7.2.3 Energy in Orbital Motion

Question 1

Energy in Orbital Motion

Answer 1

• In addition to Newton’s laws, conservation of energy can be used to understand orbital motion.
• By applying conservation of energy to an object in circular orbit, you can relate its total energy to its radius, r, and its velocity, v: and .
• For objects in a circular orbit the relationships between gravitational potential energy, U, kinetic energy, K, and total energy,, are simple and elegant: and

Question 2

Which of the following best describes the energy of a satellite in uniform circular orbit around the Earth when it moves to a higher orbit?

Answer 2

There is an increase in potential energy and a decrease in kinetic energy.

Question 3

The total energy of an orbiting satellite in uniform circular orbit around the Earth ________________.

Answer 3

approaches to zero as r approaches infinity

Question 4

A satellite is in uniform circular motion around the Earth, which has a mass of M e. The distance from the center of the Earth to the satellite is r. Which of the following is not correct?

Answer 4

A satellite is put into orbit by giving it a tangential speed sufficient to maintain it at a particular orbit; the higher the orbit, the greater the tangential speed.

Question 5

A spacecraft is in circular orbit about the Earth when a braking force is applied to the spacecraft. Because the force and displacement are in opposite directions, the spacecraft loses some energy and the total energy of the spacecraft is reduced. Which of the following statements concerning velocity, kinetic energy, and potential energy is true?

Answer 5

The velocity increases, the potential energy decreases, and the kinetic energy increases.

Question 6

A satellite of mass m is in circular orbital motion around the Earth, which has mass Me. The distance from the center of the Earth to the satellite is r. Which of the following is the equation for tangential velocity of the satellite?

Answer 6

v = (GMe/r)^1/2

Question 7

Consider a satellite of mass m in circular orbital motion around the Earth. The distance from the center of the Earth to the satellite is r and the mass of the Earth is Me. Which of the following is an incorrect equation for the kinetic energy of the satellite?

Answer 7

K = -GmMe/2r

Question 8

Which of the following is the incorrect answer? The total energy of a satellite in uniform circular orbit around the Earth is _____________.

Answer 8

E = GMe/2r - GMe/r

Question 9

The total energy of an orbiting satellite in uniform circular motion is negative because of the magnitude of U, which is also negative. Consider the equation U = -GmMe/r. Which of the following is not correct?

Answer 9

You can assume that U equal zero at some arbitrary point (e.g., at the surface of the Earth).

Question 10

Consider a satellite in uniform circular orbit around the Earth, and then consider this satellite at a higher orbit. Which of the following is correct?

Answer 10

w decreases and v decreases