Gravitational Potential Energy Well

Q: Why is gravitational potential energy defined as negative?

To show that the object is bound to the mass. We define U_g = 0 at infinity. As an object moves closer, its potential energy decreases, becoming more negative (falling into the well).

Interactive 3D potential energy well simulator. Understand negative gravitational potential energy, kinetic energy, and escape velocity.

WHAT IS A GRAVITATIONAL WELL?

A gravitational well is a conceptual model used to visualize the gravitational field of a massive body. In General Relativity, gravity is the curvature of spacetime. In AP Physics 1, we use the "rubber sheet" analogy to show how a mass creates a "dip" in potential energy, causing smaller objects to "fall" toward it or orbit around it.

ENERGY IN THE WELL

An object orbiting a planet is "trapped" in its potential well. To escape the well, the object must gain enough kinetic energy to reach a total energy of zero (at an infinite distance). This leads to the concept of escape velocity.

HOW TO USE THIS VISUALIZATION

1. **Place a Mass**: Drop a star or planet into the center to create the well.\n2. **Launch a Satellite**: Click and drag to set the initial velocity of a smaller mass.\n3. **Observe Orbits**: See how different speeds result in circular, elliptical, or hyperbolic paths.\n4. **View the Mesh**: Look at the 3D grid deformation to see the strength of the field at different points.

CORE FORMULAS

Gravitational potential energy

Total mechanical energy

AP EXAM CONNECTION

Unit: Unit 2: Force and Translational Dynamics (Topic 2.4)
Learning Objective: 2.4.2

COMMON MISCONCEPTIONS

Thinking gravity is a flat force (it follows the inverse square law).
Believing objects need a push to stay in orbit (they just need tangential velocity).
Forgetting that is measured from center to center.