Suppose that the Millennium Falcon orbits the Death Star 20,000m above the Star’s surface. Calculate the circular orbit velocity in m/s
![Suppose that the Millennium Falcon orbits the Death Star 20000m above the Stars surface Calculate the circular orbit velocity in ms class=](https://us-static.z-dn.net/files/dd4/542de9b91e39b458bafbcee847869856.png)
Answer:
18.4 m/s
Explanation:
The gravitational force between the Death Star and the Millenium Falcon is equal to the centripetal force that keeps the Millenium Falcon in circular orbit:
[tex]G\frac{Mm}{(R+h)^2}=m\frac{v^2}{R+h}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the gravitational constant
[tex]M=5.1\cdot 10^{17} kg[/tex] is the mass of the planet
[tex]m=1.36\cdot 10^6 kg[/tex] is the mass of the Millennium Falcon
[tex]v[/tex] is the orbital velocity of the Millennium Falcon
[tex]R=\frac{160,000 m}{2}=80,000 m[/tex] is the radius of the Death Star
[tex]h=20,000 m[/tex] is the altitude of the Millennium Falcon above the planet's surface
Solving the equation for v, we find the orbital velocity:
[tex]v=\sqrt{\frac{GM}{R+h}}=\sqrt{\frac{(6.67\cdot 10^{-11})(5.1\cdot 10^{17} kg)}{80,000 m+20,000 m}}=18.4 m/s[/tex]