Mastering Astronomy: Motion & Gravity

If the Sun were to shrink, its angular momentum would __________. decrease stay the same increase

stay the same

As an object shrinks in size, its mass __________. (Assume the object is not ejecting any mass and that no mass is coming in from beyond the object.) decreases increases stays the same

stays the same

There is no gravity in space. True or False?

False

Radiative energy is __________. energy that depends on an object's radius dangerous energy energy carried by light

energy carried by light

The orbital energy of an asteroid orbiting the Sun is the sum of its _________. gravitational potential energy and kinetic energy gravitational potential energy and radiative energy kinetic energy and thermal energy

gravitational potential energy and kinetic energy

As an object heats up, its thermal energy __________. increases decreases stays constant

increases

As the cloud shrinks in size, its rate of rotation __________ because __________. (Blank 1) slows down (Blank 1) speeds up (Blank 1) stays constant at all times (Blank 2) the force of gravity strengthens as the cloud shrinks (Blank 2) its total energy is conserved (Blank 2) its total angular momentum is conserved

(Blank 1) speeds up (Blank 2) its total angular momentum is conserved (Total angular momentum is always conserved. In this case, because nothing is carrying angular momentum into or out of the cloud, the cloud's angular momentum stays constant. Maintaining constant angular momentum as the cloud shrinks requires that its rate of rotation increase because angular momentum depends on the product of rotation rate and radius.)

Doubling the distance between two objects halves the gravitational force between them. True or False?

False

Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid? It will stay on its original orbit. It will end up on an orbit that is farther from the Sun. It will also end up on an orbit that is closer to the Sun. It will become much cooler.

It will end up on an orbit that is farther from the Sun. (Total energy must be conserved, so if one asteroid loses energy and moves to a closer orbit, the other must gain energy and move to a more distant orbit.)

According to Kepler's third law: Mercury travels fastest in the part of its orbit in which it is closest to the Sun. Jupiter orbits the Sun at a faster speed than Saturn. All the planets have nearly circular orbits.

Jupiter orbits the Sun at a faster speed than Saturn.

Which of the following examples describes a situation where a car is experiencing a net force? The car is moving at constant speed. The car is making a gradual turn. The car is floating on a stationary boat. The car is stopped on a hill.

The car is making a gradual turn.

The law of conservation of angular momentum

The law of conservation of angular momentum states that, in the absence of external influences (torques), the angular momentum of an object or a system of objects stays constant. For example, once the ice skater pushes off with her foot to start her spin, there are no more external influences on her spin rate (except for friction with the ice, which is small enough for us to ignore), so her angular momentum stays constant. Recall that an object's angular momentum depends both on its size (radius) and rotation rate. Therefore, to keep her angular momentum constant, the skater must spin faster when she pulls in her arms (decreasing her radius) and slower when she puts her arms back out.

Which of the following statements is NOT one of Newton's Laws of Motion? For any force, there always is an equal and opposite reaction force. What goes up must come down. The rate of change of momentum of an object is equal to the net force applied to the object. In the absence of a net force acting upon it, an object moves with constant velocity.

What goes up must come down.

The planets never travel in a straight line as they orbit the Sun. According to Newton's second law of motion, this must mean that ________. the planets are always accelerating the planets will eventually fall into the Sun a force is acting on the planets the planets have angular momentum

a force is acting on the planets

We say that the force of gravity follows an inverse square law with distance. This means that the force attracting two objects _________ as two objects come closer together. changes direction becomes stronger becomes weaker

becomes stronger

For the situations shown, the two objects we are concerned with are the Moon and the spaceship, which both have constant masses. Therefore, the strength of gravity between them __________. increases with the square of their distance apart increases in direct proportion to their distance apart decreases with the square of their distance apart decreases in direct proportion to their distance apart

decreases with the square of their distance apart

Which of the following represents a case in which you are not accelerating? driving in a straight line at 60 miles per hour driving 60 miles per hour around a curve going from 0 to 60 miles per hour in 10 seconds slamming on the brakes to come to a stop at a stop sign

driving in a straight line at 60 miles per hour

A net force acting on an object will always cause a change in the object's ________. mass momentum speed direction

momentum

An object's angular momentum depends on its mass and its __________. rotation rate only size (radius) and rotation rate size (radius) only

size (radius) and rotation rate

The video shows a spinning ice skater pulling in her arms at the same time that it shows a spinning gas cloud shrinking in size. The relevance of the skater to the cloud comes from the fact that __________. the same law explains the change in both of their spin rates the low temperature of the gas cloud is similar to the low temperature of the ice their spins are both governed primarily by the law of gravity

the same law explains the change in both of their spin rates

When we say that a quantity is conserved, we mean that its value does not change. Which of the following are examples of quantities that are conserved for a system of objects? Check all that apply. total gravity total angular momentum total momentum total energy

total angular momentum total momentum total energy

The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity draws the cloud inward __________ because __________. (Blank 1) gradually becomes stronger (Blank 1) gradually becomes weaker (Blank 1) stays constant at all times (Blank 2) the strength of gravity follows an inverse square law with distance (Blank 2) the mass of the cloud increases as it collapses (Blank 2) the total gravitational force is a conserved quantity

(Blank 1) gradually becomes stronger (Blank 2) the strength of gravity follows an inverse square law with distance The force of gravity between any two particles increases as the particles come closer together. Therefore, as the cloud shrinks and particles move closer together, the force of gravity strengthens. This will tend to accelerate the collapse as long as no other force resists it. This is the case during the early stages of the collapse before the internal gas pressure builds up. (Once the gas pressure builds up, the outward push of the pressure can counteract the inward pull of gravity, which is why the cloud eventually stops contracting.)

As the cloud shrinks in size, its central temperature __________ as a result of its __________. (Blank 1) stays constant (Blank 1) decreases (Blank 1) increases (Blank 2) gravitational potential energy being converted to thermal energy (Blank 2) kinetic energy being converted to radiative energy (Blank 2) thermal energy being converted to radiative energy

(Blank 1) increases (Blank 2) gravitational potential energy being converted to thermal energy (As the cloud shrinks in size, its gravitational potential energy decreases. Because energy cannot simply disappear, the "lost" gravitational potential energy must be converted into some other form. Some of it is converted into thermal energy, which raises the temperature of the gas cloud. The rest is mostly converted into radiative energy, which is released into space as light.)

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. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). 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.

(Strongest force) Spaceship closest to earth | | | Spaceship closest to the Moon (Weakest force) (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.)

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.

(Strongest force) Spaceship closest to the Moon | | | Spaceship closest to Earth (Weakest force) (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.)

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.

(Strongest force) [d=1, M=2, M=2] [d=1, M=1, M=2] [d=1, M=1, M=1] [d=1, M=1, M=2] [d=2, M=1, M=1] (Weakest force)

Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result? •A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more slowly. •A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. •Both the total amount of energy and the rotation rate would remain the same. •The Sun would gain more energy and more angular momentum.

A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. (The dramatic shrinkage of the Sun would mean the loss of a huge amount of gravitational potential energy. Because energy is always conserved, this "lost" gravitational potential energy must reappear in other forms, such as heat (thermal energy) and light (radiative energy). Meanwhile, conservation of angular momentum would ensure that the collapsed Sun would spin much faster.)

If the Sun were to shrink in size, its gravitational potential energy would __________. stay the same decrease increase

decrease

As a gas cloud collapses, shrinking in size, its total gravitational potential energy __________. increases stays constant decreases

decreases

For the situations shown, the two objects we are concerned with are Earth and the spaceship, which both have constant masses. Therefore, the strength of gravity between them: __________. increases with the square of their distance apart increases in direct proportion to their distance apart decreases with the square of their distance apart decreases in direct proportion to their distance apart

decreases with the square of their distance apart

To calculate the gravitational force between two objects we __________, and then multiply by the gravitational constant G. add the two masses together, divide by their distance multiply the two masses together, divide by their distance square the two masses, divide by their distance add the two masses together, divide by their distance squared multiply the two masses, divide by their distance squared

multiply the two masses, divide by their distance squared