Dependence of force on relative position and velocity

[Felipe Lincoln]

I read that a force between two bodies can only depend on their relative position and relative velocity. But I can't understand in what is this statement leaning on and what it means.

 

[.Scott]

It means that it can't be dependent on their position of velocity relative to anything else.
In other words, if we moved planet Earth to another galaxy, but you were in the same position relative to the Earth, then you would still have the same weight.

 

[Delta2]

I think this statement is leaning (at least partially) on the translational and rotational symmetry of space. Due to those symmetries the potential V of one body due to the presence of the other body, depends only on their relative position so it is ##V(r)## where ##r=|r1-r2|##. The force is the gradient of V, ##\vec{F}=-\nabla V##.

What it means is that whether we consider gravitational forces or electrostatic forces (between electrically charged bodies), or magnetostatic forces (between magnetized bodies), or electromagnetic forces (for example the Lorenz force and the Laplace force), or nuclear forces (for example between quarks and gluons), all of these types of forces have something in common, that they can only depend on the relative position of the bodies and their relative velocities.

 

[Felipe Lincoln]

Thanks for the answers.
On what subject will I learn more about these symmetries?

 

[Delta2]

https://en.wikipedia.org/wiki/Symmetry_(physics)

I was talking about the continuous symmetries of spacetime https://en.wikipedia.org/wiki/Symmetry_(physics)#Continuous_symmetries

Which can be described by Lie Groups https://en.wikipedia.org/wiki/Lie_group

So Lie groups, Continuous symmetries, Spacetime symmetries are the subjects.