The period of moon's rotation around the earth is nearly $29$ days. If moon's mass were $2$ fold, its present value and all other things remained unchanged, the period of moon's rotation would be nearly ......... $days$.

The speed of a satellite in a circular orbit of radius $R_0$ around the earth is $v_0$. Another satellite is in an elliptic orbit around the earth. If the minimum and maximum speeds of the second satellite are $\alpha v_0$ and $\beta v_0$ respectively,then its time period is

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

If $r$ denotes the distance between the sun and the earth,then the angular momentum of the earth around the sun is proportional to

$Assertion$ : An astronaut experiences weightlessness in a space satellite.
$Reason$ : When a body falls freely,it does not experience gravity.

$A$ satellite revolving around the earth at a certain height experiences acceleration due to gravity equal to $\frac{16}{49} g_0$,where $g_0$ is the acceleration due to gravity on the earth's surface. If $R$ is the radius of earth,then the square of time period of the satellite's revolution is equal to $K\left[\frac{\pi^2 R^3}{G M}\right]$. The value of $K$ is