Question

A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?

Answer 1

The equation which represent the velocity, if the satellite is moved to an orbital radius of 5r is $V = \frac{V}{\sqrt{5}}$

Given the following data:

• Radius = 5r

To find the equation which represent the velocity, if the satellite is moved to an orbital radius of 5r:

Orbital velocity can be defined as the minimum velocity at which a satellite must move to remain in orbit.

Mathematically, orbital velocity is given by the formula:

$V = \sqrt{\frac{GM}{r}}$

Where:

• V is the orbital velocity.

• G is the gravitational constant.

• M is the mass of a satellite.

• r is the radius.

Substituting the value of r, we have:

$V = \sqrt{\frac{GM}{5r}}$

$V = \frac{1}{\sqrt{5}}$ × $\sqrt{\frac{GM}{r}}$

Recall, $V = \sqrt{\frac{GM}{r}}$

$V = \frac{1}{\sqrt{5}}$ × $V$

$V = \frac{V}{\sqrt{5}}$

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