Question

Suppose that the Millennium Falcon orbits the Death Star 20,000m above the Star’s surface. Calculate the circular orbit velocity in m/s

Answer 1

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:

$G\frac{Mm}{(R+h)^2}=m\frac{v^2}{R+h}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant

$M=5.1\cdot 10^{17} kg$ is the mass of the planet

$m=1.36\cdot 10^6 kg$ is the mass of the Millennium Falcon

$v$ is the orbital velocity of the Millennium Falcon

$R=\frac{160,000 m}{2}=80,000 m$ is the radius of the Death Star

$h=20,000 m$ is the altitude of the Millennium Falcon above the planet's surface

Solving the equation for v, we find the orbital velocity:

$v=\sqrt{\frac{GM}{R+h}}=\sqrt{\frac{(6.67\cdot 10^{-11})(5.1\cdot 10^{17} kg)}{80,000 m+20,000 m}}=18.4 m/s$