A satellite moves in an elliptical orbit with the Earth at one focus. At the perigee its
speed is v and its distance from the centre of the Earth is R . If the eccentricity of its
orbit is 0.5, calculate its speed at the apogee.
1
Expert's answer
2019-04-15T10:15:36-0400
Let va denote the speed of the satellite at the apogee to be found, and let its distance from the center of the Earth at the apogee be Ra. The conservation of energy of the satellite gives the equation
2mva2−RaGmM=2mv2−RGmM,
where m and M are the masses of the satellite and of the Earth, respectively, and G is Newton's gravitational constant. Solving this equation with respect to va, we have
va=v2−RGM(1−RaR).
The ratio of the distances in the perigee and apogee is related to the eccentricity ϵ as
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