# A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R= 6400 km is the radius of the earth.

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A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R= 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R ?

[G = 6.67 × 10–11 SI units and M = 6 × 1024 kg]

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Conservation of angular momentum:

angular momentum at perigee = angular momentum at apogee

mvprp = mvara

va/vp = 1/3.

Conservation of Energy:

Energy at perigee = Energy at apogee

Hence to transfer to a circular orbit at apogee, we have to boost the velocity by Δ = (3.23 – 2.28) = 0.95 km/s. This can be done by suitably firing rockets from the satellite.