Answer :
Final answer:
To move the satellite into a circular orbit at a higher altitude, we need to calculate the change in potential energy. The energy needed to move the satellite into the new orbit is equal to the change in potential energy.
Explanation:
To move the satellite into a circular orbit with altitude 208 km, we need to calculate the change in potential energy. The potential energy of an object in orbit is given by the equation PE = -rac{GMm}{r}, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance from the center of the Earth. We know the mass of the satellite is 989 kg and the distance from the center of the Earth is 109 km for the original orbit, so we can plug in these values to calculate the initial potential energy.
Next, we can calculate the potential energy for the new orbit with altitude 208 km. The only difference is the distance from the center of the Earth, so we can plug in this new value and calculate the final potential energy. The change in potential energy is then the difference between the final and initial potential energies.
The energy needed to move the satellite into the new orbit is equal to the change in potential energy. This energy can be added to the system by using a rocket or other means of propulsion.
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