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What is the apogee velocity of a spacecraft in an elliptical orbit if the eccentricity and semi-major axis of the orbit are 0.9 and 50,000 km2/s respectively?

Correct Answer: 0.648 km/s
Given, Gravitational Parameter (μ) = 398,600 km3/s2 Semi-major axis (a) = 50,000 km Eccentricity (e) = 0.9 From orbit equation for ellipse, Specific angular momentum (h) = (μa(1-e2))1/2 = (398,600*50,000*(1-0.92))1/2 = 61,536 km2/s Apogee radius (ra) = a(1 + e) = 50,000 (1 + 0.9) = 95,000 km Apogee velocity (va) = h/ra = 61,536/95,000 = 0.6477 km/s

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