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What is the eccentricity of an orbit if tangential and radial velocity are 9.08 km/s and 2.01 km/s respectively. Specific angular momentum is 63,585 km2/s. Standard gravitational parameter is 398,600 km3/s2.

What is the eccentricity of an orbit if tangential and radial velocity are 9.08 km/s and 2.01 km/s respectively. Specific angular momentum is 63,585 km2/s. Standard gravitational parameter is 398,600 km3/s2. Correct Answer 0.551

Given, Radial velocity (vr)= 2.01 km/s (vt) = 9.08 km/s Specific angular momentum (h) = 63,585 km2/s Satellite distance from earth’s center (r) = h/vt = 63,585/9.08 = 7,002.75 km From orbit equation, ecos(θ) = h2/(μr) – 1 = 63,5852/(398,600*7002.75) – 1 = 0.448 esin(θ) = vr h/μ = 2.01*63,585/398,600 = 0.321 esin(θ)/ecos(θ) = 0.321/0.448 θ = atan(0.716) = 35.59° Eccentricity (e) = 0.448/cos(θ) = 0.551

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