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.
1 answer