The time period of a satellite of the Earth is $5 \text{ hours}$. If the separation between the Earth and the satellite is increased to four times the previous value, the new time period of the satellite will be: (in $\text{ hours}$)

The radius of the Martian orbit around the Sun is about $4$ times the radius of the orbit of Mercury. The Martian year is $687$ Earth days. What is the length of $1$ year on Mercury?

Choose the incorrect statement from the following.

Two planets are at mean distances $d_1$ and $d_2$ from the sun,and their orbital frequencies are $n_1$ and $n_2$ respectively. Then:

Assume that the earth moves around the sun in a circular orbit of radius $R$ and there exists a planet which also moves around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is

When a satellite moves around the earth in a certain orbit,the quantity which remains constant is: