Two satellites are launched simultaneously into orbits of radius $R$ and $4R$. At an instant,the two satellites are on the same radial line. The time after which they have maximum separation is (mass of Earth = $M_e$). Assume the same sense of rotation.

The period of a satellite in a circular orbit around a planet is independent of

$A$ planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is

On a hypothetical planet,a satellite can only revolve in quantized energy levels,i.e.,the magnitude of the energy of a satellite is an integer multiple of a fixed energy. If two successive orbits have radii $R$ and $\frac{3R}{2}$,what could be the maximum radius of the satellite (in $R$)?

$A$ 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 $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

The orbital velocity of an artificial satellite in a circular orbit very close to the Earth is $v$. The velocity of a geostationary satellite orbiting in a circular orbit at an altitude of $3R$ from the Earth's surface will be