System of two masses interacting and the notion of work Assume an isolated system consisting only of the earth and a basketball interacting through the gravitational force: No air, no other planets/stars etc. Are the following statements accurate?


*

*The total kinetic energy for the system depends on the speed at which the earth and the ball are moving toward or away from one another

*The potential energy depends on the distance between the earth and the ball

*The internal system-work of earth on ball depends only on the change in speed of the ball (and the current size of the gravitational force of earth on ball)

*The internal system-work of ball on earth depends only on the change in speed of the earth (and the current size of the gravitational force of ball on earth... which would be the equal/opposite of earth on ball).

*Potential energy changes never come into the bookkeeping for one of the work calculations from #3 because work is defined to depend on the change in speed of a mass (and the force on the mass).

 A: You can determine the net work done on an object two ways.
1) Calculate it's change in kinetic energy:
$$W_{net}=\Delta K$$ 
2) Directly add up the work done by all forces on the object. 
$$W_{net}=\sum_i\int \mathbf F_i\cdot\text d \mathbf x$$
In your case, we only have one force acting on each of our objects, and it is conservative. Therefore, we can also use the fact that the work done on an object is equal to the negative of its change in potential energy
$$W_{cons}=-\Delta U$$
It seems like your points 3-5 is trying to get you to say that only one of these three is the "right way" to find the work done on an object, when in reality all three are equivalent and equally valid. 
Another point to be made. The work done does not depend on the speed of the object alone. It depends on the kinetic energy, which depends on the mass of the object in addition to its speed. A more massive object moving slowly can have the same kinetic energy as a less massive object moving fast.
Similarly, the work done by a force does not depend on the magnitude of the force alone. It depends on the distance over which the force acts as well. A large force acting over a small distance can perform the same amount of work as a small force acting over a large distance.
With all of that being said, your question seems to have some areas where it could be more specific.
