Gravitational Potential Energy & Orbits – AP Physics C | ShowMeClass

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Gravitational Orbits

AP Physics C · Unit 7: Gravity

Learning Objectives

Apply Newton's law of gravitation: F = GMm/r²

Derive orbital velocity: v = √(GM/r)

Analyze gravitational PE: U = −GMm/r

Determine orbit type from total energy E

Key Equations

Orbit Types

E < 0: Bound orbit (ellipse/circle)
E = 0: Parabolic escape
E > 0: Hyperbolic escape

Circular orbit: v = √(GM/r)
Escape velocity: v = √(2GM/r)

Colors

Central mass (star/planet)

Orbiting body trail

Velocity vector

Gravitational force

GravityOrbitsKeplerAP Physics C

r =—

v =—

E =—

T =—

ENERGY vs RADIUS

Preset

Central Mass M (×10²⁴ kg) 5.97

Initial r (×10⁶ m) 7.0

Initial v (×10³ m/s) 7.55

Launch Angle (°) 90

Speed 1×

Display

Orbital Analysis

📝 Quick Quiz▼

1. For a circular orbit, the orbital speed is:

√(GM/r) √(2GM/r) GM/r² √(GMr)

2. Gravitational potential energy is:

GMm/r −GMm/r −GMm/r² mgh

3. A bound orbit requires total energy E to be:

Positive Zero Negative Infinite