In a satellite,if the time of revolution is $T$,then the kinetic energy $(K.E.)$ is proportional to:

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).

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication purposes. The height of such a satellite is $(M_{E} = 6 \times 10^{24} \,kg, R_{E} = 6400 \,km)$.

Which of the following quantities remains constant for a satellite in an orbit?

$A$ particle of mass $m$ is under the influence of the gravitational field of a body of mass $M (\gg m)$. The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then,the particle is subjected to an additional central force,corresponding to the potential energy $V_c(r) = m \alpha / r^3$,where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_c(r)$,but with a new time period $T_1$,then $(T_1^2 - T_0^2) / T_1^2$ is given by [ $G$ is the gravitational constant.]

What is a polar satellite? What is the orbital period of a polar satellite?