at an altitude 2R.. the centripetal force = GMm/9R2 = gm/9 = mv2/3R
So, v2 = Rg/3 .. (i)
Applying conservation of energy,
[mRg/3 - mv2/2] + [-GMm/3R + GmM/R] = 0
==> mv2/2 = mRg/3 + 2GmM/3R
this is the minimum energy..
Find the minimum energy required to launch a m kg satellite from earth's surface in a circular orbit at an altitude 2R where R is earth's radius
at an altitude 2R.. the centripetal force = GMm/9R2 = gm/9 = mv2/3R
So, v2 = Rg/3 .. (i)
Applying conservation of energy,
[mRg/3 - mv2/2] + [-GMm/3R + GmM/R] = 0
==> mv2/2 = mRg/3 + 2GmM/3R
this is the minimum energy..