# The effect of gravitational lensing during the lunar eclipse

During the lunar eclipse, the Moon turns into bloody colour while the shadow of the Earth is casting over the lunar surface. The red hue can be explained by means of the refraction of light and Thomson scattering. Besides these two, will the gravitational lensing effect take a role in the eclipse? That is, the Sun light is bent due to the Earth and shone onto the lunar surface, and then the light is reflected towards the Earth. If so, how significant will this effect be?

• The moon's red hue can be explained by scattering, but not by refraction. Shorter wavelengths are bent more than long, so any color shift from refraction will be towards blue, not red. This is apparent in the "green flash" sometimes seen seconds after sunset. If you observed the eclipse from the Moon (it would be a Solar eclipse, not a Lunar eclipse) the Earth's disk would be rimmed in red since you would be observing every sunset and sunrise at the same time. Nov 22, 2021 at 0:17

Yes, the Earth will act as a (very, very weak) gravitational lens bending light from the Sun on its way to the Moon. No, this won't have any noticeable effect, unless you are looking at the Sun with an array of radio detectors spanning the surface of the Moon (maybe).

We can use the following equation to calculate the angle of deflection for light that passes within a distance $$b$$ of some mass $$M$$ (source) $$$$\alpha = \frac{4 G M}{c^2 b}$$$$ Taking $$M$$ to be the mass of the Earth and $$b$$ to be the radius of the Earth, we find $$$$\alpha = \frac{4 G M_\oplus}{c^2 R_\oplus} = 3\times 10^{-9}\ {\rm rad} = 0.6\ {\rm milliarcseconds\ (mas)}$$$$

Remarkably, apparently this level of lensing is around the order of magnitude that modern technology can resolve (https://arxiv.org/abs/1902.07046) which is able to detect gravitational lenses at the milliarcsecond level. However to see the effect of Earth's lensing, I imagine you would need a very long baseline radio telescope array on the Moon (although, I am not an expert on the technology, so take what I'm saying with a grain of salt). In this context, "very long baseline" means an array spanning thousands of miles. Regardless, this nanoradian level of deflection is not something that would have a noticeable effect on a photograph of the eclipse you would take with an ordinary camera.

• Would the variation in the refraction due to Earth's atmosphere swamp this effect? Would it be possible to filter that out? Nov 21, 2021 at 13:51
• @Barmar Let me put it this way. I found it interesting that VLBI has the angular resolution to be able to see milliarcsecond deflections. If for some reason one actually wanted to measure this effect, there is a lot more work to do to control for factors beyond angular resolution that would affect the observation, and there likely are many (including the atmosphere) that could ruin the experiment before it even starts. But, experimentalists are also very clever at figuring out what these things are and controlling them. Take this as more "not obviously impossible" than "definitely possible." Nov 21, 2021 at 14:01

Earth's gravity is far to weak to make much difference. But the Sun's gravity makes a solar lens that could be used as a telescope, if we devoted enough resources and ingenuity to it. We could literally map the surface of an exoplanet $$100$$ light years away at $$25$$ km/pixel. See The Solar Gravitational Lens will Map Exoplanets. Seriously.