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Gravitation

Name                                 Definition   Formulae
                                                            GRAVITATIONAL FIELDS
Gravitational fields A gravitational field is caused by mass & it affects mass
Gravitational field lines show the direction that a positive mass will move in that field. The field line spacing tells us the field strength
Gravitational field
strength		 Force acting on unit mass in the field g=frac{F}{m}
GPE Work done in moving a distance h in the field int _{o}^{h}Fdx =mgh
Total energy E=KE=-frac{GPE}{2}
Gravitational
potential		 Phi =frac{GM}{r}
Change in
gravitational potential		 Change in GPE per unit mass

 Delta Phi =gh

g=-frac{Delta Phi }{dx}
Newton’s law of
universal gravitation		 The attractive gravitational force between two point mass
Is directly proportional to the product of their mass
And inversely proportional to the square of distance between them		 g=frac{GM}{r^{2}}

F=frac{GMm}{r^{2}}
Escape velocities The speed of the object so that it just reach ∞ v_{esc}=sqrt{frac{2GM}{R}}
                                                               KEPLER LAW OF PLANETARY ORBITS
Kepler’s first law The planets orbit the sun in elliptical orbit with the sun at one focus of the ellipse
Kepler’s second law The line joining the planet to the sun sweep out equal area in equal times
Kepler’s third law If T is measured in year, d is measured in AU,

T^{2}=d^{3}

 T^{2}=(frac{4Pi ^{2}}{GM_{sun}})d^{3}
                                                                                  SATELLITES
Near Earth orbit   v^{2}=frac{GM}{R}
Geosynchronous Above equator, T=24h rightarrow d=4.2times 10^{7}
                                                                           BLACK HOLES
Schwarzschild radius Radius of a black hole of mass M
For Earth R_{s}=8.89times 10^{-3}m		 R_{s}=frac{2GM}{c^{2}}