It's a classic movie cliche. We see the surface of the Moon with the Earth in the distance and a dark shadow of an invading alien spaceship slowly covering the landscape.

We see this in the opening sequence of the 1996 movie Independence Day, and I can think of a few other movies which have done this effect.

What's really important is that the spaceship moves into visible frame as it passes overhead. So it's not a shadow from another orbital position, and so that also means the Sun would be directly overhead of the observer.

I've thought about where the Moon is in its orbit, where the Earth is in its orbit and where the Sun would be.

Is it possible for this to actually happen? If you were standing on the Moon, is there a time where the Earth is directly in front of you and the Sun is directly overhead. So that if something passed overtop of you the shadow would be directly on top of you?

enter image description here

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    $\begingroup$ In addition, it depends on the apparent phase of the Earth (full, new, half). In fact from the phase of Earth you know the direction of the Sun and hence whether the shadow can be correct. $\endgroup$
    – Walter
    Nov 18 '21 at 0:42
  • $\begingroup$ Is the picture under your Q a frame from such a movie? Because in that frame there is no spaceship, the observer is standing in a (ship?)shadow, the sun is not directly overhead as evidenced by the terrain-shadows, and the earth has a marked self-shadow on its underside, so my intuitive guess for the suns position would be compatible with all observations in that frame... does the movie then proceed to put the ship to the left, or something? $\endgroup$
    – loonquawl
    Nov 19 '21 at 6:37
  • $\begingroup$ Can you post a simple diagram, showing the positions of Sun, Earth, Moon, observer and spaceship? As it is, figuring out what you're describing seems like a great deal of work… $\endgroup$ Nov 19 '21 at 22:10
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    $\begingroup$ The sun could be behind the observer in the shot. The camera tilts up first, and then we finally see the alien spacecraft, when the ground is already not longer in view. This would add up with the earth being illuminated. If the sun was directly above, we should see the terminator line across the earth. Also, the orientation of the earth is wrong. We can clearly see madagascar and the horn of africa, this means we have north pole on top and south pole on bottom. If you were standing on the moon and seeing the earth, the earth should be "sideways". $\endgroup$
    – Polygnome
    Nov 20 '21 at 0:17

The Moon is always almost exactly the same distance from the Sun as the Earth is (+/- 0.25%) so shadows on the Moon work the same way they work on Earth.

What scientists have learned watching cartoons

We know from cartoons that if a piano is dropped at noon, directly above us from a very high altitude, we have no indication of this (except for the faint, descending falling piano sound that the audience recognizes) until the piano gets to only perhaps a thousand feet above us. Then a small shadow appears on the ground around our feet, slowly increasing in size.

(It's amazing how long it takes to fall a few hundred feet at terminal velocity in cartoons!)

If we were to look up, we'd see the small black outline of the piano against the disk of the Sun, growing larger, and larger.

As the piano approaches, the shadow gets bigger and darker and more piano-shaped, until the final, gratifying appearance of the smashed piano on the ground, from which the coyote slowly emerges with a big bump on their head.

We also know from cartoons that an airplane flying even higher than the piano drop point doesn't make a shadow at all.

How this works in the real world.

The Sun is about 0.5 degrees wide. If you draw a triangle from the center to the edge of the Sun with us at the vertex, that angle is 0.25 degrees.

The ratio of the short to long side is roughly 0.005 and long/short is 200.

So an eight foot grand piano starts making a noticeable shadow at 8 x 200 = one thousand feet.

The central area of a jumbo jet where the widest part of the wings meet the body is a "blob" about 70 feet in diameter (the fuselage and wings alone are skinnier extensions from that blob) so we can expect it to start making a noticeable shadow at about 70 x 200 at 14,000 feet! Yes, if a jumbo jet flew directly between you and the Sun at this altitude you'd see a fuzzy black shadow fly right over you at about 150 meters per second; it would be about 1/5 of a second blink.

Okay, and on the Moon?

Is it possible for this to actually happen? If you were standing on the Moon, is there a time when the Earth is directly in front of you and the Sun is directly overhead? So that if something passed overtop of you the shadow would be directly on top of you?

With no air nor coyotes to fall into their own falling piano traps, we'll have to assume it's a space ship passing over you on the Moon.

Below is a typical space ship we might see in space. The diameter of the saucer section is 127 meters. Using our same triangle we can then calculate that if it passes between us and the Sun closer to us than about 25 kilometers, we'll notice a substantial shadow pass over us.

But don't blink!

If it is orbiting at at 25 km altitude in low lunar orbit it will be moving at about 1700 m/s and that 173 meter diameter dish will pass by in about 1/10 of a second.

USS Enterprise

Source: quora

Just for fun (no piano)

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    $\begingroup$ Poor Wile E.! He remains my idol, though, for his perseverance, his dedication, and his never-ending supply of ACME products! ACME = American Company Making Everything! Your “falling-piano” analogy reminded me of this one: “I was wondering why the baseball was getting larger. Then it hit me.” $\endgroup$ Nov 18 '21 at 0:37
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    $\begingroup$ Wile E reminds me of climate change deniers - with all their scheme they just can't get the science right. $\endgroup$
    – Fred
    Nov 18 '21 at 0:54
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    $\begingroup$ Small remark regarding the last part: the size of the space ships from Independence day was ~25km, which would affect the visibility time window immensely. $\endgroup$
    – kopaka
    Nov 18 '21 at 12:01
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    $\begingroup$ what a great, perfect answer... for different question. This question is about angles being strange, not distances $\endgroup$ Nov 19 '21 at 20:00
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    $\begingroup$ I have seen shadows from passenger jets many times in my life. +1 $\endgroup$ Nov 19 '21 at 22:15

If the moon was at half-moon (as seen from Earth) and you were standing near the equator at 90 degrees W (ironically this puts you close to Mare Orientale) The the sun would be overhead, and Earth would be on the horizon.

This gives you the configuration you need.

However it would very hard for observers on Earth to see the shadow. If the Earth is on the horizon, then you must be on the edge of near and far sides of the moon, and the perspective would make it hard to see anything as small as a spacecraft or its shadow..

  • $\begingroup$ Great answer. Which way would the polar caps on the Earth be facing? From the perspective of the observer on the Moon, would the caps be on the top/bottom of the Earth or on the left/right? Because every time I've seen this cliche scene the caps are on the top/bottom. The Earth is in it's classical orientation. $\endgroup$
    – Reactgular
    Nov 18 '21 at 12:04
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    $\begingroup$ @Reactgular You can get an idea from the classic [“Earthrise” photo](en.wikipedia.org/wiki/Earthrise ) taken from Apollo 8 in its orbit about the Moon. In the standard “rotated” version, which makes the lunar horizon horizontal, the Earth’s South Pole is to the left and the North Pole is to the right (what you can most clearly see is that Africa is on its side). $\endgroup$ Nov 18 '21 at 14:11
  • $\begingroup$ @PeterErwin that is really cool, thanks. Shows how many times the movies get it wrong. $\endgroup$
    – Reactgular
    Nov 18 '21 at 18:20
  • $\begingroup$ Is the Earth properly illuminated in movie? $\endgroup$
    – Mazura
    Nov 20 '21 at 1:01

I think, your interpretation of the scene parameters is a bit too strict. The sun need not be exactly in zenith above your head to allow for such a shadow situation. But more on that later.

Sun in zenith with visible Earth

First, along your interpretation: It's possible, to the same amount that it is on Earth (but the screenshot doesn't match such a situation).

On Earth, to have the sun directly above you, you need to be close to the equator, and it has to be around noon. That means you have to be located close to the place on the globe pointing towards the sun. To be able to see the Moon around noon, the moon phase has to be between new moon and half moon, otherwise it would be below the horizon at noon.

The same is possible on the Moon, just exchange "Earth" and "Moon". You have to be standing close to the moon's equator, closest to the sun, earth phase must be between new earth and half earth (which implies with the moon phase being between full moon and half moon, as they complement one another).

So, the Earth could be visible, but only as a rather shallow crescent.

Relaxed constraints

If both the sun and the spaceship come from straight behind your back, the depicted visual effect is achieved as well. And with the sun lower behind your back, more of the Earth could be sunlit. A full Earth would still be impossible, as then both the sun and Earth would have to be at horizon level, meaning that the shadows wouldn't work.

Screenshot lighting

The screenshot shows an inconsistent lighting. The hills seem to be lit from the right-hand side, not too high above the horizon.

Earth is shown in nearly full phase, implying that the light source was located mostly behind the camera, slightly to the right (maybe at a 5 o'clock position), also not too high above the horizon.

As an Earth phase consistent with the hills lighting, I'd expect a half earth, with the day/night delimiter slightly tilted to the left.

And no matter which of the two inconsistent lightings we assume to be "correct", we'd end up with the spaceships's shadow being displaced to the left of its path.

  • $\begingroup$ Being on the equator will not put the sun above you during winter/summer solstice...only during the equinoxes. The tropics of cancer and capricorn define how far north/south you can be to have overhead noon sun depending on the time of year. $\endgroup$ Nov 18 '21 at 20:31

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