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Key Equations

Newton’s law of gravitation F12=Gm1m2r2r^12F12=Gm1m2r2r^12
Acceleration due to gravity
at the surface of Earth
g=GMEr2g=GMEr2
Gravitational potential energy beyond Earth U=GMEmrU=GMEmr
Conservation of energy 12mv12GMmr1=12mv22GMmr212mv12GMmr1=12mv22GMmr2
Escape velocity vesc=2GMRvesc=2GMR
Orbital speed vorbit=GMErvorbit=GMEr
Orbital period Τ=2πr3GMEΤ=2πr3GME
Energy in circular orbit E=K+U=GmME2rE=K+U=GmME2r
Conic sections αr=1+ecosθαr=1+ecosθ
Kepler’s third law Τ2=4π2GMa3Τ2=4π2GMa3
Schwarzschild radius RS=2GMc2RS=2GMc2
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