HW 4 CHP 3, 4 (AS 101)

C) You are driving along the highway at a speed of 60 miles per hour when you slam on the brakes. If your acceleration is at an average rate of -10 miles per hour per second, how long will it take to come to a stop?

t stop = 6 sec

E) 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.

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

more than 56 days.

J) Galileo challenged the idea that objects in the heavens were perfect by _________.

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

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

one-quarter as strong.

C) 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.

3.49) A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 126 million kilometers. Its orbital eccentricity is 0.1. A) Find the planet's orbital period.

9.28 months

Which of the cars is accelerating?

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

Which person is weightless?

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

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.

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.

According to Kepler's third law:

Jupiter orbits the Sun at a faster speed than Saturn.

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

The planet actually goes backward in its orbit around Earth.

D) How did the Ptolemaic model explain the apparent retrograde motion of the planets?

The planets moved along small circles that moved on larger circles around the Earth. This created a "loop-the-loop" motion that made the planets in the model appear to sometimes go backward as viewed from Earth.

B) Find the planet's nearest orbital distance from its star.

.76 AU

C) Find the planet's farthest orbital distance from its star.

.93 AU

I) Suppose a comet orbits the Sun on a highly eccentric orbit with an average (semimajor axis) distance of 1 AU. How long does it take to complete each orbit, and how do we know?

1 year, which we know from Kepler's third law Kepler's third law tells us that any object with the same average distance as Earth will orbit in the same time of 1 year.

3.47 A) Find the perihelion distance of Mars. Hint: You'll need data from the table below.

1.382 AU Perihelion is point closest to sun

B) Find the aphelion distance of Mars.

1.666 AU Aphelion is point farthest from sun

H) All the following statements are true. Which one follows directly from Kepler's third law (p^2 = a^3)?

Venus orbits the Sun at a slower average speed than Mercury. Kepler's third law tells us that orbital speed declines with distance, so Venus must orbit the Sun at a slower speed than Mercury.

P) Imagine for a moment that despite all the evidence, Earth actually is not rotating and orbiting the Sun. Which of these hypothetical observations (none of them are real) would be inconsistent with our Sun-centered view of the solar system?

We discover a small planet beyond Saturn that rises in the west and sets in the east each day. If Earth is rotating from west-to-east, then all celestial objects must move from east to west across our sky. (The only exception is satellites in low-Earth orbit, where they orbit faster than Earth rotates.) So a planet going in the opposite direction across the sky would pose a direct challenge to our view of Earth as a rotating planet.

F) Earth is farthest from the Sun in July and closest to the Sun in January. During which Northern Hemisphere season is Earth moving fastest in its orbit?

Winter Kepler's second law tells us that planets move fastest when they are nearest to the Sun. Since this in January for Earth, it is Northern Hemisphere winter.

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.

D) 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.

D) Which of the following statements correctly state general principles of motion? (Assume that the moving object's mass is not changing.)

-Accelerated motion includes any motion involving a change in speed, change in direction, or both. -An object that is accelerating is also undergoing a change in momentum. -An object that is accelerating is also being acted upon by a (nonzero) net force. As long as an object's mass is not changing, a net force will cause an object to undergo some type of acceleration. Because acceleration is a change in velocity, and momentum is mass times velocity, the accelerating object is also undergoing a change in momentum.

G) According to Kepler's third law (p^2 = a^3), how does a planet's mass affect its orbit around the Sun?

A planet's mass has no effect on its orbit around the Sun. Kepler's third law makes no allowance for planetary mass, and in fact the planet's mass has virtually no effect on its orbit of the Sun. (The Sun's mass has a major effect, however.)

M) Which of the following is not part of a good scientific theory?

A scientific theory cannot be accepted until it has been proven true beyond all doubt. Scientific theories can never be proven true beyond all doubt; they can only be supported by a wide body of evidence.

Concept Quiz A) Suppose the planet Uranus were much brighter in the sky, so that it was as easily visible to the naked eye as Jupiter or Saturn. Which one of the following statements would most likely be true in that case?

A week would have eight days instead of seven. A week has seven days because seven naked-eye objects appear to move among the stars: the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn. If Uranus had been an eighth object visibly moving among the stars, a week very likely would have eight days.

To understand the meaning of these key terms of motion: acceleration, momentum change, and net force. First, launch the video below. Then, close the video window and answer the questions at right. You can watch the video again at any point. A) Drag each statement into the correct bin based on whether it describes motion that involves acceleration or motion at constant velocity. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth's rotation or orbit.

Acceleration -a planet is orbiting the Sun in an elliptical orbit -a car is holding a steady speed around a curve -a planet is orbiting the Sun in a circular orbit -a car is speeding up after being stopped -a car is slowing down for a stop sign -a ball is in freefall after being dropped from a high window Constant Velocity -an elevator is going upward at constant speed -a car is driving 100 km/hr on a straight road -a spaceship is coasting without engine power in deep space Acceleration refers to any change in velocity. Because velocity includes both speed and direction, acceleration is occurring whenever there is any change in speed, direction, or both. Constant velocity means that both speed and direction are unchanging.

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.

All same 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.

D) 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.

All same 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.

This tutorial will help you understand the shape, speed, and period of a planet's orbit in terms of Kepler's Laws. Launch the Orbits and Kepler's Laws tutorial. Answer the ungraded questions in the tutorial and the graded follow-up questions below. A) 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.

B) Drag each statement into the correct bin based on whether it describes motion in which the object's momentum is changing. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth's rotation or orbit.

Change in Momentum -a car is holding a steady speed around a curve -a car is speeding up after being stopped -a car is slowing down for a stop sign -a ball is in freefall after being dropped from a high window -a planet is orbiting the Sun in a circular orbit -a planet is orbiting the Sun in an elliptical orbit Constant Momentum -an elevator is going upward at constant speed -a car is driving 100 km/hr on a straight road -a spaceship is coasting without engine power in deep space Momentum is defined as mass times velocity, so if an object's velocity is changing (that is, if it is accelerating), then its momentum must also be changing.

C) 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

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

Completely false.

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

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

B) Consider again the set of observations from Part A. This time, classify each observation according to whether it is consistent with only the Earth-centered model, only the Sun-centered model, both models, or neither model. (Note that an observation is "consistent" with a model if that model offers a simple explanation for the observation.)

Earth-centered only -a planet beyond Saturn rises in west, sets in east Sun-centered only -Mercury goes through a full cycle of phases -positions of nearby stars shift slightly back and forth each year Both models -a distant galaxy rises in east, sets in west each day -stars circle daily around north or south celestial pole -Moon rises in east, sets in west Neither model -we sometimes see a crescent Jupiter

N) Only one of the statements below uses the term theory in its correct, scientific sense. Which one?

Einstein's theory of relativity has been tested and verified thousands of times.

3.48) The recently discovered Eris, which is slightly larger than Pluto, orbits the Sun every 560 years. A) What is its average distance (semimajor axis) from the Sun?

Eris's semimajor axis= 67.9 AU

C) 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.)

Fastest -Smallest circle -Small oval -Small circle -Long oval -Big circle 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.

F) 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.

Fastest -below sun -lower right -upper left -above sun Slowest 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.

C) 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.

Fastest -side left 2,1 -lower right 2,1 -upper right 1,2 -side right 1,2 Slowest 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.

B) How does a 12-month lunar calendar differ from our 12-month solar calendar?

It has about 11 fewer days. This is true because the lunar cycle averages about 29.5 days, so 12 of these cycles makes about 354 days, or 11 days short of our 365-day solar year.

B) 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.

D) 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.)

Longest -2 AU One Earth Mass -? -One Earth Mass 1AU -? Shortest - 2AU: One Earth Mass & Three Earth Mass - 1AU: One Earth Mass & Two Earth Mass 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 whenver the planet's mass is small compared to the mass of the star.

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.)

Longest -Big circle -Long oval -Small circle -Small oval -Smallest circle Shortest 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.

B) 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.)

Longest -Big circle -Long oval -Small circle -Small oval -Smallest circle Shortest 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.

E) 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.

Longest -below sun -lower right -upper left -above sun Shortest 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.

B) 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.

Longest -side left 2,1 -lower right 2,1 -upper right 1,2 -side right 1,2 Shortest 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.

C) Drag each statement into the correct bin based on whether the motion requires the action of a net force. Note: For the motions that are on Earth (e.g., car, ball, elevator), ignore any effects of Earth's rotation or orbit.

Net Force (nonzero) -a car is holding a steady speed around a curve -a car is speeding up after being stopped -a car is slowing down for a stop sign -a ball is in freefall after being dropped from a high window -a planet is orbiting the Sun in a circular orbit -a planet is orbiting the Sun in an elliptical orbit No Net Force -an elevator is going upward at constant speed -a car is driving 100 km/hr on a straight road -a spaceship is coasting without engine power in deep space The only way to change an object's momentum is to apply a net force to it, so if an object's momentum is changing, then a net force must be acting upon it. For example, in the case of the planets orbiting the Sun, the net force is from gravity. In the case of the accelerating cars, the net force is from the engine.

K) Galileo observed all of the following. Which observation offered direct proof of a planet orbiting the Sun?

Phases of Venus Galileo's observed that Venus goes through all the phases, which cannot be explained unless Venus is orbiting the Sun. (In the Ptolemaic system, Venus's phases vary only from new to crescent and back.)

D) 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

B) How does its average distance compare to that of Pluto? (Pluto's orbital period is 248 years)

Pluto's semimajor axis= 39.5 AU

A) Consider the following observations. Classify each observation based on whether it is a real observation (a true statement of something we can actually see from Earth) or one that is not real (a statement of something that does not really occur as seen from Earth).

Real (true statements) -stars circle daily around north or south celestial pole -Moon rises in east, sets in west -positions of nearby stars shift slightly back and forth each year -a distant galaxy rises in east, sets in west each day -Mercury goes through a full cycle of phases Not real (false statements) -we sometimes see a crescent Jupiter -a planet beyond Saturn rises in west, sets in east

Which of the following is not true about scientific progress?

Science advances only through the scientific method.

L) Which of the following is not consistent with the major hallmarks of science?

Science consists of proven theories that are understood to be true explanations of reality.

C) Which of the following best describes a set of conditions under which archaeoastronomers would conclude that an ancient structure was used for astronomical purposes?

The structure has holes in the ceiling that allow viewing the passage of constellations that figure prominently in the culture's folklore, and many other structures built by the same culture have ceiling holes placed in the same way. In fact, this answer describes the evidence for Pawnee lodges, as described in Section 3.1 of The Cosmic Perspective.

4.42 A) If you drop a rock from a very tall building, how fast will it be going after 2 seconds?

V rock = 20 m/s

B) As you sled down a steep, slick street, you accelerate at a rate of 5 meters per second squared. How fast will you be going after 7 seconds?

V sled = 35 m/s

3.45) You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 79 ∘. What is the circumference of Nearth?

circumference of Nearth = 4.9×10^4 km

O) The astrology practiced by those who cast predictive horoscopes can be tested by __________

comparing how often the predictions come true to what would be expected by pure chance. And in such tests, astrological predictions have never proven to be more successful than is expected by chance.

F) 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.

Compared to their values on Earth, on another planet

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