Module 15: Newton's Laws of Gravity and Orbits

No, orbiting every 24 hours only happens at one specific orbital distance.

A communications company requests that their satellite be placed 100,000 meters above the Earth's surface and then launched so that it moves in a geosynchronous orbit (meaning an orbit that takes exactly 24 hours to complete). Is this possible?

About 2.8 times as long

According to Kepler's third law of planetary motion, if the Earth's orbit was twice as large as it is, how long would it take for the Earth to go around the Sun once?

(rA + d + rB)^2

Consider the two spheres, A and B, placed near each other. Each sphere has its own radius and the surfaces of the spheres are a distance d apart, as shown. If you are calculating the gravitational attraction between spheres A and B, what quantity would go in the denominator of Newton's law of universal gravitation?

Less than 27.3 days.

Currently, the Moon takes 27.3 days to go around the Earth. Suppose a supervillain shifted the Moon into a new, lower, circular orbit. How long would it take for the Moon to go around the Earth in its new circular orbit?

Roughly 12 m/s2

Exoplanets (planets outside our solar system) are an active area of modern research. Suppose astronomers find such a planet that has the same mass as Earth, but has a radius that is about 10% less. Roughly, what acceleration due to gravity would you expect if you were standing on the surface of this new planet?

Roughly 9 m/s2

Exoplanets (planets outside our solar system) are an active area of modern research. Suppose astronomers find such a planet that has the same radius as Earth, but is about 10% less massive. Roughly, what acceleration due to gravity would you expect if you were standing on the surface of this new planet?

This is not possible, since it would violate Kepler's third law of planetary motion.

Exoplanets (planets outside our solar system) are an active area of modern research. Suppose you read an article stating that there is a newly discovered planetary system with three planets. The article states that the outermost planet (Planet C) goes all the way around its star in less time than the innermost planet (Planet A). According to Kepler's laws of planetary motion, is this possible?

The orbit is shaped like an ellipse.

If a planet is orbiting a star, what is the most accurate way to describe the shape of the orbit?

The Earth is big enough and close enough to cause a noticeable effect.

If every object is attracted to every other object in the universe via gravity, why is it that you feel only one force of gravity on a day-to-day basis (the one from Earth)?

The people walking past you do exert a gravitational force on you, but it is far too small to physically sense.

If gravity attracts every object in the universe to every other object in the universe, why don't you feel a gravitational pull on you from other people as you walk past them?

Yes, this is about the rock's mass, which is the same on the Moon as on the Earth.

If you kick a big rock very hard while on the Earth, you might break a toe. If you kicked a similar rock while on the Moon, would you still be in danger of breaking your toe?

it moves with a higher speed during some parts of its orbit and a slower speed during other parts.

In general, when a planet orbits a star, ______.

The Sun is at one focus of the ellipse, with nothing at the other focus.

Kepler's first law of planetary motion tells us that planets move in ellipses. If we picture the elliptical orbit of a planet orbiting the Sun, where does the Sun fit into the picture?

planets move faster when they are near the Sun, and move more slowly when they are farther away.

Kepler's second law of planetary motion describes the area "swept out" by the line connecting a planet and the Sun during equal time intervals. The conceptual message of the law is that ______.

A planet's orbital period and the size of the planet's orbit are related.

Kepler's third law of planetary motion states that which two quantities are related?

The height of a tall mountain is a tiny amount when compared to the radius of the Earth. So even going to the top of a tall mountain barely changes your distance to the center of the Earth.

Newton's law of universal gravitation states that the force of gravity between you and the Earth gets smaller when you get further away from the center of the Earth. Why is it that we use the same acceleration due to gravity (g = 9.8 m/s2) for all physics problems without paying attention to whether the problem takes place at sea level or at the top of a tall mountain?

The magnitude of the net force on each object is the same.

Objects A and B are near each other in space and isolated from all other influences. Object A has a mass of 6m while object B has a mass of 2m. How does the magnitude of the net force on each object compare?

The magnitude of the force you exert on the Moon is equal to F(moon).

On a clear night you look up at the Moon overhead. At that moment the Moon is pulling on you via gravity with a certain amount of force, F(moon). Considering only magnitudes, how does the force you exert on the Moon via gravity compare to F(moon)?

The empty toolbox has a much smaller mass, so it is much easier to move it around.

Suppose you are floating in deep space (in a space suit). You grab onto two identical toolboxes, one of which is full of metal tools and the other of which is empty. As you shake the two tool boxes around by their handles, which is the correct statement about what you would notice?

Mass and weight have different units.

Which of the following is an important difference between an object's mass and its weight?

Weight is determined by the environment of an object, while mass is a fixed property of the object.

Which of the following is an important difference between an object's mass and its weight?

is proportional to the mass of the Sun.

The force exerted by our Sun on the planets in our solar system ______.

2F

The force of gravity between object A and B is F. If the mass of object A was twice as large as it is, but if everything else was kept the same, what would be the new force of gravity between objects A and B?

1/2 F

The force of gravity on object A by object B is F. If the mass of object B was only half as large as it is, but everything else was kept the same, what would be the new force of gravity on object B by object A?

1/9F

The force of gravity on object B by object A is F. If the distance between the objects was tripled, but everything else was kept the same, what would be the new force of gravity on object B by object A?