A satellite mass 200 kg is launchedfrom a site on earth’s equator into an orbit

Question

A satellite mass 200 kg is launchedfrom a site on earth’s equator into an orbit 200 km above theearth’s surface. Assuming a circular orbit, whatis

(a) the orbital period of thissatellite,

(b) its speed, and

(c) the minimum energy necessary to be suppliedin order to place the satellite in orbit from thesurface?

Explanation / Answer

a) the gravitation force is the centripetal force : F = GMm/(R+h)^2 = mV^2/(R+h) => V = (GM/(R+h)) = 7798.76 m/s => period : T = 2(R+h)/V = 5301.27s b) its speed : V = 7798.76 m/s c) the minimum energy when we launch the satellite with thesame direction to the velocity of Earth's surface at equator => initial velocity : Vo = R =(2/(24*3600))*6380x10^3 = 463.967 m/s =. minimum energy : E = (1/2)mV^2 - GMm/(R+h) - (-GMm/R) - (1/2)mVo^2 =6.442x10^9 J

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