To determine the orbital velocity of a satellite, we can use the formula for the orbital velocity \( v \):
\[ v = \sqrt{\frac{GM}{r}} \]
where:
- \( v \) is the orbital velocity,
- \( G \) is the gravitational constant,
- \( M \) is the mass of the celestial body (e.g., Earth) around which the satellite is orbiting, and
- \( r \) is the distance from the center of the celestial body to the satellite (the orbital radius).
If the orbital radius is tripled, the new orbital radius \( r' \) can be expressed as:
\[ r' = 3r \]
We can now substitute this into the orbital velocity equation to find the new orbital velocity \( v' \):
\[ v' = \sqrt{\frac{GM}{r'}} = \sqrt{\frac{GM}{3r}} \]
This can be simplified:
\[ v' = \sqrt{\frac{GM}{3}} \cdot \frac{1}{\sqrt{r}} = \frac{1}{\sqrt{3}} \sqrt{\frac{GM}{r}} = \frac{1}{\sqrt{3}} v \]
Therefore, when the orbital radius is tripled, the new orbital velocity is:
\[ v' = \frac{v}{\sqrt{3}} \]
This means that the orbital velocity decreases by a factor of \( \frac{1}{\sqrt{3}} \).