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Cheat sheet · JEE Preparation Physics

Gravitation cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Physics

Cheat sheet

Class 11 · Chapter 7Gravitation

Kepler: Orbits are ellipses, Areas equal, T² ∝ a³.

1. Newton's Law

F=Gm1m2r2F = \dfrac{Gm_1m_2}{r^2}
G=6.67×10−11 N m2kg−2G = 6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}

g=GMR2≈9.8 m s−2g = \dfrac{GM}{R^2} \approx 9.8\ \text{m s}^{-2} at the surface.

2. Variation of g

Whereg
Height h (h ≪ R)g(1−2hR)g(1 - \tfrac{2h}{R})
Depth dg(1−dR)g(1 - \tfrac{d}{R})
Centre of Earth0

3. Energy, Escape & Orbits

U=−GMmrU = -\dfrac{GMm}{r}ve=2gR≈11.2 km/sv_e = \sqrt{2gR} \approx 11.2\ \text{km/s}
vo=GMrv_o = \sqrt{\dfrac{GM}{r}}T=2πr3GMT = 2\pi\sqrt{\dfrac{r^3}{GM}}

Orbiting satellite: KE=GMm2rKE = \dfrac{GMm}{2r}, total energy E=−GMm2rE = -\dfrac{GMm}{2r} (bound).

4. Kepler's Laws

  • Orbits: planets move in ellipses with the Sun at one focus.
  • Areas: equal areas in equal times (angular momentum conserved).
  • Periods: T2∝a3T^2 \propto a^3.

5. Key Points

  • Geostationary satellite: T = 24 h, h ≈ 36 000 km.
  • Weightlessness in orbit: free fall.
  • Escape speed doesn't depend on the mass of the body.
  • Gravitational force is always attractive.

Remember: F = Gm₁m₂/r² | g with h, d | v_e = √(2gR) | Kepler's 3 laws

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