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) Responses 15√v the fraction with numerator 1 and denominator square root of 5 v 15v 1 fifth v 5–√v square root of 5 v 5v

To determine the velocity of a satellite at a new orbital radius, we can use the formula for orbital velocity, which is given by:

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

where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth, and
- \( r \) is the orbital radius.

If the satellite is moved to an orbital radius of \( 5r \), the new velocity \( v' \) at that radius can be expressed as:

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

This can be simplified to:

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

Substituting \( v = \sqrt{\frac{GM}{r}} \) (the original velocity at radius \( r \)), we get:

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

Thus, the new orbital velocity when the satellite is at an orbital radius of \( 5r \) is:

**The fraction with numerator 1 and denominator square root of 5 v**

This is the correct answer.