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Question
Speed of a planet in an elliptical orbit, with semimmajor axis `a` about sun of mass M. at a distance r from sun is :
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Solution
Total energy of a planet in an elliptical orbit isE=−GMm2aE=−GMm2a (m= mass of planet )By conservation of mechanical energyKE+P.E=E
12mv2−GMmr=−GMm2av=√GM(2r−1a)
KE+P.E=E
mv2−GMmr=−GMm2a
Total energy of a planet in an elliptical orbit is
E=−GMm2aE=−GMm2a (m= mass of planet )
By conservation of mechanical energy
KE+P.E=E
12mv2−GMmr=−GMm2a
v=√GM(2r−1a)
KE+P.E=E
KE+P.E=E
mv2−GMmr=−GMm2a
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