The work required to bring the stationary satellite back to the Earth's surface is simply the work done to change its gravitational potential energy. Recall the gravitational potential energy was defined as the amount of work required to bring an object from infinity to some distance away from the planet. Therefore additional work is required to bring an object even closer however, the work is done by the system and not by an external force.
You may be confused as to why the work is positive. Here's an explanation, although it may also seem somewhat confusing!
First of all, gravity is considered a conservative force.
A force is conservative if the work done by that force acting on an object moving between two points is independent of the path the object takes between the points.
A conservative force also has another property that can be derived from the above condition.
If an object moves from point A to point B, then the work done by a conservative force in the reverse path (i.e. point B to point A) is equal to the negative of the work done from point A to point B.
Now since the work done is a function only of the object's initial and final positions, we are free to define the potential energy function such that the work done equals the decrease in the potential energy.
In other words, the work done by a conservative force equals the negative of the change in the potential energy associated with that force, that is .
This means that while an external agent must do positive work to move an object further away from a planet, gravity itself does negative work. Conversely, while an external agent does negative work to bring an object back to the planet, gravity itself does positive work.
The law of conservation of energy tells us that a change in gravitational potential energy must be accompanied by a change in kinetic energy. Since the satellite is no longer in orbit but simply falling toward the planet .
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