At which height from the surface of the Earth does a polar satellite revolve around the Earth?

$A$ spherical asteroid having the same density as that of Earth is floating in free space. $A$ small pebble is revolving around the asteroid under the influence of gravity near the surface of the asteroid. What is the approximate time period of the pebble?

An object is projected horizontally with speed $\frac{1}{2} \sqrt{\frac{GM}{R}}$ from a point at height $3R$ (where $R$ is the radius and $M$ is the mass of the Earth). The object will:

The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

The distance of a geostationary satellite from the surface of the Earth (radius $R_e = 6400 \ km$) in terms of $R_e$ is ....... (in $R_e$)

Earth is moving around the sun in an elliptical orbit as shown. The ratio of $OB$ and $OA$ is $R$. Then the ratio of Earth's velocities at $A$ and $B$ is