I hadn't thought about this effect! You're absolutely right. Thanks very much. (For others:) A diagram of the umbra makes this clear: https://c.tadst.com/gf

I hadn't thought about this effect! You're absolutely right. Thanks very much. (For others:) A diagram of the umbra makes this clear: https://c.tadst.com/gfx/750x500/total-solar-eclipse-com.png?1 https://c.tadst.com/gfx/750x500/total-solar-eclipse-com.png?... If you draw a few triangles, you can get an analytic expression.