Change of radiation pressure of sunlight w.r.t. distance

[HastiM]

Hello,

Let me first describe the situation I am thinking of:
suppose we consider an object in the form of a square with some thickness (e.g. a mirror). Suppose further, that the gravitational force pulling the object towards the sun and the radiation pressure due to the sunlight are in balance (so that the object has no acceleration). If the object is far away from the sun we may consider the sun as a point source such that the radiation pressure depends on the distance r>0 between the sun and the object proportional to 1/r² (similar as the gravitational force). Hence, if we change the position of the mirror a "little bit", both forces will still cancel each other out. Now, I am wondering what would happen if we move the mirror 'close enough' towards the sun, such that it would not be appropriate anymore to treat the sun as a point source?

I would expect that the radiation pressure will not maintain proportional to 1/r². But I have no idea how it will depend on the distance r? Do you know how to investigate the situation?

I would appreciate your help very much! Best wishes

 

[jtbell]

I would expect that the radiation pressure will not maintain proportional to 1/r².

Wouldn't the gravitational force also not maintain that proportionality, in the same way?

 

[HastiM]

Thank you for your question. Honestly, I am not sure if the gravitational force would change...I assumed that it would stay the same because I thought the sun can be treated like a particle located at its center (when we assume the sun to be a perfect ball). Hence by Newton's law of gravitation, the gravitational force will point towards its center. But probably you are right, and my assumption is just wrong. Why do you think the gravitational force would change and how would it change?

 

[jtbell]

My point is that if radiation pressure is always locally outwards along a radial line, with a 1/r2 dependence (measured from the center of the sun of course), and the gravitational force is always locally radially inwards along that line, also with a 1/r2 dependence, then they should always cancel for an object with suitable mass and reflectivity.

Hmmm... can reflectivity depend on the angle of incidence? If so, that might make a difference for an extended object. The amount of momentum that radiation transfers to an object depends on whether the radiation is absorbed or reflected.

 

[jartsa]

Do we take this thing into account:
https://en.wikipedia.org/wiki/Limb_darkening

Or do we ignore the above thing so that we can use this information:
https://en.wikipedia.org/wiki/Lambert's_cosine_law

 

[jartsa]

My point is that if radiation pressure is always locally outwards along a radial line, with a 1/r2 dependence (measured from the center of the sun of course), and the gravitational force is always locally radially inwards along that line, also with a 1/r2 dependence, then they should always cancel for an object with suitable mass and reflectivity.

Near the sun the sunlight is diffuse, because the light source is large. Far from the sun the sunlight is directional, because the light source appears small.

 

[HastiM]

Thank you both very much for your help! I think Lambert's law could be a reason why the object appears some acceleration towards the sun, when the distance is not far enough. Best wishes