Question

The Millennium Falcon is trying to stay in the Death Star’s blind spot by following a geosynchronous orbit above it. The Falcon is 2.1x10^5m above the surface of the Death Star,

which has a radius of 80 km. The Death Star has a mass of 2.3x10^18 kg and it makes one full rotation about its central axis every 22 hours. What speed does the Falcon need to maintain in order to stay in geosynchronous orbit with the Death Star ?

(Note: there is enough information given in this problem to solve it via two different, independent methods. Try to figure both of them out! They both give the same correct answer.)

Answer 1

Given:

The altitude of Millennium Falcon,

The radius of Death Star,

The orbital radius of Millennium Falcon,

Mass of Death Star,

The time period of Death Star,

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Method 1:

Given that the Millennium Falcon is in a geosynchronous orbit above the Death Star.

So the time period of the Millennium Falcon should be the same as the time period of Death Star.

Consider the Millennium Falcon

Orbital velocity = Orbital Distance/Time Period

Orbital velocity = Circumference of the Orbit/Time Period

ANSWER:

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Method 2:

Given that the Millennium Falcon is in a geosynchronous orbit above the Death Star.

The Gravitational force experienced by the Falcon will be equal to the centripetal force.

ANSWER:

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