$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth ($R$ is the radius of the earth). The time period of another satellite at a height of $2.5R$ from the surface of the earth is:

What is the direction of areal velocity of the earth around the sun?

Kepler's third law states that the square of the period of revolution $(T)$ of a planet around the sun is proportional to the cube of the average distance $(r)$ between the sun and the planet,i.e.,$T^2 = Kr^3$,where $K$ is a constant. If the masses of the sun and the planet are $M$ and $m$ respectively,then according to Newton's law of gravitation,the force of attraction between them is $F = \frac{GMm}{r^2}$,where $G$ is the gravitational constant. The relation between $G$ and $K$ is:

Does the speed of a planet remain constant in its orbit?

An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is ........ $days$.

The period of a planet around the sun is $8$ times that of earth. The ratio of the radius of the planet's orbit to the radius of the earth's orbit is: