If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a , find the orbital speed of the satellite when it is at a distance r from the focus

Question

If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a , find the orbital speed of the satellite when it is at a distance r from the focus, v 2 = G M 2 r - 1 a, v 2 = G M 2 r 2 - 1 a, v 2 = G M 2 r 2 - 1 a 2, v 2 = G 2 r - 1 a

MARKS App · Accepted Answer

As in case of elliptic orbit of a satellite mechanical energy remains constant, at any position of satellite in the orbit, K E + P E = - G M m 2 a ...(i) Now, if at position r , v is the orbital speed of satellite K E = 1 2 m v 2 and P E = - G M m r ...(ii) So, from Eqs. (i) and (ii), we have 1 2 m v 2 - G M m r = - G M m 2 a , i . e . , v 2 = G M 2 r - 1 a

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