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

1/5v
1 fifth v

5–√v
square root of 5 v
5v

Answer 1

To determine the velocity \( v' \) of a satellite moved from an orbital radius \( r \) to an orbital radius of \( 5r \), 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 and \( M \) is the mass of the Earth.

For the new orbital radius \( 5r \):

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

Thus, the velocity of the satellite at the orbit of radius \( 5r \) is:

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

So, the correct response is:

1/5√v