A satellite of mass 210 kgis launched from a site on Earth\'s equator into an or

Question

A satellite of mass 210 kgis launched from a site on Earth's equator into an orbitat 205 km above the surfaceof Earth. (a) Assuming a circular orbit, what is the orbital period of thissatellite?
s

(b) What is the satellite's speed in its orbit?
m/s

(c) What is the minimum energy necessary to place the satellite inorbit, assuming no air friction?
J
(a) Assuming a circular orbit, what is the orbital period of thissatellite?
s

(b) What is the satellite's speed in its orbit?
m/s

(c) What is the minimum energy necessary to place the satellite inorbit, assuming no air friction?
J

Explanation / Answer

mass of the Earth=M, radius of the Earth=R~6380 km mass of the satellite=m=210kg, satellite’s altitude above the Earth’ssurface=r=205km a) the gravitation force is the centripetal force : F = GMm/(R+h)^2 = mV^2/(R+h) V = (GM/(R+h))    =___ m/s period : T = 2(R+h)/V =____ s b) its speed : V = __m/s from parta 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    = 6.442x10^9J

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