To determine how the velocity of a satellite changes when its orbital radius is altered, we can use the formula for the orbital velocity of a satellite in a circular orbit, which is given by:
\[ v = \sqrt{\frac{GM}{r}} \]
where \( v \) is the orbital velocity, \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the orbital radius.
If the satellite is moved to an orbital radius of \( 4r \), the new velocity \( v' \) can be calculated as follows:
\[ v' = \sqrt{\frac{GM}{4r}} \]
This can be rewritten using the original velocity \( v \):
\[ v' = \sqrt{\frac{1}{4}} \cdot \sqrt{\frac{GM}{r}} = \frac{1}{2} \cdot v \]
Thus, when the satellite is moved to an orbital radius of \( 4r \), its new velocity will be:
\[ v' = \frac{1}{2} v \]
So the correct response is:
1 half v.
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