The periodic time of a communication satellite is ......... $hours$.

$A$ satellite is in an elliptical orbit around a planet $P.$ It is observed that the velocity of the satellite when it is farthest from the planet is $6$ times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is $......$

$A$ planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^6 \text{ km}$ and $60 \times 10^6 \text{ km}$,respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angles $30^{\circ}$ and $60^{\circ}$ with the major axis of the orbit is:

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

The orbital period of a geostationary satellite is (in $\,h$)

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).