Gravitation formulas

Every formula JEE Advanced expects you to know for Gravitation, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 32
Subject: Physics
Exam: JEE Advanced
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Gravitation, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

Universal law of gravitation
$F = \frac{G m _{1} m _{2}}{r ^{2}}$
Gravitational constant
$G = 6.67 \times 1 0^{- 11} N m^{2} kg^{- 2}$
Gravitational field
$E = \frac{F}{m} = \frac{GM}{r ^{2}}$
Acceleration due to gravity
$g = \frac{GM}{R ^{2}}$
Variation with height (h≪R)
$g_{h} \approx g (1 - \frac{2 h}{R})$
Variation with height (exact)
$g_{h} = \frac{GM}{( R + h ) ^{2}}$
Variation with depth
$g_{d} = g (1 - \frac{d}{R})$
Effect of rotation
$g^{'} = g - R ω^{2} cos^{2} λ$
λ = latitude
Gravitational potential
$V = - \frac{GM}{r}$
Field from potential
$E = - \frac{d V}{d r}$
Gravitational PE
$U = - \frac{GM m}{r}$
Escape velocity
$v_{e} = \frac{2 GM}{R} = 2 g R \approx 11.2 km/s$
Orbital velocity
$v_{o} = \frac{GM}{r}$
Orbital velocity near surface
$v_{o} = g R \approx 7.9 km/s$
Escape–orbital relation
$v_{e} = 2 v_{o}$
Time period of a satellite
$T = 2 π \frac{r ^{3}}{GM}$
Minimum time period
$T = 2 π \frac{R}{g} \approx 84.6 min$
KE of a satellite
$K = \frac{GM m}{2 r}$
PE of a satellite
$U = - \frac{GM m}{r}$
Total energy of a satellite
$E = - \frac{GM m}{2 r}$
Kepler's first law
$orbit is an ellipse with the Sun at a focus$
Kepler's second law (areal velocity)
$\frac{d A}{d t} = \frac{L}{2 m} = constant$
Kepler's third law
$T^{2} \propto r^{3}$
Field of a ring (on axis)
$E = \frac{GM r}{( a ^{2} + r ^{2} ) ^{3/2}}$
Field inside a solid sphere
$E = \frac{GM r}{a ^{3}}$
r<a
Potential at centre of a solid sphere
$V = - \frac{3 GM}{2 a}$
Field inside a shell
$E = 0$
r<a
Potential inside a shell
$V = - \frac{GM}{a}$
r<a
g at pole vs equator
$g_{p o l e} > g_{e q u a t or}$
Tunnel oscillation period
$T = 2 π \frac{R}{g}$
Maximum height (projectile)
$H = \frac{v ^{2}}{2 g - \frac{v ^{2}}{R}}$
Geostationary broadcast angle
$θ = cos^{- 1} (\frac{R}{R + h})$

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Gravitation formulas

Gravitation, every formula

Universal law of gravitation

Gravitational constant

Gravitational field

Acceleration due to gravity

Variation with height (h≪R)

Variation with height (exact)

Variation with depth

Effect of rotation

Gravitational potential

Field from potential

Gravitational PE

Escape velocity

Orbital velocity

Orbital velocity near surface

Escape–orbital relation

Time period of a satellite

Minimum time period

KE of a satellite

PE of a satellite

Total energy of a satellite

Kepler's first law

Kepler's second law (areal velocity)

Kepler's third law

Field of a ring (on axis)

Field inside a solid sphere

Potential at centre of a solid sphere

Field inside a shell

Potential inside a shell

g at pole vs equator

Tunnel oscillation period

Maximum height (projectile)

Geostationary broadcast angle

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