Gravitation – Complete Intermediate Notes
Stage 1 • Page 6 • Orbital Velocity & Escape Velocity
1. Satellites and Circular Motion
A satellite is a body that revolves around a planet under the influence of gravitational force.
The gravitational force provides the necessary centripetal force for circular motion.
Key Idea:
In satellite motion, gravity acts as centripetal force.
2. Orbital Velocity
Orbital velocity is the minimum velocity required by a satellite to revolve in a circular orbit around Earth.
vo = √(GM / r)
- M → Mass of Earth
- r → Radius of orbit from Earth’s centre
For a satellite near Earth’s surface (r = R):
vo = √(gR)
- Independent of satellite mass
- Decreases with increase in orbit radius
IIT Tip:
Never use mgh for satellite problems — always use energy relations.
3. Time Period of a Satellite
Time period of satellite in circular orbit:
T = 2πr / v = 2π √(r³ / GM)
- Depends only on orbit radius
- Independent of satellite mass
Kepler Connection:
This relation is a direct result of Kepler’s third law.
4. Escape Velocity
Escape velocity is the minimum velocity with which a body must be projected from Earth so that it escapes Earth’s gravitational field completely.
ve = √(2GM / R)
In terms of g:
ve = √(2gR)
- Independent of mass of body
- Independent of direction of projection
- Assumes no air resistance
Important Result:
ve = √2 × vo
5. Comparison: Orbital Velocity vs Escape Velocity
| Orbital Velocity | Escape Velocity |
|---|---|
| Keeps body in orbit | Removes body from gravity |
| √(GM/r) | √(2GM/R) |
| Lower | Higher |
6. Common Mistakes to Avoid
- Confusing orbital and escape velocity
- Using mgh instead of −GMm/r
- Assuming escape velocity depends on mass
- Forgetting √2 factor
Stage 1 • Page 6 Completed Successfully ✅
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