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

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

Answer 1

To find the new velocity of a satellite when the orbital radius is changed, we can use the formula for the orbital velocity of a satellite in circular orbit, which is given by:

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

where:

• \( G \) is the gravitational constant,
• \( M \) is the mass of the Earth,
• \( r \) is the orbital radius.

If the radius is changed from \( r \) to \( 5r \), we can calculate the new velocity \( v' \) at this new radius:

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

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

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

So, the correct response is:

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