Question

A satellite orbits the Earth at a radius r and a velocity v . If the radius of its orbit is doubled, what is its velocity?

• A. $v/2$
• B. $v/\sqrt{2}$
• C. v
• D. $\sqrt{2}/v$
• E. $2v$

Answer 1

The correct option is B $v/\sqrt{2}$

Orbital velocity of satellite $v=\sqrt{\frac{GM}{r}}$

Radius of new orbit $r^{\prime }=2r$

Thus new orbital velocity of satellite $v^{\prime }=\sqrt{\frac{GM}{2r}}=\frac{v}{\sqrt{2}}$