1687)__ 
* Observations of stellar parallax 
* Mathematical description of how gravity determines planetary orbits
* Explanation 
* The Earth-centered (geocentric) model was favored in ancient Greece, even though Aristarchus proposed that Earth might orbit the Sun. One reason was that the Greeks knew that a Sun-centered model should produce stellar parallax, but they were unable to observe this parallax. Ptolemy’s Earth-centered model could predict planetary positions within a few degrees of arc.
* Copernicus published a detailed, Sun-centered model with circular orbits in 1543. During the next few decades, Tycho made naked eye observations of planetary positions accurate to within 1 minute of arc.
* Galileo began his telescopic observations, including his observations of the phases of Venus, in 1609. That same year, Kepler published his first two laws of planetary motion (which state that planets have elliptical orbits) and his laws could be used to predict planetary positions in agreement with Tycho’s observations (as well as subsequent observations).
* Newton published the universal law of gravitation in 1687, which explains how gravity determines planetary orbits. Stellar parallax was not observed until much later (1838).

__In which of the four time periods did the Sun-centered model gain widespread acceptance, meaning that nearly everyone who looked at the evidence concluded that it was correct?__

* Ancient Greece (through Ptolemy, \~150 A.D.)
* Early Copernican Revolution (about 1543 – 1600)
* Later Copernican Revolution (about 1609-1630)
* Newton and beyond (after about 1687)

* Later Copernican Revolution (about 1609-1630)
* __Explanation__
* Notice that this widespread acceptance of the Sun-centered model came before Newton explained why the model works or observations of parallax provided direct proof that Earth orbits the Sun.

__Which of the following were key pieces of evidence that led to widespread acceptance of the Sun-centered model “extraordinary claim” during the period from about 1609 to 1630?__

* The discovery of planets around other stars.
* Observations of stellar parallax.
* The fact that the Copernican model explained apparent retrograde motion of the planets.
* Galileo’s telescopic observations.
* The fact that Kepler’s laws allowed virtually perfect prediction of planetary positions.

* Galileo’s telescopic observations.
* The fact that Kepler’s laws allowed virtually perfect prediction of planetary positions.
* __Explanation__
* Apparent retrograde motion had a more natural explanation in the Sun-centered model than in Ptolemy’s Earth-centered model, but that had already been known since the time of ancient Greece. So the key evidence that causes the change from general acceptance of the Earth-centered model to the Sun-centered model came from Kepler and Galileo. Kepler’s laws offered a precise mathematical model of planetary motion that gave a virtual perfect match to planetary observations, and Galileo’s telescopic observations revealed phenomena (such as the phases of Venus) that could not be explained by an Earth-centered system. Observations of stellar parallax and planets around other stars both represent even further evidence for the Sun-centered model, but that model was already well-accepted long before this additional evidence was discovered.

__In Carl Sagan’s statement “Extraordinary claims require extraordinary evidence,” what does he mean by “extraordinary evidence”?__

* Evidence that is extremely strong.
* Evidence that no one could possibly dispute, even if they believe the Earth is flat.
* Evidence that is of a highly unusual type compared to standard scientific evidence.
* Evidence that was very difficult to obtain.

* Evidence that is extremely strong.
* __Explanation__
* In this context, Sagan is clearly talking about evidence that is extremely strong.

__Match the correct laws to their statements.__ 

**Newtons first, second and third law of motion** ; **Keplers first, second and third law of planetary motion**:

* the orbit of each planet about the Sun is an ellipse with the Sun at one focus.


* more distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p2 =a3.
* an object moves at constant velocity if there is no net force acting upon it.
* force = mass x acceleration
* a planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times.
* for any force, there is an equal and opposite reaction force.

* **Keplers first law of planetary motion**: the orbit of each planet about the Sun is an ellipse with the Sun at one focus.target 1 of 6
* **Keplers third law of planetary motion**: more distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p2 =a3.target 2 of 6
* **Newtons first law of motion**: an object moves at constant velocity if there is no net force acting upon it.target 3 of 6
* **Newtons second law of motion**: force = mass x accelerationtarget 4 of 6
* **Leplers second law of planetary motion**: a planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times.target 5 of 6
* **Newtons third law of motion**: for any force, there is an equal and opposite reaction force.

__Match the correct laws to the examples in which they apply. Use each law only once.__

**Newtons first, second and third law of motion** ; **Keplers first, second and third law of planetary motion**:

* explains why Earth orbits the Sun at a faster average speed than Mars.
* explains why Earth's distance from the Sun varies over the course of each year.
* explains why Earth's orbital speed varies over the course of each year
* explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand
* tells us that, when you are standing, the ground is pushing up on you with a force that precisely balances the downward force of your weight
* explains why a spaceship with no forces acting on it will continue moving even if it has no fuel.

* **Keplers third law of planetary motion**  explains why Earth orbits the Sun at a faster average speed than Mars
* **Keplers first law of planetary motion** explains why Earth's distance from the Sun varies over the course of each year
* **Keplers second law of planetary motion** explains why Earth's orbital speed varies over the course of each year
* **Newtons second law of motion** explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand
* **Newtons third law of motion** tells us that, when you are standing, the ground is pushing up on you with a force that precisely balances the downward force of your weight
* **Newtons first law of motion** explains why a spaceship with no forces acting on it will continue moving even if it has no fuel.

__Which of the following best explains why the ancient Greek atomists (including Epicurus) believed that other worlds with life must exist?__

* They believed Earth to be the center of the universe.
* They could not imagine a god who would put life on only one world.
* They believed Earth to be a planet orbiting the Sun.
* They believed that the stars were other suns, each orbited by planets.
* They believed the universe was made from an infinite number of atoms

* They believed the universe was made from an infinite number of atoms
* __Explanation__ 
* As explained in the video and your textbook, the idea of an infinite number of atoms leads naturally to the idea that there must be an infinite number of Earth-like worlds.

__Which of the following best explains why Aristotle argued that other worlds with life could not exist?__

* He believed that other worlds existed, but they did not contain the elements needed for life.
* He believed that his Christian faith ws incompatible with the idea of extraterrestrial life. 
* He believed that Earth was the center of everything, and therefore that no other similar centers could exist. 
* He believed Earth to be a planet orbiting the Sun in a unique orbit, and that no other orbit could allow for life.

* He believed that Earth was the center of everything, and therefore that no other similar centers could exist. 
* __Explanation__ 
* As explained in greater detail in your textbook, Aristotle believed that there were four elements -- fire, water, earth, and air -- and that earth naturally fell toward the center of things. Therefore, all the earth that existed must be here on our Earth, and there could not be other worlds, with or without life. That is why the Copernican revolution, which proved that Earth is not the center of the universe, undermined Aristotle's argument against extraterrestrial life. 

__Which of the following are key hallmarks of science?__

* Scientific models must be structured so that they can be proved true by a single good observation or experiment. 
* Modern science seeks explanations for observed phenomena that rely solely on natural causes.
* Models must make testable predictions that will force us to revise or abandon the model if they do not agree with observations.
* Science progresses through the creation and testing of models of nature that explain the observations as simply as possible.
* Science progresses only through careful application of what is called the scientific method. 
* Science can be used to investigate the supernatural or divine.

* Modern science seeks explanations for observed phenomena that rely solely on natural causes.
* Models must make testable predictions that will force us to revise or abandon the model if they do not agree with observations.
* Science progresses through the creation and testing of models of nature that explain the observations as simply as possible.

__According to its scientific definition, a scientific theory__ __________.__

* is a collection of individual facts that have been revealed by observations and experiments
* must always be built around one or more mathematical equations
* explains a wide variety of observed facts in terms of simple underlying principles
* makes predictions that have been confirmed by repeated and varied testing
* is essentially an educated guess about how some aspect of nature works

* explains a wide variety of observed facts in terms of simple underlying principles
* makes predictions that have been confirmed by repeated and varied testing

__Consider the image below showing two objects, called M 1 and M 2, separated by a distance d. Demonstrate your understanding of the universal law of gravitation by completing each sentence that follows.__ 

decrease by a factor of four ; decrease by a factor of four ; increase by a factor of four ; double

* Doubling the distance between M1 and M2 would cause the gravitational force between them to **__**
* Increasing the distance between M1 and M2 by a factor of 10 would cause the gravitational force between them to **__**
* Halving (dividing by two) the distance between M1 and M2 would cause the gravitational force between them to **__**
* Doubling the mass of M1 (while leaving M2 and the distance between them unchanged) would cause the gravitational force between them to **__**

* Doubling the distance between M1 and M2 would cause the gravitational force between them to **decrease by a factor of four**
* Increasing the distance between M1 and M2 by a factor of 10 would cause the gravitational force between them to **decrease by a factor of 100**
* Halving (dividing by two) the distance between M1 and M2 would cause the gravitational force between them to **increase by a factor of four**
* Doubling the mass of M1 (while leaving M2 and the distance between them unchanged) would cause the gravitational force between them to **double**

__All of the following statements are true. Which one can be explained by Kepler’s third law?__

* Venus orbits the Sun at a faster orbital speed than Earth.
* The Sun is not in the precise center of Saturn’s orbit.
* Earth is slightly closer to the Sun in January than in July.
* Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.
* All the planets orbit the Sun in nearly the same plane.

* Venus orbits the Sun at a faster orbital speed than Earth.
* __Explanation__ 
* Kepler’s third law can be stated as the precise mathematical relationship  p2=a3 ; (where p is the planet’s orbital period in years and a is its average orbital distance in  AU ). The essence of the law, however, is that it means planets closer to the Sun orbit at faster average speeds than planets farther from the Sun. Therefore, Venus orbits at a faster orbital speed than Earth, because Venus is closer to the Sun.

__The radius of Earth's orbit is approximately __________ times as large as the radius of Earth itself.__

* 2.3
* 23,000
* 230

23,000

__The video states that the planetary orbits are shown to scale. Which statement correctly describes the way the planet sizes are shown compared to their orbits?__

* Jupiter is shown correctly to scale with its orbit, but all the other planets are too large.
* The planet sizes are correctly shown on the same scale as the orbits.
* The planets are all much too large compared to their orbits.
* The planets should all be about twice as large as shown.

* The planets are all much too large compared to their orbits.
* __explanation__
* On the scale used to show the orbits in the video, all the planets would be microscopic in size.

__Kepler's first law states that the orbit of each planet is an ellipse with the Sun at one focus. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's first law?__

* Inner planets orbit the Sun at higher speed than outer planets.
* All the planets orbit the Sun in nearly the same plane.
* The Sun is located slightly off-center from the middle of each planet's orbit.
* Venus orbits the Sun faster than Earth orbits the Sun.
* Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.
* Earth is slightly closer to the Sun on one side of its orbit than on the other side.

The Sun is located slightly off-center from the middle of each planet's orbit.

* Earth is slightly closer to the Sun on one side of its orbit than on the other side.
* __Explanation__ 
* None of the planets has a perfectly circular orbit, which means that all planets (including Earth) are closer to the Sun on one side of their orbit than on the other. The Sun's off-center position arises because it is located at a focus of each planet's elliptical orbit, rather than at the center of the ellipse.

__Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. Which of the following statements describe a characteristic of the solar system that is explained by Kepler's second law?__

* Venus orbits the Sun faster than Earth orbits the Sun.
* Inner planets orbit the Sun at higher speed than outer planets.
* Earth is slightly closer to the Sun on one side of its orbit than on the other side.
* Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.
* The Sun is located slightly off-center from the middle of each planet's orbit.
* All the planets orbit the Sun in nearly the same plane.

* Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.
* __Explanation__ 
* The same ideas holds for any object orbiting the Sun: An object must move faster when it is closer to the Sun and slower when it is farther from the Sun.

__Kepler's third law states that a planet's orbital period, p, is related to its average (semimajor axis) orbital distance, a, according to the mathematical relationship  p2=a3 . Which of the following statements describe a characteristic of the solar system that is explained by Kepler's third law?__

* Earth is slightly closer to the Sun on one side of its orbit than on the other side.
* The Sun is located slightly off-center from the middle of each planet's orbit.
* All the planets orbit the Sun in nearly the same plane.
* Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.
* Venus orbits the Sun faster than Earth orbits the Sun.
* Inner planets orbit the Sun at higher speed than outer planets

* Venus orbits the Sun faster than Earth orbits the Sun.
* Inner planets orbit the Sun at higher speed than outer planets
* __Explanation__
* From the relationship  p2=a3 , it follows that planets closer to the Sun must orbit at higher average speeds than planets farther from the Sun. For example, Venus must orbit the Sun faster than Earth because Venus is closer to the Sun.

__Beginning about 55 seconds into the video, you'll see an animation of a photographer looking through her camera at a man, a set of trees, and distant mountains. Notice that, as viewed through the camera, the positions of the man and the trees change (relative to distant mountains) as the photographer moves. Which of the following statements correctly describes what is really happening in this situation?__

* \
* The photographer, the man, and the trees are all moving at the same speed.
* The photographer is moving, but the man and the trees are staying still.
* The photographer is staying still, but man and the trees are moving.
* The trees are moving more slowly than the man, who is moving more slowly than the photographer.

* The photographer is moving, but the man and the trees are staying still.
* __Explanation__ 
* In other words, the photographer's motion causes her to see parallax for the man and the trees, because their positions appear to shift even though they are not really moving.
* Parallax is the apparent shift in position of an observed object due to a change in the position of the observer.

__Consider again the portion of the video discussed in Part A.  Notice that in the view through the cameara, the parallax is larger (the apparent movement is larger) for the man than for the trees, and that the mountains do not appear to shift at all. Why?__

* The amount of parallax depends on an object's distance, with larger  parallax for nearer objects.


* The amount of parallax depends on an object's size, with larger parallax for larger objects.


* The amount of parallax depends on an object's size, with larger parallax for smaller objects.
* The amount of parallax depends on an object's distance, with larger parallax for more distant objects.

* The amount of parallax depends on an object's distance, with larger  parallax for nearer objects.
* __Explanation__ 
* The farther away an object, the smaller its parallax. In the animation, the mountains are so far away that they do not have a noticeable parallax shift at all. The trees are farther away than the man, so they have a smaller parallax shift.

__Just as you found for parallax on Earth, stellar parallax is larger for stars that are nearer and smaller for stars that ar more distant. Which statement best summarizes why stellar parallax occurs? You may find it helpful to watch the animation of stellar parallax that begins at about 1:20 into the video.__ 

* We view nearby stars from different positions on Earth as Earth rotates on its axis.
* Nearby stars move in tiny circles as Earth orbits the Sun.
* We view nearby stars from different positions in Earth's orbit at different times of year.
* Nearby stars move at higher speeds relative to the Sun than more distant stars.

* We view nearby stars from different positions in Earth's orbit at different times of year.
* __Explanation__ 
* Stellar parallax works just like the parallax of the man and trees discussed in Parts A and B. Just as the man and trees appeared to move because the photographer moved, we see stellar parallax because we view stars from different positions in our orbit at different times of year. And just as the man had a larger parallax shift than the more distant trees and mountains, nearer stars have larger parallax shifts than more distant stars. 

__Observations of stellar parallax therfore provide direct evidence that:__

* Earth is smaller than the Sun
* stars move through space
* some stars are more distant than others
* Earth orbits the Sun

* some stars are more distant than others
* Earth orbits the Sun
* __Explanation__ 
* In other words, stellar parallax provides direct proof that Earth is not stationary at the center of the universe, but rather is a planet orbiting the Sun; if Earth did not move around the Sun, there would be no apparent shift in stellar positions. In addition, the fact that different stars have different amounts of parallax proves that stars lie at different distances from us.

__As you saw in Part D, stellar parallax exists only because Earth orbits the Sun. Therefore, if the ancient Greeks had measured stellar parallax, they would have known that their belief in an Earth-centered universe was wrong. Why didn't the ancient Greeks measure stellar parallax?__

* Their belief in an Earth-centered universe meant that they did not expect parallax, and therefore did not look for it.
* Even for the nearest stars, parallax angles are too small to measure with the naked eye.
* Some Greeks actually did measure it, but they did not understand the importance of their measurements.
* The Greeks thought all the stars were the same distance away, residing on a celestial sphere.

* Even for the nearest stars, parallax angles are too small to measure with the naked eye.
* __Explanation__ 
* The nearest stars (the three stars of the alpha Centauri system) are located a little over 4 light-years away. As discussed in the video, this gives them a parallax angle smaller than 1 arcsecond, which is far too small to detect with the naked eye. Because the ancient Greeks did not have telescopes, they could not measure stellar parallax.

__Based on their inability to detect stellar parallax, the ancient Greeks concluded that _________.__

* the stars must be extremely far away
* Earth must be the center of the universe
* either Earth is the center of the universe or stars are extremely far away
* they lacked the technology necessary for detecting stellar parallax

* either Earth is the center of the universe or stars are extremely far away
* __Explanation__ 
* The ancient Greeks were aware that either of these possibilities could be the correct answer. As discussed in the video and your textbook, most of them (with notable exceptions like Aristarchus) favored the first possibility — that Earth is the center of the universe — because it was difficult for them to believe that stars really could be so far away as to make stellar parallax undetectable to the eye.  

__As discussed in the video, parallax measurements allow us to calculate distances to stars for which parallax is detectable. Suppose you have a telescope capable of measuring parallax shifts of a particular amount (for example,  0.001 arcsecond). Which of the following locations for the telescope would allow you to measure distances to the most distant stars?__

* a telescope placed on the same orbit of the Sun as Earth, but on the opposite side of the Sun 
* a telescope on a clear mountaintop on Earth
* a telescope orbiting Earth
* a telescope on Mars
* a telescope on the Moon
* the location would not affect the maximum distance to which the telescope could detect parallax

* a telescope on Mars
* __Explation__ 
* As you can see in the parallax diagram in the video or your textbook, the base of the parallax triangle is the Earth-Sun distance, and making this baseline distance larger would increase the parallax angle to any star, making the angle easier to measure. Of the choices given, only locating the telescope on Mars would make this baseline distance larger. Therefore, the telescope on Mars would be able to measure parallax for more distant stars than it would in any of the other locations. 

__For most of the ancient Greek philosophers, the lack of observable stellar parallax was interpreted to mean that ________.__

* stars were too far away for parallax to be measured with available technology
* stars must all lie at the same distance from Earth on the celestial sphere
* Galileo's theories of the universe were essentially correct
* Earth is stationary at the center of the universe

* **Earth is stationary at the center of the universe**
* __**Explanation**__ 
* **The Greeks mistakenly took the lack of detectable parallax as evidence in favor of their Earth-centered model, rather than as evidence that the stars are really far away.**

__Galileo challenged the idea that objects in the heavens were "perfect" by ________.__

* proving Kepler's laws were correct
* inventing the telescope
* showing that heavy objects fall at the same rate as lighter objects
* observing sunspots on the Sun and mountains on the Moon

* observing sunspots on the Sun and mountains on the Moon
* __Explanation__ 
* Both the Sun and Moon had been generally assumed to have "perfect" surfaces.