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I am reposting an edited version of this problem from a previous post of mine, due to it not being entirely relevant to that post, and also the question was asked after the thread had been replied to, so looks like an answered question. I also aim to give more detail here.

In the American Rocket Society Journal, number 29 page 422-427, there is an article which details, amongst other things, the equations of motion for a solar sail. I would like to know how these have been arrived at.

"Let us now consider a ship propelled by solar sail in interplanetary space. The forces acting on it are Fg (the sun's gravitational force) and Fs, the force due to radiation pressure on the sail, and is equal to pA (p=p0 cos^2θ (r0/r)^2 where p0 is solar radiation pressure on a normally reflecting surface at Earth orbit, r0 = 1AU; A is the area of the sail)

Space drag is not considered. We also neglect gravitational forces due to other planets.

Under the specified conditions, the equations of motion are:

(-Fg + Fs cos θ)/m = du/dt - v^2/r ; where u is radial velocity and v is tangential velocity (making v^2/r angular velocity?) and r is distance from Sun, and m is total mass of spacecraft

and

(-Fs sin θ)/m = dv/dt + uv/r"

I can't fathom how these have been arrived at. They appear to be resolving horizontally and vertically, but why is the radial component involved in the vertical resolution and vice versa?

Also, what is the value obtained my multiplying radial and tangential velocity?

Any hints/tips would be great, or links to other resources that explain the same thing.

Many thanks.

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Equations of Motion of a Solar Sail HELP!

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