Solid angle from closed loop

Question

I have a function $f(\theta (t),\phi(t))$ (parameterized in $t$ with $r=1$) which describes an arbitrary closed loop on the surface of a unit sphere. How do I obtain from this the solid angle subtended by the loop?

Is this closed loop a circle on the spherical surface? if not, what is the angle subtended by a generic loop? — Antonio Ragagnin, Aug 04 '14 at 13:14
A formula in terms of a line integral over some second derivative along the curve on the unit sphere has been proposed in https://arxiv.org/abs/1205.1396 — R. J. Mathar, Feb 03 '22 at 11:06
Closely related https://math.stackexchange.com/q/1200781/532409 — Quillo, Dec 23 '23 at 11:36

score 2 · Answer 1 · answered Aug 06 '14 at 00:04

2

It appears that you can indeed describe the solid angle as a contour integral along the loop, see this link.

answered Aug 06 '14 at 00:04

Victor Liu

3,771

Hello! The link is broken, may you add an updated reference? – Quillo Dec 23 '23 at 11:29

Solid angle from closed loop

1 Answers1

Linked