Question

Speed of a planet in an elliptical orbit with semi major axis 'a' about sun of mass M at a distance r from sun is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Total energy of a planet in an ellipitcal orbit is:

$E=-\frac{GMm}{2a}$ (m = mass of planet)

From conservation of mechanical energy

KE + PE = E

or $\frac{1}{2}m{v}^2-\frac{GMm}{r}=-\frac{GMm}{2a}$

or $v=\sqrt{GM(\frac{2}{r}-\frac{1}{a})}$