Superpositon of energies vs. Superposition of forces

[kmarinas86]

I cannot see how the two can be mutually inclusive. If you super impose particles with potential energies that fall off as 1/r that are homogeneously distributed through space then take the gradient of them, I hardly believe that they will result in the exactly the same thing than if you take the 1/r^2 distance for each one.

Must superposition of forces be mathematical equivalent to superposition of energies, without exception? I have a feeling they clash and contradict each other. Can someone let me know how, why? Thanks

 

[tiny-tim]

I cannot see how the two can be mutually inclusive. If you super impose particles with potential energies that fall off as 1/r that are homogeneously distributed through space then take the gradient of them, I hardly believe that they will result in the exactly the same thing than if you take the 1/r^2 distance for each one.

Must superposition of forces be mathematical equivalent to superposition of energies, without exception? I have a feeling they clash and contradict each other. Can someone let me know how, why? Thanks

Hi kmarinas86!

Gradient(a) = ( ∂a/dx , ∂a/∂y , ∂a/∂z ) …

Gradient(a + b + c + … ) = Gradient(a) + Gradient(b) + Gradient(c) + …

 

[kmarinas86]

Hi kmarinas86!

Gradient(a) = ( ∂a/dx , ∂a/∂y , ∂a/∂z ) …

Gradient(a + b + c + … ) = Gradient(a) + Gradient(b) + Gradient(c) + …

I had trouble understanding how L4 and L5 points works if they were simply the superposition of forces.

How does an object orbit an L4 and L5 point work in relation to the superposition of forces and energies? Thanks for your participation so far! :)

 

[tiny-tim]

Lagrange points

I had trouble understanding how L4 and L5 points works if they were simply the superposition of forces.

How does an object orbit an L4 and L5 point work in relation to the superposition of forces and energies? Thanks for your participation so far! :)

Hi kmarinas86!

It's the same as a geostationary satellite … the geostationary satellite feels a force, but a "laboratory" frame, rotating with the earth, regards it as stationary.

Similarly, the L4 etc points are orbiting the sun as fast as we are … they're only stationary as seen in the appropriately rotating frame …see http://en.wikipedia.org/wiki/Lagrange_points …

As seen in a rotating reference frame with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the centrifugal force are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies.