Energy of an Orbiting Satellite

Two satellites $A$ and $B$ have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius $R$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $\frac{T_{\mathrm{A}}}{T_{\mathrm{B}}}$ is

An artificial satellite moving in a circular orbit around the earth has a total ($\mathrm{kinetic} +\mathrm{potential}$) energy $E_0$. Its potential energy and kinetic energy respectively are

The satellites when launched from the earth are not given an orbital velocity initially. A multi-stage rocket propeller carries the spacecraft up to its orbit and during each stage rocket has been fired to increase the velocity to acquire the desired velocity for a particular orbit. The last stage of the rocket brings the satellite in circular/elliptical (desired) orbit. Consider a satellite of mass 150 kg in a low circular orbit. In this orbit, we cannot neglect the effect of air drag. This air opposes the motion of satellite and hence the total mechanical energy of earth-satellite system decreases. That means the total energy becomes more negative and hence the orbital radius decreases which causes the increase in kinetic energy. When the satellite comes in the low energy orbit, excessive thermal energy generation due to air friction may cause the satellite to burn up. Based on the above information, answer the following question.

If due to air drag, the orbital radius of the earth decreases from $R$ to $R-∆R,∆R\ll R$. Then, the change in kinetic energy $∆\mathrm{K}$ is:

A satellite has kinetic energy $K,$ potential energy $V$ and total energy $E$ . Which of the following statement is true?

Satellite $\mathit{A}$ has mass $\mathit{m}$ and orbital radius $\mathit{R}.$ Satellite $\mathit{B}$ has mass $2\mathit{ }\mathit{m}$ and orbital radius $2\mathit{ }\mathit{R}.$ The ratio of kinetic energy of satellite $\mathit{A}$ and $\mathit{B}$ will be:

Speed of a satellite is $V$ in its circular orbit. What is the kinetic energy of mass $m,$ which is ejected from satellite so that it escape from gravitational field of Earth.

A satellite of mass $m$ revolves around the earth with a velocity $v$. The total energy of the satellite is:

Two identical satellites are moving around the earth in circular orbit at heights $3R$ and $R$ respectively, where $R$ is the radius of the earth. The ratio of their kinetic energies is :

The total energy of a satellite is -

When a satellite in a circular orbit around the earth enters the atmospheric region, it encounters small air resistance to its motion. Then

(1) its kinetic energy increases
(2) its kinetic energy decreases
(3) its angular momentum about the earth decreases
(4) its period of revolution around the earth increases

Correct options are –

The figure shows a planet in elliptical orbit around the sun S.Where is the kinetic energy of the planet maximum ?


       

A rocket is fired with a speed, $u=\mathrm{3}\sqrt{gR}$  from the earth surface. What will be its speed at interstellar space?

Speed of a planet in an elliptical orbit with semimajor axis $a$ about sun of mass $M$ at a distance $r$ from sun is  

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is