Gravitation – Complete Intermediate Notes
Stage 1 • Page 5 • Gravitational Potential & Potential Energy
1. Gravitational Potential Energy (GPE)
Gravitational potential energy of a body at a point is defined as the work done against gravitational force in bringing the body from infinity to that point.
U = − GMm / r
- M → Mass of attracting body
- m → Mass of test body
- r → Distance between their centres
Important:
Reference level of gravitational potential energy is taken as zero at infinity.
2. Why Is Gravitational Potential Energy Negative?
Gravitational force is attractive. Hence, work done by gravitational force in bringing a body from infinity is positive, so potential energy becomes negative.
- U = 0 at infinity
- U becomes more negative as body comes closer
- Minimum at Earth’s centre (theoretically)
Board Favourite:
Explain why gravitational potential energy is always negative.
3. Gravitational Potential
Gravitational potential at a point is the gravitational potential energy per unit mass.
V = U / m = − GM / r
- Scalar quantity
- SI unit: J kg⁻¹
- Independent of test mass
IIT Insight:
Potential is preferred over potential energy in multi-particle systems.
4. Relation Between Gravitational Field & Potential
Gravitational field is the negative gradient of gravitational potential.
g = − dV / dr
- Field points in direction of decreasing potential
- Potential decreases faster where field is stronger
IIT Advanced Concept:
This relation connects force-based and energy-based approaches.
5. Gravitational Potential Energy Near Earth’s Surface
For small heights h ≪ R, gravitational potential energy becomes:
U ≈ mgh
- This is an approximation
- Valid only near Earth’s surface
- Not valid for satellites or large heights
Common Mistake:
Using mgh in satellite problems (always wrong).
6. Comparison: Gravitational Potential vs GPE
| Potential (V) | Potential Energy (U) |
|---|---|
| Per unit mass | Depends on mass |
| J kg⁻¹ | J |
7. Common Errors Students Make
- Forgetting negative sign in U and V
- Using mgh universally
- Confusing potential with potential energy
- Wrong reference level
Stage 1 • Page 5 Completed Successfully ✅
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