Today is your first day as the Pilot Officer of the Imperial Super Star Destroyer Executor. Darth Vader himself has given you the order to place...

First, let's calculate the radius of the orbit of your ship, which is the distance between the ship and the center of the Death star. So it is the sum of the radius of the Death star and the altitude above its surface: 900 km + 450 km = 1350 km, or `R = 1.35*10^6`

meters.

Now we can figure out how fast the ship has to move to maintain the period of 19 hours. The period is the interval of time it takes for the ship to orbit around the star one time, that is, to cover the distance equal to the circumference of the circle with the radius of the orbit: `2piR`

The speed with which the ship has to move is distance divided by time, or

`v = (2piR)/T = (2*pi*1.36*10^6)/(19*3600) =124.9 m/s`

The speed of the ship has to be 124.9 m/s.

The mass of the Death star can now be found from the second Newton's Law. The centripetal acceleration of the ship equals `v^2/R` , and the gravitational force is

`(GMm)/R^2 = mv^2/R` , where m is the mass of the ship and M is the mass of the Death star. From here

`M = (v^2R)/(G) = 3.12*10^20`

kg.

The acceleration due to gravity on the surface of the star is

`g = (GM)/R_(star) = (6.67*10^(-11)*3.12*10^20)/(900000) =2.34*10^4`

m/s^2.

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