The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is ___ .

Open in App

Solution

K.E. required for satellite to escape from earth's gravitational field $\frac{1}{2} m v_{e}^{2} = \frac{1}{2} m (\sqrt{\frac{2 G M}{R}})^{2} = \frac{G M m}{R}$
K.E. required for satellite to move in circular orbit
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m (\sqrt{\frac{G M}{R}})^{2} = \frac{G M m}{2 R}$
The ratio between these two energies=2

Suggest Corrections

Similar questions

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

Q. The ratio of the kinetic energy required to be given to a satellite so that it escapes the gravitational field of earth to the kinetic energy required to put the satellite in a circular orbit just above the free surface of earth is

Q. A satellite is revolving in a circular orbit at a height

h

from the earth surface (radius of earth

R h << R

). The minimum increased in its orbital velocity required, so that the satellite could escape from the earths gravitational field, is close to: (Neglect the effect of atmosphere.)

Q. A satellite is revolving in a circular orbit at a height 'h' from the earth's surface(radius of earth R

;

<<

R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is closed to(Neglect the effect of atmosphere.)

Q. A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :

Join BYJU'S Learning Program

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is ___ .

K.E. required for satellite to escape from earth's gravitational field 12mv2e=12m(√2GMR)2=GMmR K.E. required for satellite to move in circular orbit 12mv20=12m(√GMR)2=GMm2R The ratio between these two energies=2