Earth Satellites

A satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3\pi }{Gd}$ represents :

Two satellites $A$ and $B$ move round the earth in the same orbit. The mass of $A$ is twice the mass of $B$. The quantity which is same for the two satellites will be

The time period of a satellite, revolving above earth's surface at a height equal to $\mathrm{R}$ will be (Given $g={\pi }^2 \mathrm{m} {\mathrm{s}}^{-2},R=$ radius of earth)

Two satellites of masses $\mathrm{m}$ and $3 \mathrm{m}$ revolve around the earth in circular orbits of radii $\mathrm{r} \& 3\mathrm{r}$ respectively. The ratio of orbital speeds of the satellites respectively is

Choose the incorrect statement from the following:

A satellite of mass $5M$ orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes into two pieces, one of mass $M$ and the other of mass $4M$. After the explosion the mass $M$ ends up travelling in the same circular orbit, but in opposite direction. After explosion the mass $4M$ is:

Two satellites $A$ and $B$ are orbiting a planet in circular orbits with radii $2R$ and $R$ respectively. If the speed of satellite $A$ is $2v$, then the speed of satellite $B$ is

Two planets revolve with same angular velocity about a star. The radius of orbit of outer planet is twice the radius of orbit of the inner planet. If $T$ is time period of the revolution of outer planet, find the time in which inner planet will fall into the star. If it was suddenly stopped.

What should be the percentage increase in the orbital velocity to escape velocity?

An artificial satellite circles around the earth at a distance of $3400 km$. Calculate the orbital velocity. Given the radius of the earth is $6400 km. (g=9·8 m{s}^{-2})$.

Find the orbital velocity of an artificial satellite of the earth in an orbit close to the earth?

A planet revolves about the sun in elliptical orbit. The areal velocity $\left(\frac{dA}{dt}\right)$ of the

A satellite is launched into a circular orbit $1600 \mathrm{km}$ above the surface of the earth. Find the period of revolution in nearest integer (in hours) if the radius of the earth is $R=6400 \mathrm{km}$ and the acceleration due to gravity is (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and ${\pi }^2=10$). 

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

Define time period of a satellite.

Which of the following is the expression for orbital velocity of a satellite in a circular orbit.

Define orbital velocity of a satellite.

When a satellite falls to an orbit of smaller radius its kinetic energy

Consider a system of six stars which have equal masses $\mathrm{m}$, they are moving in circular motion about the center of mass of the system such that they are always on the vertices of a regular hexagon of side length $a$. Their common time period will be,

The work done by satellite against gravity in a complete orbit is :-