Astronomy Exam #2

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 rapidly.

If we say that a material is opaque to ultraviolet light, we mean that it _________.

Absorbs ultraviolet light.

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.

The following five diagrams show pairs of astronomical objects that are all separated by the same distance 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.

According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass?

Earth's orbit would not change.

The animation 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 drawing the cloud inward __________ because __________.

Gradually becomes stronger because the strength of law 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—which 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 an interstellar gas cloud shrinks in size, its gravitational potential energy:

Gradually transforms into other types of energy.

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.

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.

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.

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.

The spectra of most galaxies show redshifts. This means that their spectral lines _________.

Have wavelengths that are longer than usual.

Blue light has higher frequency than red light. Thus, blue light has:

Higher energy and shorter wavelength.

As the cloud shrinks in size, its central temperature __________ as a result of __________.

Increases because of 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.)

Which forms of light are lower in energy and frequency than the light that our eyes can see?

Infrared and radio.

Why is Newton's version of Kepler's third law so useful to astronomers?

It can be used to determine the masses of many distant objects.

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 end up on an orbit that is farther from the Sun.

Suppose you know the frequency of a photon and the speed of light. What else can you determine about the photon?

Its wavelength and energy.

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 __________.

Less than your normal weight at rest.

The Moon orbits Earth in an average time of 27.3 days at an average distance of 384,000 kilometers. Use these facts to determine the mass of Earth. (Hint: You may neglect the mass of the Moon, since its mass is only about 180 of Earth's.)

MEarth = 6.0×1024 kg

Jupiter's moon Io orbits Jupiter every 42.5 hours at an average distance of 422,000 kilometers from the center of Jupiter. Calculate the mass of Jupiter. (Hint: Io's mass is very small compared to Jupiter's.)

MJupiter = 1.9×1027 kg

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.

As the cloud shrinks in size, its rate of rotation __________ because __________.

Speeds up, because 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.)

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 the Earth, because it has a smaller mass.

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?

The elevator moves downwards while decreasing in speed.

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

The force you exert on the scale.

Compared to its angular momentum when it is farthest from the Sun, Earth's angular momentum when it is nearest to the Sun is:

The same.

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.

According to the universal law of gravitation, if you triple the distance between two objects, than the gravitational force between them...

decreases by a factor of 9.

If the Moon were closer to Earth...

high tides would be higher than they are.

When a spinning ice skater pulls in his arms, he spins faster because...

his angular momentum must be conserved, so reducing his radius must increase his speed of rotation

Compared to an atom as a whole, an atomic nucleus:

is very tiny, but has most of the mass.

Thermal radiation is defined as _________.

radiation with a spectrum whose shape depends only on the temperature of the emitting object

You discover a planet orbiting a distant star that has about the same mass as the Sun. Your observations show that the planet orbits the star every 59 days. What is its orbital distance?

rplanet = 4.4×1010 m

The circles in the diagrams below represent energy levels in an atom, and the arrows show electron (blue dot) transitions from one energy level to another. (The spacing between circles represents differences in energy: A larger spacing means a greater difference in energy.) Assuming that the transitions occur as photons are emitted, rank the atoms based on the photon energy, from highest to lowest.

the emitted photon must have exactly the same amount of energy that the electron loses in moving from the higher to the lower energy level. Therefore the ranking of the photon energies must be in the same order as the amounts of energy lost by the electrons, and longer arrows mean greater changes in energy.