Maths challenge

Can anyone see them?

Yes I can see them on your second try.
I agree with your assessment… both umbra and penumbra are curved to a smaller radius than your overlaid circular arc.

As an alternative to cut and paste , there is an upload button

I have extended the “Earth Moon FourTangents” drawing to include the min an max (apogee and perigree) distances of the Moon from the Earth

Clearly at apogee the penumbra shadow will be smaller and at apogee the umbra shadow will be smaller.

The Sun Earth min/max distances will also affect the result.

1 Like

Great thinking
I will get the dates of those eclipse photos, and lookup the distances in an almanac. The program astronomical almanac will do it.