Rotating Systems: Energy & Momentum

The total energy doubles.

The total energy is halved.

The total energy remains the same.

The total energy is quadrupled.

$v_a = v_p$

$v_a = 2v_p$

$v_a = \frac{v_p}{2}$

$v_a = \frac{v_p}{4}$

Only gravitational potential energy

Only kinetic energy

Total mechanical energy and angular momentum

Total mechanical energy, gravitational potential energy, kinetic energy, and angular momentum

Only kinetic energy is constant.

Only gravitational potential energy is constant.

Total mechanical energy and angular momentum are constant.

Total mechanical energy, kinetic energy, gravitational potential energy, and angular momentum are all constant.

The velocity required to maintain a stable orbit.

The minimum speed needed to break free from the central object's gravity.

The average speed of a satellite in orbit.

The speed at which a satellite burns up in the atmosphere.

$E_{\text{total}} = -\frac{GMm}{r}$

$E_{\text{total}} = \frac{GMm}{r}$

$E_{\text{total}} = -\frac{GMm}{2r}$

$E_{\text{total}} = \frac{GMm}{2r}$

The central object's motion is equal to the satellite's motion.

The central object is stationary.

The central object's motion must always be calculated.

The central object's motion is negligible compared to the satellite's orbit.

It becomes less negative.

It remains constant.

It becomes increasingly negative.

It becomes zero.

$K = U$

$K = 2U$

$K = -\frac{1}{2}U$

$K = -2U$

Apoapsis (farthest point)

Periapsis (closest approach)

Kinetic energy is constant throughout the orbit.

At a point where potential energy is zero.