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Gravitation
Universal gravitation, orbital motion, escape velocity
Key Concepts
- Kepler's 1st law: planets move in ellipses with sun at one focus
- Kepler's 2nd law: equal areas are swept in equal times (L conserved)
- Kepler's 3rd law: T² ∝ r³
- Gravitational field is zero at centre of a uniform spherical shell
- g decreases both above and below Earth's surface
Important Formulae
| Gravitational force | F = Gm₁m₂/r² |
| Surface gravity | g = GM/R² |
| Escape velocity | v_esc = √(2GM/R) = √(2gR) |
| Orbital velocity | v_orb = √(GM/r) |
| Orbital period | T = 2πr/v_orb |
| g at height h | g_h = g(1 − 2h/R) for h ≪ R |
Quick Tips
- Escape velocity ≈ 11.2 km/s for Earth; orbital velocity for near-orbit ≈ 7.9 km/s.
- Geostationary orbit: T = 24 h, height ≈ 36,000 km above equator.
- Gravitational PE = −GMm/r (negative because bound system).
Sample Practice Questions
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On Moon, g is 1/6 of Earth's. Weight of 60 kg person on Moon:
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Answer: 100 N
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Acceleration due to gravity at height h above surface, where h << R:
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Answer: g(1 − 2h/R)
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If radius of Earth is compressed to half keeping mass same, escape velocity:
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Answer: Doubles
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Kepler's third law: T² ∝ :
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Answer: a³
Practice Questions
Practice 20 randomly selected NEET questions on Gravitation. Answers are revealed after each question.
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