University Physics Volume 1

# Key Equations

### Key Equations

 Newton’s law of gravitation $F→12=Gm1m2r2r^12F→12=Gm1m2r2r^12$ Acceleration due to gravityat the surface of Earth $g=GMEr2g=GMEr2$ Gravitational potential energy beyond Earth $U=−GMEmrU=−GMEmr$ Conservation of energy $12mv12−GMmr1=12mv22−GMmr212mv12−GMmr1=12mv22−GMmr2$ 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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