AP Physics Test: Circular Motion And Gravitation! Trivia Quiz

1. How would the speed of Earth's orbit around the sun change if Earth's distance from the sun increased by 4 times?

It would increase by a factor of 2.

It would increase by a factor of 4.

It would decrease by a factor of 2.

The speed would not change.

If Earth's distance from the sun increased by 4 times, the speed of Earth's orbit around the sun would decrease. This is because according to Kepler's laws of planetary motion, the speed of a planet in its orbit is inversely proportional to its distance from the sun. Therefore, if the distance increases by a factor of 4, the speed would decrease by a factor of 2.

Explanation

If Earth's distance from the sun increased by 4 times, the speed of Earth's orbit around the sun would decrease. This is because according to Kepler's laws of planetary motion, the speed of a planet in its orbit is inversely proportional to its distance from the sun. Therefore, if the distance increases by a factor of 4, the speed would decrease by a factor of 2.

2. In the figure above, according to Kepler's laws of planetary motion,

A1 = A2.

Delta t1 > delta t2.

If delta t1 = delta t2, then the orbit is circular

If delta t1 = delta t2, then A1 = A2.

According to Kepler's laws of planetary motion, the area swept out by a planet in a given time is equal for equal time intervals. This means that if delta t1 (the time taken for planet 1 to sweep out an area) is equal to delta t2 (the time taken for planet 2 to sweep out an area), then the areas A1 and A2 swept out by the two planets will also be equal. Therefore, the correct answer is "if delta t1 = delta t2, then A1 = A2."

Explanation

According to Kepler's laws of planetary motion, the area swept out by a planet in a given time is equal for equal time intervals. This means that if delta t1 (the time taken for planet 1 to sweep out an area) is equal to delta t2 (the time taken for planet 2 to sweep out an area), then the areas A1 and A2 swept out by the two planets will also be equal. Therefore, the correct answer is "if delta t1 = delta t2, then A1 = A2."

3. The equation for the speed of an object in circular orbit is to the left. What does m represent in this equation?

The mass of the sun

The mass of Earth

The mass of the central object

The mass of the orbiting object

The variable "m" in the equation represents the mass of the central object. This means that the speed of an object in a circular orbit is dependent on the mass of the central object.

Explanation

The variable "m" in the equation represents the mass of the central object. This means that the speed of an object in a circular orbit is dependent on the mass of the central object.

4. The law of planetary motion that relates the speed of a planet to its position in its orbit about the Sun is:

Kepler's first law

Kepler's third law

The Law of Equal Areas

The Law of Inertia

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun. This means that the farther a planet is from the Sun, the longer it takes to complete one orbit. This law helps to explain the relationship between a planet's speed and its position in its orbit, as the speed of a planet will vary depending on its distance from the Sun. Therefore, Kepler's third law is the correct answer to the question.

Explanation

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun. This means that the farther a planet is from the Sun, the longer it takes to complete one orbit. This law helps to explain the relationship between a planet's speed and its position in its orbit, as the speed of a planet will vary depending on its distance from the Sun. Therefore, Kepler's third law is the correct answer to the question.

5. How would the speed of Earth's orbit around the sun change if Earth's mass increased by 4 times?

It would increase by a factor of 2.

It would increase by a factor of 4.

It would decrease by a factor of 2.

The speed would not change.

If Earth's mass increased by 4 times, according to the law of conservation of angular momentum, the product of the mass and velocity must remain constant. Since the mass has increased, the velocity must decrease in order to maintain the same angular momentum. Therefore, the speed of Earth's orbit around the sun would decrease by a factor of 2.

Explanation

If Earth's mass increased by 4 times, according to the law of conservation of angular momentum, the product of the mass and velocity must remain constant. Since the mass has increased, the velocity must decrease in order to maintain the same angular momentum. Therefore, the speed of Earth's orbit around the sun would decrease by a factor of 2.