Solar eclipse - What science can you do?

The only thing I can think of is the famous experiment that confirmed that gravity causes light to bend around it, basically you'd need to take higher quality images at totality and be lucky to have the sun in a bright rich starfield and then later go and compare the star field with a night sky image and see if the stars have "moved". I suppose you talking arc second measurements here.
Would you be bothered ??, I'm not.

I stand corrected, but I think what you'r suggesting Dave requires 2 very accurate time pieces at 2 points on Earth. I think something like that was done in the 1800's somewhere.

Like I implied, my knowledge on it is sketchy!

This experiment was a fake, I have read. They had manipulated the data.
It is impossible to get correct data this way, that's why no one else has tried it since then.

Maybe with todays more accurate and ease-of-synchronisation timepieces, especially from online sources (online timekeepers, that is), it could be done again?

compare the star field with a night sky image and see if the stars have "moved".

That experiment was done by Arthur Eddington et al. on 29th May 1919

en.wikipedia.org/wiki/User:Carcharoth/Ar...Eddington_experiment

It ranks as one of the greatest scientific experiments ever because it vindicated Einstein and "demoted" Newton.

Neat headline:
upload.wikimedia.org/wikipedia/commons/4..._theory_triumphs.png

Einstein was given a ticker tape parade through Broadway in New York as a result of the eclipse experiment.