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Explain Bot To determine the amount of work required to keep a satellite in orbit, we need to consider the gravitational potential energy and the work done against it.
The work done against gravity to keep the satellite in orbit is equal to the change in potential energy. The potential energy is given by the formula:
Potential Energy = mass x gravitational acceleration x height
In this case, the mass of the satellite is 25,000 kg, the height is 15 miles, and the gravitational acceleration is approximately 9.8 m/s^2.
First, let's convert the height from miles to meters:
1 mile = 1609.34 meters
So, 15 miles = 15 x 1609.34 meters = 24140.1 meters.
Now we can calculate the potential energy:
Potential Energy = 25,000 kg x 9.8 m/s^2 x 24140.1 meters.
The work done against gravity is the negative change in potential energy when the satellite stays in orbit. Therefore, the work done to keep the satellite in orbit is the negative of the potential energy.
Hence, to find the work done, we multiply the potential energy by -1.
Work done = -1 x potential energy
Calculating the potential energy will give you the answer to your question.