Answer:
The speed of the spacecraft should be 719.35m/s
Explanation:
if the spacecraft is orbiting the planet with a circular orbit, the gravitational force must act as a centripetal force. This means:
[tex]F_G=F_c\\\frac{GmM}{d^2}=m\frac{v^2}{d}[/tex]
In this case, the pluto's mass M is 1.3099·10^22 kg. The radius of the planet R is 1188.3Km and G is the gravitational constant. Therefore:
[tex]\displaystyle\frac{G M}{d^2}=\frac{v^2}{d}\\v=\sqrt{\frac{GM}{d} } =\sqrt{\frac{GM}{(R + 500km)} } =719.35m/s[/tex]
