An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth.

The escape velocity from Earth (

v_e

) is the speed needed to break free from Earth's gravitational pull without further propulsion. The formula for escape velocity is:

v_e = \sqrt{2gR}

Where:

$g$ is the acceleration due to Earth's gravity (approximately $9.8 \, \text{m/s}^2$ ),
$R$ is the radius of the Earth (approximately $6,371 \, \text{km}$ or $6.371 \times 10^6 \, \text{m}$ ).

The satellite is moving at half the escape velocity, so its speed

v

is:

v = \frac{1}{2} v_e

Substituting the expression for

v_e

v = \frac{1}{2} \sqrt{2gR}

Simplifying:

v = \sqrt{\frac{1}{2} gR}

Related content