Light takes 1.2 sec to get from the moon to the Earth. Assume you are looking at the moon with noticeable earth shine. If the Su
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Answer:
R=4.22*10⁴km
Explanation:
The tangential speed of the geosynchronous satellite is given by:
Because is the circumference length (the distance traveled) and T is the period (the interval of time).
Now, we know that the centripetal force of an object undergoing uniform circular motion is given by:
If we substitute the expression for in this formula, we get:
Since the centripetal force is the gravitational force between the satellite and the Earth, we know that:
Where G is the gravitational constant () and M is the mass of the Earth (
). Since the period of the geosynchronous satellite is 24 hours (equivalent to 86400 seconds), we finally can compute the radius of the satellite:
This means that the radius of the orbit of a geosynchronous satellite that circles the earth is 4.22*10⁴km.