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?(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
5 v

Answer 1

To determine the velocity of a satellite in orbit at a new radius, we can use the formula for the orbital velocity of a satellite, 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 original orbital radius is \( r \) and the corresponding velocity is \( v \), then at a new orbital radius of \( 5r \), the velocity \( v' \) would be:

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

This can be expressed in terms of the original velocity \( v \):

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

Thus, the new velocity \( v' \) becomes:

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

This corresponds to the option:

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

So the correct answer is:
**the fraction with numerator 1 and denominator square root of 5 v.**