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If a satellite is revolving around a pla...

If a satellite is revolving around a planet of mass `M` in an elliptical orbit of semi-major axis `a`. Show that the orbital speed of the satellite when it is a distance `r` from the focus will be given by
`upsilon^(2) = GM[(2)/(r ) - (1)/(a)]`

Text Solution

Verified by Experts

In elliptical orbit, total energy
`E=-(GMm)/(2a)=` constant
At position `r`,if `v` is orbital speed of satellite the
`KE=1/2mv^(2)` and `PE =(GMm)/r`
`:. 1/2mv^(2)-(GMm)/r=-(GMm)/(2a)impliesv^(2)=GM(2/r-1/a)`
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