A satellite orbits a non-uniform asteroid where the magnitude of the inward gravitational force \(F\) exerted on the satellite varies with distance \(r\) from the center of the asteroid, as shown in the graph. The satellite activates its thrusters to transition slowly from an initial stable circular orbit of radius \(r = 2.0 \times 10^6 \text{ m}\) to a final stable circular orbit of radius \(r = 6.0 \times 10^6 \text{ m}\). What is the total mechanical work done by the thrusters on the satellite during this orbital transition?