Rotating Systems: Energy & Momentum

Which of the following quantities are conserved for a satellite in a circular orbit around a planet?

A small satellite orbits a much larger planet. Which of the following statements is most accurate regarding the motion of the planet?

A satellite with mass $m = 100 ,\text{kg}$ orbits a planet with mass $M = 5.97 \times 10^{24} ,\text{kg}$ at a distance of $r = 6.37 \times 10^6 ,\text{m}$. What is the gravitational potential energy of the satellite-planet system? (Assume $G = 6.674 \times 10^{-11} ,\text{N} \cdot \text{m}^2/\text{kg}^2$)

In an elliptical orbit, how do the kinetic energy (KE) and potential energy (PE) change as a satellite moves from the apoapsis to the periapsis?

A satellite in an elliptical orbit has a perihelion distance of $r_p$ and an aphelion distance of $r_a$. What is the ratio of its speed at perihelion ($v_p$) to its speed at aphelion ($v_a$)?

What is the escape velocity from the surface of a planet with mass $M = 3.0 \times 10^{24} ,\text{kg}$ and radius $r = 5.0 \times 10^6 ,\text{m}$? (Assume $G = 6.674 \times 10^{-11} ,\text{N} \cdot \text{m}^2/\text{kg}^2$)

A satellite moves from a distance $r_1$ to a distance $r_2$ away from a planet, where $r_2 > r_1$. What is the change in gravitational potential energy of the satellite?

A satellite of mass $m$ is orbiting a planet of mass $M$ at a distance $r$. If the mass of the satellite is doubled, what happens to the escape velocity?

Derive the formula for escape velocity from energy conservation principles. Which of the following correctly represents the escape velocity?

What is the value of gravitational potential energy between two objects when they are an infinite distance apart?