The time period of an artificial satellite in a circular orbit of radius $R$ is $2 \, days$ and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16 \, days$,then:

Which force is responsible for the necessary centripetal force of a satellite revolving around the Earth?

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height,then the satellite will

Two satellites $A$ and $B$ of same mass are moving around a planet at an altitude of $3R$ and $5R$ respectively. Select the correct statement.

$A$ 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.]

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to