The moon and light that bends around it

[hsdrop]

If there was a hole or a cave throw the center of a moon that would allow light to pass throw it on a solar eclipse and the moon was of big enuf mass to bend light around it during the eclipse. Which would hit the planet first? the light throw the cave or the light being bent around the moon it self and why (I am keeping in mind that the time difference would only be a very small fraction of a secant )

sorry for the crude drawing it was the best my teenage son could do when he asked me the question. and no the moon is not a death star trying to blow up the planet...

 

[PeterDonis]

Which would hit the planet first?

I don't think this question can be answered at the "B" level because there isn't an obvious simple way to decide. The light that bends around the moon will be slightly delayed (as compared to the time it would take light to travel if the moon weren't there at all); but the light that passes through the cave will as well.

There are two effects involved:

(1) Space is slightly curved by the mass of the moon, so the distance the light has to travel is greater than it would be if the moon weren't there. This is true for both paths--bending around the moon and going through the cave. I think the distance bending around the moon is slightly longer, but I would have to do the detailed math to check.

(2) The light is slightly time delayed because of gravitational redshift--it goes down into a gravity well and comes back up again. This is also true for both paths. I think the light passing through the cave is delayed slightly more because it is going deeper into the gravity well, but again I would have to do the detailed math to check.

As you can see, the two effects above, if my guesses about their relative magnitudes are correct, work in opposite directions--the first makes the light bending around arrive later, the second makes the light going through the cave arrive later. And there's no easy way to tell which one has the larger overall magnitude. So answering your question would require a detailed calculation, which can't be done at the "B" level; it requires fairly detailed math.

 

[hsdrop]

it's ok you did just fine breaking it down for him to understand what is going on with the light. thank you so much for taking the time and not going to far over his head I have tried to urge him to understand general physics better than most kids his age hopefully it will help him farther down the road in life and I'm thrilled that he is coming up with questions of this caliber on his oun

 

[Fervent Freyja]

Don't apologize for the drawing, it's more than fine and serves a purpose. I think it would be useful to have a drop-down tool with the reply box that allows members to draw a quick diagram (though smaller).

 

[hsdrop]

I believe that would be really helpful for a lot of people that have trouble visualising a lot of what other are try to describe in the thirds. Myself I got lost some of time when someone is describing something that is somewhat complex
It would also help with math coordinates as well to have a y,x or an y,x,z grid to plot on with the equations