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Energy of an Orbiting Satellite

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notes

Energy of an orbiting satellite:

m = mass of the satellite, v = velocity of the satellite

the kinetic energy of the satellite in a circular orbit with speed v is 

`"K.E" = 1/2"mv"^2`

`="GmM"_E/(2("R"_E+"h"))`

Considering gravitational potential energy at infinity to be zero, the potential energy at distance (Re+h) from the center of the earth is

`"P.E"=-"GmM"_E/(("R"_E +"h"))`

The K.E is positive whereas the P.E is negative. However, in magnitude, the K.E. is half the P.E so that the total E is

`"E" ="K.E"+"P.E"=-"GmM"_E/(2("R"_E +"h"))` 

The total energy of a circularly orbiting satellite is thus negative, with the potential energy being negative but twice is the magnitude of the positive kinetic energy. When the orbit of a satellite becomes elliptic, both the K.E. and P.E. vary from point to point.  The total energy which remains constant is negative as in the circular orbit case. 

If the total energy is positive or zero, the object escapes to infinity.   Satellites are always at a finite distance from the earth and hence their energies cannot be positive or zero.

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