Final answer:
To change a satellite's orbit, work must be done against Earth's gravitational field, represented by the change in gravitational potential energy due to the difference in radii of the orbits. The calculation involves gravitational potential energy formulas but an exact numerical answer was not provided here.
Step-by-step explanation:
To find the work that must be done by an external force to change a satellite's circular orbit, it is essential to consider the change in gravitational potential energy associated with the different orbital radii. The orbiting satellite is initially in a circular orbit, which implies that the gravitational force provides the necessary centripetal force to keep it in motion along its path.
The work done by an external force (not the gravitational force, but the force exerted to change the orbit) in taking the satellite from one circular orbit to another is equal to the change in the gravitational potential energy, because the gravitational force is conservative. The energy required for such a maneuver is related to the work-energy principle, which for gravity is given by
W = Uinitial - Ufinal, where U is the potential energy at a given radius r from the planet center.
The potential energy for an object in Earth's gravitational field at a distance r is given by U = -G * Mearth * msat / r, with G being the gravitational constant, Mearth the mass of the Earth, and msat the mass of the satellite. As the satellite moves to a lower orbit, its potential energy increases (becomes less negative) since the radius decreases, which implies that the work done by the external force is positive.
The exact work needed should factor in the specific masses and radii involved in the scenario, as provided in your question. However, the actual calculation was not performed here and should be done using the formulas and concepts discussed.