Problem with going from plane polar coordinates to spherical polars/harmonics.
I've read that in plane polars, the function 1/R-r where R(R, theta1) and r(r, theta2) are different and at different angles can be expanded by the cosine rule(I think it is) and the binomial expansion. Seems to produce a Legendre series.

BUT that's for the case of R and r being in the same plane.
If they're not, I THINK that I've read that spherical polar coordinates are needed, and that the expansion becomes a series in spherical harmonics.
R(R, theta1, phi1), r(r, theta2, phi2)

My source, an old book on

Question

Problem with going from plane polar coordinates to spherical polars/harmonics.
I've read that in plane polars, the function 1/R-r where R(R, theta1) and r(r, theta2) are different and at different angles can be expanded by the cosine rule(I think it is) and the binomial expansion. Seems to produce a Legendre series.

BUT that's for the case of R and r being in the same plane.
If they're not, I THINK that I've read that spherical polar coordinates are needed, and that the expansion becomes a series in spherical harmonics.
R(R, theta1, phi1), r(r, theta2, phi2)

My source, an old book on

osprey · Answer

My source, an old book on Elec and Mag goes throug it in about a page and a half, most of which is ... well ... hmmmmm.
Anyone got any thoughts ?

holsteremission · Answer

Could you post a picture of the text? It might help to see how exactly the material is treated.

osprey · Answer

@HolsterEmission
Rather loud title for the scan of two of the pages.

osprey · Answer

4-4 Our galaxy is about 10^5 light years across, and the most energetic particles known have an energy of about 10^19eV. How long would it take a proton with this energy to traverse the galaxy as measured in the rest frame of The galaxy ? (10^5 yrs) The particle ? (5 mins)