Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $A$ is $3 v$,the speed of $B$ will be:

$A$ geostationary satellite is orbiting the earth at a height $5R$ above the surface of the earth,where $R$ is the radius of the earth. What is the time period (in hours) of another satellite orbiting at a height of $2R$ from the surface of the earth?

$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth,where $R$ 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

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication.
$(a)$ Calculate the height of such a satellite.
$(b)$ Find out the minimum number of satellites that are needed to cover the entire Earth,so that at least one satellite is visible from any point on the equator.
Given: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.

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 International Space Station is maintained in a nearly circular orbit with a mean altitude of $330 \, km$ and a maximum of $410 \, km$. An astronaut is floating in the space station's cabin. The acceleration of the astronaut as measured from the Earth is: