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:

When the period of rotation of a satellite from west to east is the same as that of the earth, then the relative velocity of a satellite is equal to

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

Weight of a body of mass $m$ in its free fall above the surface of the earth 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.

How much faster than its present speed should the earth rotate so that bodies lying on the equator may fly off into

Define zero gravity.

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 small body of mass $\text{'}m\text{'}$ is projected from the surface of a spherical planet of mass $M$ and radius $R$ with escape velocity in the radially outward direction. Assuming that only gravitational force due to the planet acts on the body during its motion, which of the following options are CORRECT.

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 ${\pi }^2=10$). 

A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is $\frac{1}{2}$. Time taken by planet to move from $D$ to $B(D\to A\to B)$ and $B$ to $D$ $(B\to C\to D)$ are respectively $T_{DAB}$ and $T_{BCD}$

What are the applications of geostationary satelllites?

The apparent weight of a body in an elevator moving with downward acceleration is greater than that of the actual weight of a body.