Chapter 14, Problem 25A

Does the speed of a satellite around Earth depend on its mass? Its distance from Earth? The mass of Earth?

To determine

Whether speed of satellite around earth depends on its mass, distance from earth or mass of earth.

Answer to Problem 25A

Speed of satellite around earth depends on distance from earth and mass of earth.

Explanation of Solution

Introduction:

The speed of satellite around earth is given by

  $v=\sqrt{\frac{GM}{r}}$

Where

  $v=$ Speed of satellite

  $\text{M =}$ Mass of earth

  $\text{r =}$ Distance of satellite from earth

  $\text{G =}$ Gravitational constant

The speed of satellite depends directly on thesquare root of the mass of earth and inversely on the square root of the distance from earth.

Conclusion:

Hence, speed of satellite around earth depends on distance from earth and mass of earth.