A satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r?(1 point)

Responses

16√v
the fraction with numerator 1 and denominator square root of 6 v

16v
1 sixth v

6v
6 v

6–√v

1 answer

To find the velocity of a satellite orbiting Earth at a new orbital radius, we can use Kepler's laws of planetary motion or the formula for the orbital velocity of a satellite.

The orbital velocity \( v \) of a satellite at a distance \( r \) from the center of Earth is given by the formula:

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

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

If we move the satellite to an orbital radius of \( 6r \), the new velocity \( v' \) becomes:

\[ v' = \sqrt{\frac{GM}{6r}} = \sqrt{\frac{1}{6}} \cdot \sqrt{\frac{GM}{r}} = \sqrt{\frac{1}{6}} \cdot v \]

Thus, the new velocity \( v' \) can be expressed as:

\[ v' = \frac{v}{\sqrt{6}} \]

This can be represented in fractional form as \( \frac{1}{\sqrt{6}} v \).

So the correct answer is:

the fraction with numerator 1 and denominator square root of 6 v