Question

if the orbital radius of a satellite is doubled, how does the orbital speed change? (no calculation required.)

Explanation:

To determine how orbital speed changes when orbital radius is doubled, we use the formula for orbital speed \( v = \sqrt{\frac{GM}{r}} \), where \( G \) is the gravitational constant, \( M \) is the mass of the central body, and \( r \) is the orbital radius. If \( r \) is doubled (new \( r' = 2r \)), the new speed \( v'=\sqrt{\frac{GM}{2r}}=\frac{1}{\sqrt{2}}\sqrt{\frac{GM}{r}}=\frac{v}{\sqrt{2}}\). So the orbital speed decreases by a factor of \( \sqrt{2} \) (or is divided by \( \sqrt{2} \)).

Answer:

The orbital speed is divided by \(\boldsymbol{\sqrt{2}}\) (or decreases by a factor of \(\boldsymbol{\sqrt{2}}\)).