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Q. A planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is

WBJEEWBJEE 2013Gravitation

Solution:

A planet revolves around the sun, is an elliptical orbit under the effect of gravitational pull on the planet.
image
So, torque, $C = r \times F =r F \sin 180^{\circ} n =0$
As $C =\frac{ d L }{d t} ; so L = a$ constant
$\Rightarrow $ Angular momentum is constant.