Answer:
[tex]\frac{v}{\sqrt{2}}[/tex]
Explanation:
To solve the problem, we can equate the gravitational force that keeps the satellite in orbit with the centripetal force:
[tex]G\frac{Mm}{r^2}=m\frac{v^2}{r}[/tex]
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the satellite
v is the orbital speed of the satellite
r is the distance of the satellite from the planet's centre
Solving the formula for v,
[tex]v=\sqrt{\frac{GM}{r}}[/tex]
If the planet has half of the initial mass: [tex]M' = \frac{M}{2}[/tex], the new orbital speed of the satellite will be
[tex]v'=\sqrt{\frac{GM'}{r}}=\sqrt{\frac{GM}{2r}}=\frac{1}{\sqrt{2}}\sqrt{\frac{GM}{r}}=\frac{v}{\sqrt{2}}[/tex]
