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Formula Sheets / Physics

Chapter 10

Gravitation

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Law of gravitation and field Acceleration due to gravity Potential, energy and escape velocity Satellites and Kepler's laws

Law of gravitation and field

$F = \frac{G m _{1} m _{2}}{r ^{2}},$ $E = \frac{GM}{r ^{2}}$
Shell and sphere
shell: $E = 0 (r < R);$ solid sphere: $E = \frac{GM r}{R ^{3}} (r < R)$

Acceleration due to gravity

$g = \frac{GM}{R ^{2}}$
Height h
$g_{h} = \frac{g}{( 1 + h / R ) ^{2}} \approx g (1 - \frac{2 h}{R}) (h ≪ R)$
Depth d
$g_{d} = g (1 - \frac{d}{R})$
Latitude
$g_{ϕ} = g - ω^{2} R cos^{2} ϕ$

Potential, energy and escape velocity

$V = - \frac{GM}{r},$ $U = - \frac{GM m}{r}$
Escape velocity
$v_{e} = \frac{2 GM}{R} = 2 g R \approx 11.2$ km/s

Satellites and Kepler's laws

Orbital speed and period
$v_{o} = \frac{GM}{r},$ $T = 2 π \frac{r ^{3}}{GM}$
Energy
$K = \frac{GM m}{2 r},$ $T^{2} \propto a^{3};$ $E = - \frac{GM m}{2 r}$
Kepler's laws
$T^{2} \propto a^{3};$ $\frac{d A}{d t} = \frac{L}{2 m} =$ constant

Rotational Motion Mechanical Properties of Solids