If a satellite is shifted towards the Earth,then the time period of the satellite will be:

Two particles of equal mass $m$ move in a circle of radius $r$ under the action of their mutual gravitational attraction. The speed of each particle will be ($G=$ Universal gravitational constant).

The height of a geostationary satellite is approximately ........ $km$.

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of the two stars is ($G$ is the universal gravitational constant).

Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

The Earth moves around the Sun in an elliptical orbit as shown in the figure. The ratio $OA/OB = x$. The ratio of the speed of the Earth at $B$ to that at $A$ is nearly