An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re)

Question

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re) (A) h = R2e (B) h = Re (C) h = 2Re (D) h = 4Re

Tardigrade Admin · Accepted Answer

The escape velocity from earth is given by

v_{e} = 2 g R_{e}

...(i)
The orbital velocity of a satellite revolving around earth is given by

v_{0} = \frac{G M _{e}}{( R _{e} + h )}

where,

M_{e} =

mass of earth,

R_{e} =

radius of earth,

h =

height of satellite from surface of earth.
By the relation

G M_{e} = q R_{ρ}^{2}

so,

v_{0} \frac{g R _{e}^{2}}{( R _{e} + h )}

...(ii)
Dividing equation

(i)

by

(ii)

, we get

\frac{v _{e}}{v _{0}} \frac{2 ( R _{e} + h )}{R _{e}}

Squaring on both side, we get

4 = \frac{2 ( R _{e} + h )}{R _{e}}

or

R_{e} + h = 2 R_{e}

i.e.,

h = R_{e}

Q. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height $(h)$ of the satellite above the earth’s surface is (Take radius of earth as $R_{e}$ )

$h = R_{e}^{2}$

$h = R_{e}$

$h = 2 R_{e}$

$h = 4 R_{e}$

Q. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height (h) of the satellite above the earth’s surface is (Take radius of earth as Re​)

h=Re2​

h=Re​

h=2Re​

h=4Re​

Q. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth. The height $(h)$ of the satellite above the earth’s surface is (Take radius of earth as $R_{e}$ )

$h = R_{e}^{2}$

$h = R_{e}$

$h = 2 R_{e}$

$h = 4 R_{e}$