Exam 2 ASTR 101

Two planets are observed going around a star. Planet Xoron has an orbital period that is twice as long as planet Krypton. Which planet has a shorter average orbital radius?

-planet krypton

A planet with twice Earth's mass orbiting at a distance of 1 AU A U from a star with the same mass as the Sun.

1 yr

A planet with the same mass as Earth orbiting at a distance of 1 AU A U from a star with four times the Sun's mass.

6 months

Which person is weightless?

A child in the air as she plays on a trampoline.

HW 6——-Why do the planets orbit the Sun (i.e. why don't they crash into the Sun)?

Although the planets experience a force of gravity from the Sun, since they are moving, their trajectories bend around the Sun rather than lead directly into the Sun.

How does its average distance compare to that of Pluto?

Eris orbits farther than Pluto.

Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. (Assume the spaceship has the same mass throughout the trip; that is, it is not burning any fuel.)

Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth.

If an astronomer claims to have discovered an object with a very eccentric orbit, which of the following best describes the orbital trajectory of the object?

It looks like a very squashed oval.

According to Kepler's third law:

Jupiter orbits the Sun at a faster speed than Saturn.

Each of the following diagrams shows a planet orbiting a star. Each diagram is labeled with the planet's mass (in Earth masses) and its average orbital distance (in AU). Assume that all four stars are identical. Use Kepler's third law to rank the planets from left to right based on their orbital periods, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

Kepler's third law tells us that the orbital period of the planet depends on its average distance from its star, but not on the planet's mass. As Newton later showed with his version of Kepler's third law, this is actually an approximation that works well whenever the planet's mass is small compared to the mass of the star.

In the Greek geocentric model, the retrograde motion of a planet occurs when:

The planet actually goes backward in its orbit around Earth.

Suppose you are in an elevator car when the elevator cable breaks. Which of the following correctly describes what happens and why.

You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate. Once the cable breaks, you and the elevator car both fall with the acceleration of gravity. This means you are no longer pressing against the scale or the elevator floor, so you float weightlessly within the car -- though only until you and the car hit the ground!

The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d=2 is twice as large as a distance of d=1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.

You have correctly taken into account both the masses of the asteroids and the distances between them.

What is its average distance (semimajor axis) from the Sun?

a = 67.7 AU

When would a new Venus be highest in the sky?

at noon (A new Venus occurs when Venus is directly between the Sun and Earth, which means a new Venus will be highest in the sky at the same time that the Sun is highest in the sky, which is around noon (local time))

Imagine that Venus is in its full phase today. If we could see it, at what time would the full Venus be highest in the sky?

at noon (Because Venus is full when it is on the opposite side of the Sun from Earth, the Sun and Venus both appear to move through the sky together at that time. Venus therefore rises with the Sun, reaches its highest point at noon, and sets with the Sun.

Tycho Brahe's contribution to astronomy included:

collecting data that enabled Kepler to discover the laws of planetary motion.

Consider the statement "There's no gravity in space." This statement is:

completely false

To make a rocket turn left, you need to:

fire an engine that shoots out gas to the right

Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.

greater than your normal weight at rest (Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.

As you learned in the video, Galileo's observations of Venus in gibbous (nearly full) phase showed conclusively that Venus orbits the Sun, not Earth. Which figure shows Venus's position when Galileo saw it in gibbous phase?

https://session.masteringastronomy.com/problemAsset/2257174/12/9280803031_a.jpg Notice that the gibbous phase occurs when Venus is farther from Earth than the Sun, and this could never happen in Ptolemy's system. That is how Galileo concluded that Venus must orbit the Sun.

When we say that a planet has a highly eccentric orbit, we mean that:

in some parts of its orbit it is much closer to the Sun than in other parts.

We never see a crescent Jupiter from Earth because Jupiter __________

is farther than Earth from the Sun. (An object must come between Earth and the Sun for us to see it in a crescent phase, which is why we see crescents only for Mercury, Venus, and the Moon.)

A planet is discovered orbiting the star 51 Peg with a period of four days (0.01 years). 51 Peg has the same mass as the Sun. Mercury's orbital period is 0.24 years, and Venus's is 0.62 years. The average orbital radius of this planet is

less than Mercury's.

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________. (Be sure to note that the video does not show a situation in which the elevator is slowing while moving upward, so you will need to decide which portion of the video is relevant to this situation; Hint 1 may be helpful.)

less than your normal weight at rest (Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward. The situation is rather like that of a ball that is still on its way up after you throw it: the ball slows as it goes upward because of the downward acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.

Galileo's contribution to astronomy included

making observations and conducting experiments that dispelled scientific objections to the Sun-centered model.

Compared to their values on Earth, on another planet your

mass would be the same but your weight would be different.

The Moon takes roughly 28 days to complete one orbit around the Earth. If the orbital radius of the Moon were twice its actual value, its orbital period would be

more than 56 days.

In Ptolemy's Earth-centered model, when would Venus appear directly behind the Sun as viewed from Earth?

never (In the Earth-centered model, Venus always remains somewhere between Earth and the Sun, and never appears behind the Sun in our sky)

When would you expect to see Venus high in the sky at midnight?

never (For Venus to be high in the sky at midnight, it would have to be on the opposite side of our sky from the Sun. But that never occurs, because Venus is closer than Earth to the Sun. )

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

***picture bebe!** 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 is the most eccentric?

*picture * 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 has the largest semimajor axis?

*picture* - 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.

Jupiter orbits the Sun at an average distance of 5.203 5.203 AU A U and takes 11.86years 11.86 y e a r s to complete each orbit. Based on these facts, which statement is true

11.86^2 = 5.203^3 Kepler's third law can be stated mathematically as p2=a3 p 2 = a 3 , where p is the planet's orbital period in years and a is its average orbital distance in AU A U .

The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.

According to Newton's second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on it by the object on the right. That is why the ranking here is the same as the ranking for Part A.

Each of the four diagrams below represents the orbit of the same comet, but each one shows the comet passing through a different segment of its orbit around the Sun. During each segment, a line drawn from the Sun to the comet sweeps out a triangular-shaped, shaded area. Assume that all the shaded regions have exactly the same area. Rank the segments of the comet's orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Although Kepler wrote his laws specifically to describe the orbits of the planets around the Sun, they apply more generally. Kepler's second law tells us that as an object moves around its orbit, it sweeps out equal areas in equal times. Because all the areas shown here are equal, the time it takes the comet to travel each segment must also be the same.

Which of the following orbits shows the planet at aphelion?

Aphelion is the point in a planet's orbit that is farthest from the Sun.

suppose two comets, comet A and comet B, were orbiting the sun, having the same average orbital radii. If comet A had a higher eccentricity than comet B, which comet would, during some portion of its orbit, have the highest orbital speed?

Comet A.

Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler's second law:

Earth travels faster in its orbit around the Sun in January than in July.

Consider again the diagrams from Parts A and B, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit based on the speed with which the comet moves when traveling from Point 1 to Point 2, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

From Parts A and B, you know that the comet takes the same time to cover each of the four segments shown, but that it travels greater distances in the segments that are closer to the Sun. Therefore, its speed must also be faster when it is closer to the Sun. In other words, the fact that that the comet sweeps out equal areas in equal times implies that its orbital speed is faster when it is nearer to the Sun and slower when it is farther away.

The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.

Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as the spaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity.

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 p 2 = a 3 . Which of the following statements describe a characteristic of the solar system that is explained by Kepler's third law?

Inner planets orbit the Sun at higher speed than outer planets. Venus orbits the Sun faster than Earth orbits the Sun. ( From the relationship p2=a3 p 2 = a 3 , 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.

Which of the following was not a major advantage of Copernicus's Sun-centered model over the Ptolemaic model?

It made significantly better predictions of planetary positions in our sky.

Each of the four diagrams below represents the orbit of the same asteroid, but each one shows it in a different position along its orbit of the Sun. Imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. Rank the positions based on the area that would be swept out by a line drawn between the Sun and the asteroid during the one-week period, from largest to smallest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Kepler's second law tells us that the asteroid will sweep out equal areas in equal time intervals. Therefore, the area swept out in any one week period must always be the same, regardless of the asteroid's location in its orbit around the Sun.

Consider again the diagrams from Part A, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Kepler's second law tells us that the comet sweeps out equal areas in equal times. Because the area triangle is shorter and squatter for the segments nearer to the Sun, the distance must be greater for these segments in order for all the areas to be the same.

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. (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.

The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.

Newton's third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be equal in magnitude, but opposite in direction to the gravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A.

The following diagrams all show the same star, but each shows a different planet orbiting the star. The diagrams are all scaled the same. (For example, you can think of the tick marks along the line that passes through the Sun and connects the nearest and farthest points in the orbit as representing distance in astronomical units (AU).) Rank the planets from left to right based on their average orbital distance from the star, from longest to shortest. (Distances are to scale, but planet and star sizes are not.)

Note that the line that passes through the star and connects the nearest and farthest points of the planet's orbit is called the major axis, and half this line is the semimajor axis — which we consider the planet's average distance from the star.

The following diagrams are the same as those from Part A. This time, rank the planets from left to right based on the amount of time it takes each to complete one orbit, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

Recall that the time it takes a planet to complete an orbit is called its orbital period. The pattern found in this Part illutrates one of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have longer orbital periods.

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?

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. 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.

As a comet orbits around the Sun, its maximum speed is twice its minimum speed. What can we say about its orbit?

The comet is twice as far from the Sun at aphelion as at perihelion

In Part A, you found that your weight will be greater than normal when the elevator is moving upward with increasing speed. For which of the following other motions would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed. (In a downward-moving elevator, the elevator can be slowing only if it has an upward acceleration. As you know from Part A, an upward acceleration will give you an increased weight. Therefore, in an elevator that moves downward while slowing in speed, the acceleration is upward and your weight is greater than normal.

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?

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

Based on the video, which Venus phase would be impossible to see (from Earth) if Venus orbited Earth as described in Ptolemy's Earth-centered model?

gibbous (nearly full) Phases that show more than a crescent are not possible in Ptolemy's Earth-centered model, so a gibbous or full Venus could never occur if Venus orbited Earth.

A car is accelerating when it is

going around a circular track at a steady 100 miles per hour.

If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be

one-quarter as strong.

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion

the Moon has a larger acceleration than Earth, because it has a smaller mass (Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.

When you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale (Your presence in an elevator cannot change either your mass or the gravitational force exerted on you by Earth. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to gravity and a force due to the elevator's acceleration.

Consider the hypothetical observation "a planet beyond Saturn rises in west, sets in east." This observation is not consistent with a Sun-centered model, because in this model

the rise and set of all objects depends only on Earth's rotation (Earth rotates from west to east, so objects in the sky must appear to go across our sky from east to west)

If Earth's orbit were very eccentric, but the average distance from the Sun were still 1 AU, its orbital period

would still be one year

The following five diagrams show pairs of astronomical objects that are all separated by the same distance d d . Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.

Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the same asteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right.

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?

Both areas are the same (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)

Consider again the diagrams from Parts D and E, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions (A-D) from left to right based on how fast the asteroid is moving at each position, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Just as you found for the comet in Parts A through C, the asteroid must be traveling at a higher speed during parts of its orbit in which it is closer to the Sun than during parts of its orbit in which it is farther away. You should now see the essence of Kepler's second law: Although the precise mathematical statement tells us that an object sweeps out equal areas in equal times, the key meaning lies in the idea that an object's orbital speed is faster when nearer to the Sun and slower when farther away. This idea explains why, for example, Earth moves faster in its orbit when it is near perihelion (its closest point to the Sun) in January than it does near aphelion (its farthest point from the Sun) in July.

Consider again the diagrams from Part D, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions from left to right based on the distance the asteroid will travel during a one-week period when passing through each location, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Notice the similarity between what you have found here and what you found for the comet in Part B. Kepler's second law tells us any object will sweep out equal areas in equal times as it orbits the Sun, which means the area triangles are shorter and squatter when the object is nearer to the Sun, so that the object covers a greater distance during any particular time period when it is closer to the Sun than when it is farther away.

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?

Pluto moves faster when it is closer to the Sun than when it is farther from the Sun. (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.

You discover an asteroid that orbits the Sun with the same 1-year orbital period as Earth. Which of the following statements must be true?

The asteroid's average (semimajor axis) distance from the Sun is 1AU (Kepler's third law tells us that an object's average orbital distance can be calculated from its orbital period using the formula p2=a3 p 2 = a 3 (where p is the planet's orbital period in years and a is its average orbital distance in AU A U ). Therefore, all objects that share Earth's orbital period of 1 year must also share Earth's average orbital distance of 1A)

Why did the Greeks conclude that the Earth was stationary, and that the Sun and the planets orbited around the Earth?

They did not observe any change in the separation of stars during Earth's orbit.

The following diagrams are the same as those from Parts A and B. This time, rank the planets from left to right based on their average orbital speed, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality. (Distances are to scale, but planet and star sizes are not.)

This pattern illustrates another of the ideas that are part of Kepler's third law: Planets with larger average orbital distances have slower average speeds.

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. (Kepler's third law can be stated as the precise mathematical relationship p2=a3 p 2 = a 3 ; (where p is the planet's orbital period in years and a is its average orbital distance in AU A U ). 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.)

Which of the following can you observe about Venus with the naked eye? Select all that apply.

Venus sometimes shines brightly in the eastern sky shortly before dawn Venus sometimes shines brightly in the western sky shortly after sunset (Venus always remains close to the Sun in our sky. Therefore, when it is visible, it is either in the evening sky for up to a few hours after sunset or in the morning sky for up to a few hours before dawn.)

In Ptolemy's Earth-centered model for the solar system, Venus always stays close to the Sun in the sky and, because it always stays between Earth and the Sun, its phases range only between new and crescent. The following statements are all true and were all observed by Galileo. Which one provides evidence that Venus orbits the Sun and not Earth?

We sometimes see gibbous (nearly but not quite full) Venus. (In the Ptolemaic system, we should never see more than a crescent for Venus. Because we do in fact see more, the Ptolemaic model must be wrong. The full range of phases that we see for Venus is consistent only with the idea that Venus orbits the Sun. Galileo was the first to observe the phases of Venus — and hence to find this evidence in support of the Sun-centered system — because he was the first to observe Venus through a telescope. Without a telescope, we cannot tell that Venus goes through phases.)

In Ptolemy's Earth-centered model for the solar system, Venus's phase is never full as viewed from Earth because it always lies between Earth and the Sun. In reality, as Galileo first recognized, Venus is __________.

full whenever it is on the opposite side of the Sun from Earth (A full Venus always occurs when it is on the opposite side of the Sun as viewed from Earth. Galileo used this fact as evidence for the Sun-centered view of the solar system: The fact that Venus goes through all the phases must mean it goes all the way around the Sun. In contrast, in the Ptolemaic model, Venus only varies between new and crescent phases.)