Position in Spherical Coordinates

[funcosed]

Homework Statement

This is a bit hard to describe without a decent picture (or a decent brain) but try to bare with me.
Picture below shows two spheres, if the origin is at centre of A, and a line d joins the centre of the two spheres, how do I describe the position of a point r from each sphere in spherical coordinates?

------------------r---------
A
------O---------------------
-----------------------------
-------------------O--------
B

Homework Equations

Polar coordinates are in terms of r and Ø
The point r described from the origin (at A) is given by (r_A,Ø_A), where r is line from origin to point r.

The Attempt at a Solution

If origin was at B it would have coordinates (r_B,Ø_B) need to write these in terms of r_A and Ø_A.
I think r_B=r_A+d and Ø=Ø_B-Ø_A

 

[tiny-tim]

hi funcosed!

why are you doing this? is it part of something else?

easiest would be to define Ø = 0 through B

(and perhaps to take the origin at the midpoint of AB instead of at A, or at the centre of mass)

 

[funcosed]

For why I am doing it see here http://www.physforum.com/index.php?showtopic=28996"

Fairly sure I know what to do for most of the question but it doesn't seem to work out because the expression I get for part 3 is a mess which I think is because of the coordinates.

 

[tiny-tim]

For why I am doing it see here http://www.physforum.com/index.php?showtopic=28996"

ah i see … there's a vertical and horizontal direction that have to be regarded as fixed

Fairly sure I know what to do for most of the question but it doesn't seem to work out because the expression I get for part 3 is a mess which I think is because of the coordinates.

the cosine and sine rules should do it …

perhaps you'd better show your work (and a diagram), so that we can see why it's a mess?

(of course, a mess might be the right answer! )

 

[funcosed]

Part.3
ψ_A(r,Θ) = (1/4)Ua²(3r/a - a/r)sin²Θ

ψ(r,Θ)_B = (1/4)Ua²((3r+d)/a - a/r)sin²Θ

Using, ψ(r,Θ) = ψ_A + ψ(r,Θ)_B
and U = U_r + U_Θ
Ur = (1/r²sinΘ)∂ψ/∂Θ
UΘ = (-1/rsinΘ)∂ψ/∂r

I get,
U = 1/2(UcosΘ)(3a/r - a³/r³ + 3a/4r²)r - 1/4(UsinΘ)(3a/r + a³/r³ + 3a/4r)Θ

which doesn't really fit with the form given in the question i.e. there are no a/d terms.

 

[funcosed]

and here's a link to a picture

http://www.picpanda.com/viewer.php?file=lxvhtadg5vbj1miuycda.png"

 

[tiny-tim]

sorry, I'm not following your equations at all