AP Physics 1 · Unit 6 · Rotating Systems

Elliptical Orbits and Gravitational Potential Energy Practice Problems

Follow a spacecraft around an ellipse, connect changing speed with gravitational energy, and compare bound orbits with escape conditions.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Elliptical Orbits and Gravitational Potential Energy lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Connect the path, the speed, and the energy balance

Read the ellipse and its motion vectors

Distinguish a focus from the geometric center and compare velocity, acceleration, and swept areas around the orbit.

Use orbital size and mechanical energy

Find the semimajor axis and period, connect speeds at different radii, and calculate changes in kinetic and gravitational potential energy.

Compare launch and escape conditions

Find the energy needed for a circular-orbit transfer, the escape threshold, and the remaining speed at large separation. Include both sources in the capsule comparison.

A question from this set

Vectors at the ends of an ellipse

A spacecraft travels counterclockwise around a planet at a focus. A is the farthest point on the right and B the nearest point on the left. Which vector description is correct?

Velocity points toward the planet at both A and B.
At A velocity points up and acceleration left; at B velocity points down and acceleration right.
Acceleration is zero at the farthest point.

Try it in the practice set

A is the farthest point and B the nearest point; the planet lies at the left focus. Motion is counterclockwise.

Key ideas

Gravity changes speed as well as direction on an ellipse

The central source is at a focus

Velocity follows the path’s tangent, while gravitational acceleration points toward the source. The spacecraft moves faster nearer the source.

Use one gravitational-energy reference

These questions set gravitational potential energy to zero at infinite separation. Keep that reference consistent when comparing bound motion and escape.

See the physics

Compare the spacecraft at different parts of its path

After attempting a question, run the original gravitational scene. Inspect near and far passages, swept areas, and physical-unit readouts, then compare the transfer or escape variants.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for elliptical orbits and gravitational potential energy?

Begin with a conceptual question, then work through the calculations.

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