Formula Sheet: Gravitation Class 11

Yashwant Parihar,

In this post, we will learn the formulas of Chapter 7, Class 11, Gravitation. We provide a complete Gravitation formula sheet, including the variation of ‘g’ with height and depth, Kepler’s Laws, and energy calculations for satellites. Use this formula list for quick revision and to solve complex gravitational numericals with ease.

Gravitation Formula Sheet

1. Newton’s Law of Gravitation

Gravitational Force:

F=Gm1m2r2F = G\frac{m_1m_2}{r^2}

Universal Gravitational Constant:

G=6.67×10−11Nm2/Kg2G = 6.67\times10^{-11}Nm^2/Kg^2

2. Acceleration due to Gravity(g)

On the surface of the earth:

g=GMR2g = \frac{GM}{R^2}

Approx = 9.8 m/s2

Variation with altitude (h):

Generalg′=g(RR+h)2General\: g’ = g\left (\frac{R}{R+h} \right)^2
Forh<<R:g′=g(1−2hR)For\: h<<R: g’ = g \left ( 1- \frac{2h}{R} \right)

Variation with depth(d):

g′=g(1−dR)g’ = g \left ( 1 – \frac{d}{R} \right)

Trick: At the centre of the Earth: d = R and g = 0.

3. Gravitational Potential and Energy

Gravitational Potential Energy (U):

U=−GMmrU = -\frac{GMm}{r}

Gravitational Potential (V):

V=Um=−GMrV = \frac{U}{m} = -\frac {GM}{r}

Escape Velocity:

Ve=2GMR=2gRV_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}

For Earth, Ve = 11.2 km/s

Gravitational Field Intensity:

E=Fm=GMr2E = \frac {F}{m} = \frac{GM}{r^2}

4. Satellite Motion

Orbital Velocity:

Vo=2GMR+hV_o = \sqrt{\frac{2GM}{R+h}}

Time Period(T):

T=2π(R+h)Vo=2π(R+h)2GMT = \frac {2\pi (R+h)}{V_o} = 2\pi \sqrt {\frac {(R+h)^2}{GM}}

Energy of Satellite:

Kinetcenergy:K=GMm2rKinetc\:energy: K = \frac{GMm}{2r}
Potentialenergy:U=−GMmrPotential\:energy: U = -\frac {GMm}{r}
TotalEnergy=−GMm2rTotal\: Energy= -\frac{GMm}{2r}
BindingEnergy=−Etotal=GMm2rBinding \: Energy = -E_{total} = \frac{GMm}{2r}

5. Kepler’s Laws of Planetary Motion

  1. Law of orbits: Planets move in elliptical orbits with the Sun at one focus.
  2. Law of Areas: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time (Conservation of Angular Momentum).
  3. Law of Periods: The square of the time period is proportional to the cube of the semi-major axis:
T2∝r3T^2 \propto r^3

Formula Sheet Physics Formula Sheet

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