An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

$A$ satellite is in an elliptic orbit around the Earth with an aphelion of $6R$ and a perihelion of $2R$,where $R = 6400 \, km$ is the radius of the Earth. Find the eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

Consider a light planet revolving around a massive star in a circular orbit of radius $r$ with time period $T$. If the gravitational force of attraction between the planet and the star is proportional to $r^{-7/2}$,then $T^2$ is proportional to:

Two planets,$A$ and $B$,orbit around a star such that the time period of $A$ is $8$ times the time period of $B$. The ratio of the orbital velocities of planets $A$ and $B$ is:

Two satellites of earth,$S_{1}$ and $S_{2}$,are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?

Weightlessness experienced while orbiting the earth in a spaceship is the result of: