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