Two Earth satellites, A and B, each of mass m = 960 kg, are launched into circular orbits around the Earth's center. Satellite A orbits at an altitude of 4500 km, and satellite B orbits at an altitude of 13600 km. a) What are the potential energies of the two satellites? b) What are the kinetic energies of the two satellites? c)How much work would it require to change the orbit of satellite A to match that of satellite B?
test
To calculate the potential and kinetic energies of the satellites, we need to use the formulas for gravitational potential energy and kinetic energy.
a) To find the potential energy of the satellite, we can use the formula for gravitational potential energy:
Potential Energy = - (G * M * m) / r
where G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2), M is the mass of the Earth (approximately 5.972 × 10^24 kg), m is the mass of the satellite (given as 960 kg), and r is the distance from the satellite to the center of the Earth.
Substituting the values for satellite A, where altitude = 4500 km:
Potential Energy of Satellite A = - (G * M * m) / (r + R)
where R is the radius of the Earth (approximately 6371 km).
Substituting the values for satellite B, where altitude = 13600 km:
Potential Energy of Satellite B = - (G * M * m) / (r + R)
Calculate these values using the given formulas and the given values of G, M, m, r, and R.
b) To find the kinetic energy of the satellite, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * m * v^2
where m is the mass of the satellite (given as 960 kg), and v is the orbital velocity of the satellite.
The orbital velocity can be calculated using the formula:
v = √(G * M / r)
Substituting the values for both satellites, calculate the orbital velocities and then use the kinetic energy formula to determine the kinetic energies of satellite A and B.
c) To calculate the work required to change the orbit of satellite A to match that of satellite B, we need to find the change in potential energy.
Work = Potential Energy of Satellite B - Potential Energy of Satellite A
This will give us the amount of work required to change the orbit of satellite A to match that of satellite B.
Substitute the values for both satellites into the formula to calculate the work.