# What linear speed must an earth satellite have to be in a circular orbit at an altitude of 164 km?

## Question:

What linear speed must an earth satellite have to be in a circular orbit at an altitude of 164 km?

## Orbital Velocity

The velocity required by a satellite in order to keep revolving around the earth is called orbital velocity. The orbital velocity of a satellite is given by

{eq}\begin{align} v_o = \sqrt{\frac{GM}{R}} \end{align} {/eq}

Where G is the universal gravitational constant, M is the mass of the planet, and R is the radius of the orbit.

Data Given

• Radius of the orbit of the satellite {eq}R = R_E + h = 6400 \ \rm km + 164 \ \rm km = 6564 \ \rm km {/eq}
• Mass of the earth {eq}M = 6 \times 10^{24} \ \rm kg {/eq}

Here the linear speed of the satellite stands for the orbital speed that is given by

{eq}\begin{align} v_o =& \sqrt{\frac{GM}{R}} \\ v_o =& \sqrt{ \frac{ 6.67 \times 10^{-11} \ \rm N.m^2 kg^{-2} \times 6.0 \times 10^{24} \ \rm kg}{6564 \times 1000 \ \rm m}} \\ \color{blue}{\boxed{ \ v_o = 7808 \ \rm m/s = 7.8 \ \rm km/s }} \end{align} {/eq}