can i get the all formulas of gravitation lesson
Answers
Answer:
Formulas for Gravitation
Gravitational force-
F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}
Acceleration due to gravity (g)
g=\frac{GM}{R^{2}}
Variation in 'g' with height
g'\alpha\, \frac{1}{r^{2}}
r=R+h
Answer:
Formulas for Gravitation
Gravitational force-
F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}
Acceleration due to gravity (g)
g=\frac{GM}{R^{2}}
Variation in 'g' with height
g'\alpha\, \frac{1}{r^{2}}
r=R+h
Gravitation- Formula- Variation in Acceleration due to gravity with height
Variation in 'g' with depth
Gravitation- Formula- Variation in Acceleration due to gravity with depth
g'\alpha (R-d)
g'=g\left [ 1-\frac{d}{R} \right ]
Variation in 'g' due to Rotation of earth
Gravitation- Formula- Variation in g due to rotation of earth
g'=g-\omega ^{2}R\cos ^{2}\lambda
Gravitational field Intensity
\vec{I}=\frac{\vec{F}}{m}
Where F=Gravitational force
Gravitational Potential
V=-\int \overrightarrow{I}\cdot \overrightarrow{dr} or V=-\frac{W}{m}=-\int \frac{\overrightarrow{F}\cdot \overrightarrow{dr}}{m}
Work done against gravity
W=\Delta U=GMm\left [ \frac{1}{r_{1}}-\frac{1}{r_{2}} \right ]
Escape velocity
V_{c}=\sqrt{\frac{2GM}{R}}
Escape energy
\frac{GMm}{R}=Escape \; Energy
Kepler's 2nd law
\frac{dA}{dt}= \frac{L}{2m}
Kepler's 3rd law
T^{2}\: \alpha\: a^{3}
or T^{2}\: \alpha \: \left ( \frac{r_{1}+r_{2}}{2} \right )^{3}
Energy of satellite
E=-\frac{GMm}{2r}