The period of revolution of planet $A$ around the sun is $8$ times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun

A spherical asteroid having the same density as that of earth is floating in free space. A small pebble is revolving around the asteroid under the influence of gravity near the surface of the asteroid. What is the approximate time period of the pebble?

Two satellites are launched at a distance $R$ from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed $v_0$ and enters a circular orbit. The second satellite, however, is launched at a speed $\frac {1}{2}v_0$ .  What is the minimum distance between the second satellite and the planet over the course of its orbit?

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 time period of another satellite in a circular orbit is $16 \,days$ then

The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas $A$ and $B$ are also shown in the figure which can be assumed to be equal. If ${t_1}$ and ${t_2}$ represent the time for the planet to move from $a$ to $b$ and $d$ to $c$ respectively, then

The ratio of kinetic energy of a planet at perigee and apogee during its motion around the sun in elliptical orbit of eccentricity $e$ is ..........