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  1. Is it ever possible to see Earth's shadow on other planets?

  2. How would the shadow present, and what would be the magnification, equipment, or other conditions necessary to see it?

  3. Is there any way of using such a phenomenon to help prove that the Earth is a spheroid?

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  • $\begingroup$ I just edited further and changed "Yes!" to "Maybe!" and saw that you'd already accepted. I don't think it changes my answer much but just wanted to let you know. I think that this is a really interesting question btw! $\endgroup$ – uhoh May 6 '20 at 3:12
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tl;dr:

Is it ever possible to see Earth's shadow on other planets?"

No but this is really interesting because the answer to

Is there any way of using such a phenomenon to help prove that the Earth is a spheroid?

is Yes Maybe!


We couldn't actually "see the shadow" as explained in other answers. Seen from the outer planets Earth would be transiting the Sun and anyone at some particular location on that planet could see the slightly-oblate profile of the Earth through a telescope, but from Earth it would be detectable as only a very slight dimming of the planet when we got between it and the Sun.

If the Sun were a sharp-edged flat disk which it's not, the shape of the light curve could reveal the shape of Earth's profile. If Earth were a point it would be a step function, if it were a square it would be a ramp, and if it were a circle (which it is almost exactly) then it would be... whatever that curve is called.

The Earth's diameter is 1/109 as big as the Sun, so if the Sun were a sharp-edged flat disk which it's not the dip in the light curve of the planet during a transit of Earth would be about $8 \times 10^{-5}$ (less than one hundredth of one percent) and it would take about 7 minutes to cross the edge of the Sun's disk (if it had an edge) seen from one point on a planet, so this is a perfectly reasonable measurement to try with the right equipment.

The actual light curve would be even longer because different parts of the planet will see the transit differently, but if we chose Mars for example the contribution due to its finite size would be smaller than that of Earth's size, so it could be accounted for.

Why do I keep saying "If the Sun were a sharp-edged flat disk which it's not"? Because it's not. The sun gets increasingly dim near the edge, so the size of the dip will be way smaller.

You don't need a large telescope to get plenty of light form Mars at opposition during an Earth transit. What you need is a very low drift and sensitive experiment, which means some experience and some clever design. However the limb darkening may make the shape of Earth's profile nearly impossible to measure because it depends so strongly on both the limb darkening itself and the model you use to account for it. For more on its shape see

and

This is a little bit like what I was thinking about in this answer to Can we detect the projected ISS shadow on the earth surface?

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    $\begingroup$ TL;DR is "the umbra generated by Earth is relatively short compared with the distance to the next planet" , right? $\endgroup$ – Carl Witthoft May 6 '20 at 14:56
  • $\begingroup$ Oh, and given current crazitheory, the shadow observations can only show the cross-sectional shape of Earth Spheroid and Disc will have the same shadow parameters :-) $\endgroup$ – Carl Witthoft May 6 '20 at 14:59
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First, the Moon is not a planet and therefore not applicable to this question. Second, the inferior planets, specifically Mercury and Venus cannot have a shadow cast by the Earth because their orbits are inside those of Earth. Notice I did not say they are between the Sun and the Earth, as they could be in superior conjunction with the Earth (opposite side of the Sun from Earth).

The superior planets (Mars out to Neptune) are candidates for the casting of shadow of the Earth by absence of light from the Sun, however we need to explain the difference between umbra (Latin:shadow) and penumbra. Let's first use the Moon as an example. The umbra (darkest part of the shadow) is the shadow cast by the Earth into space whereby an observer cannot see the Sun at all. This happens during a total Earthly eclipse of the Moon (not a lunar eclipse). You would be in complete darkness on the Moon. If the Earth and the Moon were the same size, the umbra cast by the Earth would continue out into space past the Moon the same distance that the Moon is from the Earth. However, since the Earth's diameter is about 3.5 times that of the Moon, the umbra extends further, but not all the way to the nearest planet, Mars. So the Earth's umbra will not even reach the nearest of planets.

However, the penumbra (Latin:partial shadow) in theory, extends out to infinity. First, in order to have shadow, there must be a source of light. So if you can "see" the light source, then there is also a penumbric shadow associated with that source anytime any matter comes between the observer and the source. The term "see" in your question is the matter. With the average unaided human eyeball, two of them in fact, there is not enough light sensitivity to detect a difference of penumbric shadow on a planet. However, with a ultra sensitive telescope one might be able to detect changes in the intensity of light from one time moment to the next. In fact, current research in finding planets orbiting nearby stars uses a similar method called the exoplanet transit or transit photometry method. So, a very sensitive telescope could see the Earth's penumbric shadow when measured over a long time period, but the human eye is not sensitive enough.

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    $\begingroup$ Why are people talking about the moon? I never once mentioned the moon in my question. I’m so confused. If anything, mentioning the moon for completeness would seem better as more of a P.S. $\endgroup$ – ErikE May 6 '20 at 2:08
  • $\begingroup$ First the moon comment is not @ErikE. $\endgroup$ – Hogdriver May 6 '20 at 2:18
  • $\begingroup$ more about the concept of the "very sensitive telescope" for penumbral detections (which are really photometric transit measurements of "endoplanets"! (as opposed to expolanets)) see answers to Can we detect the projected ISS shadow on the earth surface $\endgroup$ – uhoh May 6 '20 at 2:41
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    $\begingroup$ @erike moon and earth in some sense can also be regarded as double planet. The moon's path around the sun is completely convex. $\endgroup$ – planetmaker May 6 '20 at 5:52
  • $\begingroup$ @usernumber Yes. I did forget about Neptune. $\endgroup$ – Hogdriver May 6 '20 at 17:23
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  1. Although we are able to see Earth's shadow on the moon during a lunar eclipse, for other planets, the most we would see is a dot (Earth) passing across the face of the Sun. According to the link below, the farthest Earth's umbral shadow extends is 870,000 miles into space.

Earth's Shadow

  1. The size of the Earth would depend on the planet or satellite one is observing from.

  2. The only visible shadow is that in a lunar eclipse which has been used as evidence of the Earth's shape.

Lunar Eclipse

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    $\begingroup$ And second... this doesn’t really answer my questions. $\endgroup$ – ErikE May 6 '20 at 2:10
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    $\begingroup$ -1 because it doesn't answer the question $\endgroup$ – uhoh May 6 '20 at 2:38
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    $\begingroup$ People are talking about the moon because it is the obvious comparison. You can see the shadow of the Earth on the moon. Your second question is unclear by "it" do you mean the shadow or the Earth. I'd guess you mean "the shadow". This seems to answer Q1 (no the umbral shadow doesn't extend beyond 870000) and so Q2 and Q3 are therefore unanswerable, but it is worth mentioning shadows can be used. $\endgroup$ – James K May 6 '20 at 5:42
  • $\begingroup$ @JamesK I don't think it is obvious. I asked about "other planets". I am also mystified that anyone could think "How big would it be" and "clearly see it" could refer to the Earth rather than its shadow. It doesn't seem like any guessing is required. And no, I don't agree this answer does in fact answer Q1. $\endgroup$ – ErikE May 6 '20 at 19:04

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