The distances of two planets from the Sun are $10^{11} \ m$ and $10^{10} \ m$ respectively. Find the ratio of their orbital periods.

$A$ planet revolves around the sun whose mean distance is $1.588$ times the mean distance between the earth and the sun. The revolution time of the planet will be ........... $years$.

$A$ planet moves around the sun. At a given point $P$,it is closest to the sun at a distance $d_1$ and has a speed $v_1$. At another point $Q$,when it is farthest from the sun at a distance $d_2$,its speed will be:

The earth $E$ moves in an elliptical orbit with the sun $S$ at one of the foci as shown in the figure. Its speed of motion will be maximum at the point:

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law,i.e.,$F \propto 1/r^3$,but still remains a central force. Then:

If the distance of the earth from the Sun is $1.5 \times 10^8 \, km$. Then the distance of an imaginary planet from the Sun,if its period of revolution is $2.83$ years,is $............. \times 10^8 \, km$.