A satellite is revolving around the earth with a kinetic energy E . The minimum addition of kinetic energy needed to make it escape from its orbit is

Question

A satellite is revolving around the earth with a kinetic energy E . The minimum addition of kinetic energy needed to make it escape from its orbit is (A)  2E  (B)  √E  (C)  E/2  (D)  √E/2

Tardigrade Admin · Accepted Answer

Kinetic energy of satellite in its orbit

E = \frac{1}{2} m v_{o}^{2}

Or

E = \frac{1}{2} m (\frac{GM}{r}) = \frac{GM m}{2 r}

Kinetic energy at escape velocity

E = \frac{1}{2} m v_{e}^{2}

= \frac{1}{2} m (\frac{2 GM}{r}) = \frac{GM m}{r}

= 2 E

Therefore, additional kinetic energy required

= 2 E - E = E

Q. A satellite is revolving around the earth with a kinetic energy $E$ . The minimum addition of kinetic energy needed to make it escape from its orbit is

$2 E$

$E$

$E /2$

$E /2$

$E$

Q. A satellite is revolving around the earth with a kinetic energy E . The minimum addition of kinetic energy needed to make it escape from its orbit is

2E

E​

E/2

E/2​

E

Kinetic energy of satellite in its orbit E=21​mvo2​ Or E=21​m(rGM​)=2rGMm​ Kinetic energy at escape velocity E=21​mve2​ =21​m(r2GM​)=rGMm​ =2E Therefore, additional kinetic energy required =2E−E=E

Q. A satellite is revolving around the earth with a kinetic energy $E$ . The minimum addition of kinetic energy needed to make it escape from its orbit is

$2 E$

$E$

$E /2$

$E /2$

$E$