How was the direction of force lines determined.

[Little Bang]

Text books tell us that the force lines of an electrons field point to the electron. The force lines of a proton point away from the proton. Can someone point out the experiment that determined this or was it just a matter of convention about the direction they point.

[sanctus]

Just a convention as the sign of a charge. Actually it is even an antilogic convention, but back then they didn't know much of the formulas we have today. That is why for example the direction of flow of electrons is the opposite of the the current.

This is for example why the Lorentz force equation for an elctron has a minus:

[math]F=-e(\vec{v}\times\vec{B})[/math]

which is no problem, because we know that the elctron has negative charge, but since they flow in wires it would much more obvious to have the other convention.

[Little Bang]

Then the detection of an electrons field requires that we use the motion of a proton or the motion of another electron?

[Little Bang]

But with gravity the force lines of Earth point at the Earth and the force lines of the Moon point at the Moon?

[Pyrotex]

But with gravity the force lines of Earth point at the Earth and the force lines of the Moon point at the Moon?

Remember, "lines of force" are just graphical tools that we use to understand and explain. If it makes sense to put arrow-heads on a line of force for electric fields (and it does) then we draw arrowheads. If it doesn't make sense to do that for gravitational fields (and it doesn't) then we don't draw arrowheads on the lines.