A geostationary satellite is orbiting around an arbitary planet $^{\prime} P ^{\prime}$ at a height of $11 R$ above the surface of $^{\prime} P ^{\prime} ,$ $R$ being the radius of $^{\prime} P .^{\prime}$ The time period of another satellite in hours at a height of $2R$ from the surface of $^{\prime} P ^{\prime}$ is $........$.$^{\prime} P ^{\prime}$ has the time period of $24\, hours.$

Which of the following graphs represents the motion of a planet moving about the sun

Which of the following quantities does not depend upon the orbital radius of the satellite.

A binary star system consists of two stars one of which has double the mass of the other. The stars rotate about their common centre of mass :-

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 10^4 \mathrm{~km}$ )

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto {1\over r^3}$, but still remaining a central force. Then