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?(1 point)

Question

Responses

1/√5 v
the fraction with numerator 1 and denominator square root of 5 v

1/5 v

√5v
square root of 5 v

5v
5 v

Answer 1

To find the new velocity of a satellite when it is moved to an orbital radius of \(5r\), we can use the formula for the orbital speed of a satellite, which is given by:

\[ v = \sqrt{\frac{GM}{r}} \]

where \(G\) is the gravitational constant and \(M\) is the mass of the Earth.

When the orbital radius is changed to \(5r\), the new velocity \(v'\) will be:

\[ v' = \sqrt{\frac{GM}{5r}} = \sqrt{\frac{1}{5}} \sqrt{\frac{GM}{r}} = \frac{1}{\sqrt{5}} v \]

Thus, the correct response that represents the velocity of the satellite when moved to an orbital radius of \(5r\) is:

\(\frac{1}{\sqrt{5}} v\)

So, the answer is:

1/√5 v