If a satellite is revolving around a planet of mass M in an elliptic orbit of semi-major axis a, show that the orbit al speed of the satellite when it is at a distance r from the focus will be given by v^2=GM(2/r - 1/a).

If a satellite is revolving around a planet of mass M in an elliptic o

1.	If a satellite is revolving around a planet of mass M in an elliptic orbit of semi-major axis a, show that the orbit al speed of the satellite when it is at a distance r from the focus will be given by v^2=GM(2/r - 1/a).
Answer» SOLUTION :Total MECHANICAL ENERGY of the system is `E=-(GMm)/(2a)` which remains conserved `rArr` KE+PE=`-(GMm)/(2a)` At a position .r. obital speed of the SATELLITE is v. The KE=`1/2mv^2` , PE=-`(GMm)/r` So, `1/2mv^2-(GMm)/r=-(GMm)/(2a)` (or) `v^2=GM(2/r-1/a)` .