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I have seen so many schematic pictures of eclipses (solar and lunar), and in all of them, the Sun's rays are focused at a specific point (left of the Earth in lunar eclipses and a slightly left of the moon in solar eclipses, or In other words, a slightly left of the Moon's orbit in both cases).

enter image description here

I'm guessing this is near the L1 Lagrangian point.

Based on the picture in Wikipedia, the gravitational waves are denser at the Lagrangian points. So maybe these waves cause the photon beams to bend and to focus?

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The figure from Wikipedia

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    $\begingroup$ The Sun's rays do not focus anywhere . You are misunderstanding the drawings, which are showing umbras and penumbras . $\endgroup$
    – Carl Witthoft
    Commented Mar 21, 2022 at 15:20
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    $\begingroup$ Umbras and penumbras are on the right side of the picture. I'm asking about the paler blue triangles between the Sun and the Earth. $\endgroup$
    – Snack Exchange
    Commented Mar 21, 2022 at 15:54
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    $\begingroup$ those simply show the limiting angle ray from the edges of the Sun to the edges of the Earth, as those define the penumbral areas. $\endgroup$
    – Carl Witthoft
    Commented Mar 21, 2022 at 16:25
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    $\begingroup$ That's just the lines showing where the different parts of the sun become visible in the umbra and penumbra. They have absolutely nothing to do with Lagrangian points or focusing of light. $\endgroup$
    – Christopher James Huff
    Commented Mar 21, 2022 at 16:28
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    $\begingroup$ Disagree with the close votes. This question provides plenty of details and clarity for a potential answer to clear up the confusion, as evidenced by the several people answering this question in the comments. $\endgroup$
    – zephyr
    Commented Mar 21, 2022 at 18:52

2 Answers 2

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The Sun's rays don't get focused, by the Earth, at L1. The Earth can act as a gravitational lens and it does have a focal length of 15,375 AU, more than five hundred times the distance to Neptune.

The two diagrams are showing completely different things, the first is the shadow of the Earth which has two components in that image: the penumbra and the umbra. The effect of gravitational lensing at this scale (1 AU) is tiny (one fifteen thousandth of the focal length). The antumbra of the Earth in that image is at the point of the darkest triangle and is around 1.3 million km from the Earth while L2 is 1.5 million km away.

You get the same effect from any light source that has an obstruction.

https://commons.wikimedia.org/wiki/File:Antumbra.jpg (Image courtesy of Wikimedia Commons)

The second diagram is not an image of graviational waves, it shows the contours of effective potential energy, these are mostly indication of classical Newtonian effects. Note that L2 is a saddle point with the gradient rising toward L4 and L5 and falling away toward (and away from) the Earth.

https://commons.wikimedia.org/wiki/File:Saddle_point.svg (Image courtesy of Wikimedia Commons)

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Yes, L1 and L2 are roughly where you point out in the diagram. You are correct, but for totally the wrong reasons (as pointed out in other answers).

This is an excerpt from the Lagrange point Wikipedia article:

The ratio of diameter to distance gives the angle subtended by the body, showing that viewed from these two Lagrange points, the apparent sizes of the two bodies will be similar, especially if the density of the smaller one is about thrice that of the larger, as in the case of the earth and the sun.

This arises because the Lagrange points occur at at distance either side of Earth of roughly:

$R_{Lagrange} \approx \pm R_{orbit} \sqrt[3]\frac{M_{Earth}}{3M_{Sun}} $.

The masses are proportional to density times radius cubed, so this can be rewritten in terms of subtended angles and densities:

$\frac{r_{Earth}}{R_{Lagrange}}\sqrt[3]{\rho_{Earth}} \approx \frac{r_{Sun}}{R_{orbit}}\sqrt[3]{3\rho_{Sun}} $

and it just so happens that the densities $\rho_{Earth} \approx 3\rho_{Sun}$

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