Near Earth
Near-Earth Gravitational Potential
For small height changes, \(U_g=mgh\) (with chosen zero at \(h=0\)).
- When \(mgh\) applies
- Choosing \(h=0\)
- Energy changes vs absolutes
Work & Energy · Physics
Gravitational Potential Energy
Near Earth: \(U_g=mgh\). In space: \(U_g=-\frac{GMm}{r}\). Both connect to the gravitational force.
This topic includes
Subtopics to master
Use the right gravitational potential model for the situation and connect it to force.
General
Universal Gravitational Potential
For two masses: \(U_g=-\dfrac{GMm}{r}\) (usually set \(U\to 0\) as \(r\to\infty\)).
- Why it’s negative
- Reference at infinity
- Comparing two radii
Force link
Potential Energy and Force Relationship
In 1D radial motion, \(F_r=-\dfrac{dU}{dr}\). For gravity, this reproduces the inverse-square force.
- Derivative gives force
- Direction from slope
- Consistency check
Intro
Escape Energy (Intro Level)
Escape requires enough energy to reach \(r\to\infty\) with nonnegative kinetic energy.
- Energy viewpoint
- What “escape” means
- Qualitative reasoning
Practice
Practice & Exercises
Compute \(\Delta U_g\) and apply energy methods to gravitational motion problems.
- \(mgh\) change problems
- \(-GMm/r\) comparisons
- Force-from-\(U\) derivative checks
- Simple escape reasoning
- Mixed K+U conservation drills
Bridge
Toward Mechanical Energy Conservation
With only gravity acting, \(K+U_g\) stays constant — powerful for drop, launch, and orbit-style problems.
- Conservation statement
- Model assumptions
- Next topic setup