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GATE 2020 AE – Question 53

Flight Mechanics & Space Dynamics · Space dynamics: central force motion, Keplerian orbits, Kepler's laws and escape velocity · 2 marks · Numerical answer

A planet’s perihelion/aphelion tangential-speed ratio is 1.0339. Its orbit around the Sun is planar and elliptic. Find eccentricity to 3 decimals.

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Correct answer: 0.016 to 0.018

Explanation

Angular momentum conservation at the two apsides gives $v_p/v_a=r_a/r_p=(1+e)/(1-e)$. Thus $e=(1.0339-1)/(1.0339+1)=0.01667$, approximately 0.017. Apsidal velocities are tangential, so their ratio directly supplies the radius ratio.

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