Question

On November 11, 2019 SpaceX launched a rocket carrying 60 satellites that would become part of the “Starlink” constellation of satellites in low Earth orbit intended to provide global broadband access. The Falcon9 rocket delivered these satellites into a “parking orbit” at an altitude of 280 km. From this parking orbit, the satellites will rely on their own internal electric thrusters to slowly raise their altitude over the next few years to their operating orbit altitude of 550 km.

1. Assuming that both the parking orbit and operating orbit are circular orbits, determine the work required by the thrusters to raise a single 227 kg satellite from the parking orbit to the operating orbit.

Answer 1

work required in just change in gravitational potential energy given as

U = - GMm /r

Where M is mass of Central body, m is mass of satellite and r is distance from center of Central body.

in parking orbit, the energy is

U_i = - 6.67e-11 * 5.97e24 * 227 / 6370000 + 280000

U_i = - 1.36e10 J

In operating orbit,

U_f = - 6.67e-11 * 5.97e24 * 227 / 6370000 + 550000

U_f = - 1.31e10 J

so,

Work = $\Delta$ U

Work = U_f - U_i

work = - 1.31e10 - ( - 1.36e10)

work = 5.376e8 J