disk-disk intersection area

Question

I have two disks of radii $R_1, R_2$ with distance between centers, $d < R_1 + R_2$.

How can I find the surface area common to the two disks?

Rationale:

Solar irradiation / energy input in penumbra during solar eclipse, a problem for sun-synchronous satellites. Knowing apparent size of the Sun and the Moon, and position within penumbra it's possible to calculate how much of the solar disk remains unobscured, as a simple difference between its surface and the intersection area.

Circles or spheres? circles don't have common *Surface* areas. — Win Vineeth, Feb 08 '16 at 13:35
@WinVineeth: Ok, edited. Disks. Sun's irradiation is approximately constant over its apparent area. — SF., Feb 08 '16 at 13:43
this should get you started
http://math.stackexchange.com/questions/402858/area-of-intersection-between-two-circles — Charlie, Feb 08 '16 at 13:56
@Charlie: that one is for $R_1=R_2=d$. I'll see what I can do with it. — SF., Feb 08 '16 at 14:04

score 1 · Answer 1 · answered Feb 08 '16 at 20:04

1

The intersection is a composite of two circular segments. You can calculate the areas of these circular segments after finding the angles in the triangle with sides $R1$, $R2$ and $d$.

answered Feb 08 '16 at 20:04

Logophobic

1,057

disk-disk intersection area

1 Answers1