Answer :
The work done in propelling a satellite to a certain height is calculated by finding the change in gravitational potential energy. For heights of 100 miles and 300 miles above the Earth, you'll use the potential energy formula accounting for the satellite's mass and the Earth's radius plus the height.
To calculate the work done in propelling a satellite to a certain height, we need to use the concept of gravitational potential energy (GPE). The work done against gravity to lift an object is equal to the change in its potential energy. The equation for potential energy at a distance r from the center of the Earth is GPE = -G M m / r, where G is the gravitational constant, M is the mass of Earth, and m is the mass of the satellite. The negative sign indicates that we are considering the potential to be negative with respect to being infinitely far away from Earth, which is the zero reference point.
For the first part, to find the work done to lift the satellite 100 miles above the Earth, we have:
W100 = GPEfinal - GPEinitial = ( -G M m / (RE + h100) ) - ( -G M m / RE )
For the second part, the work done to lift the satellite 300 miles above the Earth, the calculation is similar:
W300 = GPEfinal - GPEinitial = ( -G M m / (RE + h300) ) - ( -G M m / RE )
To solve for the actual values, we need to convert miles to meters (1 mile = 1609.34 meters), use Earth's mass
(M = 5.97 x 1024 kg), the gravitational constant (G = 6.67 x 10-11 Nm2/kg2), and the mass of the satellite (m = 6000 kg, since 1 ton = 1000 kg).
After calculating the work done using the above expressions, we find that the work done to move the satellite to 100 miles and 300 miles above the Earth are specific values that depend on the input constants and calculations.
