This is what Earth eclipsing the Sun would look like from L2 (screenshot from SpaceEngine). It's no coincidence that they are similar size, because of their equal gravitational influence at L2.

That's a good question, you've got me curious about what the general form for the distance to L2 looks like. I found this which claims that the distance from the smaller body to L2 will be proportional to the cube root of the ratio of the two masses, which I guess makes sense. If we assume the density of big M stays constant as we increase its mass, following the formula for the volume of a sphere, the increase in its radius should also be proportional to the cube root of its mass, which is interesting. There are so many variables involved though that it's hard to visualize how this affects angular sizes of the objects at L2, and I kind of forgot where I was going with this lol.

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