EXERCISE 7.4

A double star system consists of two starts having masses $\mathrm{m}$ and $2 \mathrm{m}$ separated by a distance $r$

In a reference frame fixed to Sun,

A satellite of mass $m$ revolving in circular orbit of radius $r$ around the Earth of mass $M$ has binding energy $E$. The angular momentum of the satellite will be

Consider an attractive force which is central but is inversely proportional to the first power of distance. If a particle moves in a circular orbit under such force, which of the following statements are correct?

Suppose the gravitational force varies inversely as the $n^{\text{th }}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to 
 

A satellite is moving with a constant speed $V$ in a circular orbit about the earth. An object of mass $m$ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is 

The eccentricity of the earth's orbit is $e$. The ratio of its maximum speed in its orbit to its minimum speed is

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