<p>The short answer is no. The alignment occurs, but the eclipse does not, due to the distances and size differences involved.</p>
<p>There are a few things to consider here. You already mentioned a lot of them, I'll address those considerations separately.</p>
<hr />
<h2>Alignment</h2>
<blockquote>
<p>are alignements of the Sun and two planets actually possible (and if so, how frequent)?</p>
</blockquote>
<p>We can intuitively gauge this, as we've seen this happen during the transit of Venus:</p>
<p><a href="https://i.sstatic.net/tnQddm.jpg" rel="noreferrer"><img src="https://i.sstatic.net/tnQddm.jpg" alt="enter image description here" /></a></p>
<p>This situation describes your scenario. The sun, Venus and the Earth are aligned (within some reasonable range).</p>
<p>But, in fairness, you're asking about any of the planets, not just Earth and Venus. So is this possible for any other (or possible even all) combinations of two planets?</p>
<p>This is two questions in one: Do two planets' orbits overlap, and do these planets ever find themselves at this overlap point at the same time?</p>
<p><strong>Do two planets' orbits overlap?</strong></p>
<p>Quite interestingly, not only can they overlap, they <em>must</em> do so. The only way for two orbits to never overlap would be if they were parallel to each other (e.g. one orbit around the equator and one orbit around the tropic of cancer), but that second orbit is impossible.</p>
<p>All orbital planes must intersect with the parent body's center of mass. It's not possible to have an orbit that does not. To put it into visual terms:</p>
<p><a href="https://i.sstatic.net/uaMkZ.png" rel="noreferrer"><img src="https://i.sstatic.net/uaMkZ.png" alt="enter image description here" /></a></p>
<p>There is no way to position these two orbits in a way that they (a) are physically valid and (b) not have any overlap.</p>
<p><strong>Do these planets ever find themselves at this overlap point at the same time?</strong></p>
<p>The only way for them to <em>not</em> find themselves at this overlap point would be if their orbits were periodic. I would argue that <em>perfect</em> periodicity is unlikely to occur in nature, but that's an intuitive argument.</p>
<p>Looking at <a href="https://space-facts.com/orbital-periods-planets/" rel="noreferrer">the planets' orbital periods</a>, none stand out as being particularly periodic. I'm unsure if we can ever prove that our measurements or orbital period at any given time have perfect precision to conclude that perfect periodicity exists.</p>
<p>Other answers have already indicated the frequency with which such overlaps could occur. I'm mostly interested in whether they can occur or not, to see if we can conclude that your idea is <em>possible</em> or not.</p>
<hr />
<h2>Casting a shadow</h2>
<p>So far, we haven't actually disproven the theory. Orbital planes will overlap, and our planetal orbits are not periodic so they will eventually overlap. But now we get to the other part: the shadow. Will the shadow of the nearest planest reach the furthest planet?</p>
<p>Let's look at the expected size of the shadow. Do you think it will be larger or smaller than the planet who casts it?</p>
<p>The simple rule of thumb here is that if a shadow is larger than the object itself, then the object itself must be larger than the light source. If instead the light source is significantly bigger, then the object's shadow will shrink, and effectively disappear past its focal point.</p>
<p><em>Note: I call it a &quot;focal point&quot; because of what it looks like on a diagram, and for lack of a better name. If anyone has a more official term, I'd be happy to hear it.</em></p>
<p>To put it in visual terms:</p>
<p><a href="https://i.sstatic.net/iQ4KZ.png" rel="noreferrer"><img src="https://i.sstatic.net/iQ4KZ.png" alt="enter image description here" /></a></p>
<p>I don't think we need to explain how much bigger the Sun is compared to any of the planets.</p>
<p>The relative size of the Sun vs any planet renders the penumbra negligible. It could possible be perceived by lightsensitive equipment (edit: I don't know if it can be perceived, I just can't prove that it can't be perceived), but not by a human who observes this while standing on the further planet. It won't look like an eclipse. I refer back to the transit of Venus:</p>
<p><a href="https://i.sstatic.net/tnQddm.jpg" rel="noreferrer"><img src="https://i.sstatic.net/tnQddm.jpg" alt="enter image description here" /></a></p>
<p>Given the significant size difference between the Sun and planet, and the massive distances between the planets themselves, it doesn't seem feasible for the umbra to even reach the next planet's orbit before it hits its focal point, which is why we don't describe such a transit as an eclipse.</p>
<p>NASA explains this on <a href="https://www.nasa.gov/content/eclipses-and-transits-overview" rel="noreferrer">their website</a>:</p>
<blockquote>
<p>Like an eclipse, a transit occurs when one object appears to pass in front of another object. <strong>But in a transit, the apparent size of the first object is not large enough to cast the second into complete shadow</strong>. Instead a much smaller dark shadow makes its way across the face of the further planet or star.  Perhaps the most famous recent transit was that of Venus across the face of the sun in 2012.</p>
</blockquote>
<hr />
<h2>Casting a shadow - intuitive explanation</h2>
<p>There's a more intuitive way to express this. If a certain object (nearest planet) can block a light source (Sun), that means that from the point of view of the observer (on the furthest planet), the object must appear to be bigger than the light source. There's a quite well-known scene from Apollo 13 that showcases this:</p>
<p><a href="https://i.sstatic.net/PfbiE.jpg" rel="noreferrer"><img src="https://i.sstatic.net/PfbiE.jpg" alt="enter image description here" /></a></p>
<p>Tom Hanks (as Jim Lovell) is blocking out the moon using his thumb. Even though the moon is much bigger than Tom Hanks' thumb (citation needed), the relative closeness of his thumb to his eye (compared to that of the moon) makes the thumb <em>appear</em> bigger than the moon.</p>
<p>Let's say that Tom Hanks puts down his hand, and Chris Hadfield sticks his thumb out of the window of the ISS. His thumb is perfectly aligned between the moon and Tom Hanks' eye. We assume his thumb is the same size as Tom Hanks' (citation needed).<br />
This wouldn't block out the moon anymore from Tom. But why is that?</p>
<p>Very simply put, even though the thumb is the same size, the relative distances between the eye, thumb and moon have changed. And now, Chris Hadfield's thumb does not <em>appear</em> to be bigger than the moon, when observed by Tom Hanks. And therefore, it can no longer block the moon from Tom Hanks' view.</p>
<p>So, we can reformulate your eclipse question: <strong>Is there any planet which <em>appears</em> to be bigger than the Sun, when observed from another planet?</strong></p>
<p>The answer is no.</p>
<p><em>Edit: I've decided to make the below text easier to parse, by talking about the Earth and Venus. These are just examples, the same applies to any combination of planets, where Earth = furthest and Venus = nearest.</em></p>
<p>If you assume that the Sun is <code>X</code> times larger (in diameter!) than Venus, and the sun is <code>Y</code> times further from Earth than Venus is from Earth, then Venus will appear to be bigger than the sun (when standing on Earth) when <code>X &lt; Y</code>.</p>
<p>In other words, when measuring the distance from Earth, the sun needs to be <em>further away</em> than Venus, by a larger factor than the sun is <em>bigger</em> than Venus.<br />
As a simple example, if the sun were exactly 5 times bigger than Venus, it would have to be &gt;5 times as far from Earth as Venus is, for it to appear to be smaller than Venus.</p>
<p>If you look up the numbers for planet diameters and orbital radii, you'll notice that this doesn't happen in our solar system. Not even close. This is because the sun is simply too big relative to any ratio of two planetary orbits.</p>

CC BY-SA 4.0
2020-11-09T15:10:46.840Z
2020-11-09T15:45:13.960Z
2020-11-09T15:45:13.960Z
Flater
<p>In our solar system, it is possible for one planet to partially eclipse the sun, but it is not possible for any planet to cause a full solar eclipse as seen from another planet.</p>
<p>The sun is too big and the planets are too small and too far apart.  Transits occur, and can occur for any pair of planets, but they are very rare.  As seen from earth, Mercury only transits a dozen or so times per century, and before 2004, the last time Venus had transited the sun was 1882. <a href="http://www.eclipsewise.com/transit/transit.html" rel="noreferrer">http://www.eclipsewise.com/transit/transit.html</a> Orbital periods increase for the planets further away from the sun, so transits across the sun by the outer planets (while possible since no planets are in orbital resonance since Pluto got kicked out) are increasingly rare. Michael Seifert dug up these treasures, documenting transits of the outer planets: <a href="https://web.archive.org/web/20120609103443/https://en.wikipedia.org/wiki/Transit_of_Jupiter_from_outer_planets" rel="noreferrer">Jupiter</a>, <a href="https://web.archive.org/web/20120605054027/https://en.wikipedia.org/wiki/Transit_of_Saturn_from_outer_planets" rel="noreferrer">Saturn</a>, <a href="https://web.archive.org/web/20120605054035/https://en.wikipedia.org/wiki/Transit_of_Uranus_from_Neptune" rel="noreferrer">Uranus</a>.  As expected, the transit of Uranus from Neptune is the rarest, occurring next in October, 38172 CE.</p>
<p><strong>Proof that no planets could fully eclipse the sun from another planet:</strong>
To rule out the possibility that any eclipses are possible, We only have to verify orbits pairwise in order of increasing distance from the sun. Since, if the <span class="math-container">$nth$</span> planet can't fully eclipse the sun from the <span class="math-container">$n+1_{th}$</span> planet than it certainly won't be able to do so from any other planet.  For example, if Jupiter can't eclipse the sun from Saturn, it certainly won't be able to from Neptune.</p>
<p>As seen from a planet, if the apparent size of the sun in the sky is smaller than the apparent size of the next inner planet, then a full eclipse is possible.  The largest an inner planet can appear from an outer planet is when the inner planet is at aphelion and the outer planet is at perihelion and the pass is directly overhead of the observer.</p>
<p>The formula for angular radius of a sphere is <span class="math-container">$\delta = \arcsin (d/2D)$</span> where d is the diameter of the sphere and D is the distance between the observer and the center of the sphere.</p>
<p>I ran these calculations using matlab and data from NASA. <a href="https://nssdc.gsfc.nasa.gov/planetary/factsheet/" rel="noreferrer">https://nssdc.gsfc.nasa.gov/planetary/factsheet/</a>
For my input data, the rows are planets, and the columns are diameter (km), perihelion (e6km), and aphelion (e6km).</p>
<p>Here are my results.  Since the values in the second column are smaller than the first for each row, no inter-planetary solar eclipse is possible. As an example of how to read this table, an observer on Venus will see an angular radius of 6.48e-3 radians for the sun in the sky, but an angular radius of only 6.47e-5 radians for the next inner planet, which is Mercury.</p>
<p><a href="https://i.sstatic.net/5lGfg.png" rel="noreferrer"><img src="https://i.sstatic.net/5lGfg.png" alt="enter image description here" /></a></p>
<p>Here is my matlab code for posterity:</p>
<pre><code>sunDiameter = 1.3927e6;
planetVals = [4879,12104,12756,6792,142984,120536,51118,49528;...
46.0,107.5,147.1,206.6,740.5,1352.6,2741.3,4444.5;...
69.8,108.9,152.1,249.2,816.6,1514.5,3003.6,4545.7];
results = zeros(2,7);
for i=1:7
  innerPlanetDiam = planetVals(1,i);
  innerPlanetApogee = planetVals(3,i)*1e6;
  outerPlanetPerigee = planetVals(2,i+1)*1e6;
  outerPlanetDiam = planetVals(1,i+1);
  sunApparentSize =
    asin(sunDiameter/(2*(outerPlanetPerigee-outerPlanetDiam/2)));
  innerPlanetApparentSize =
    asin(innerPlanetDiam/(2*(outerPlanetPerigee-outerPlanetDiam/2-innerPlanetApogee)));
  results(1,i) = sunApparentSize;
  results(2,i) = innerPlanetApparentSize;
end
results'
</code></pre>

CC BY-SA 4.0
2020-11-10T17:33:29.020Z
Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/116056/discussion-on-answer-by-connor-garcia-can-one-planet-in-our-system-eclipse-anoth).
called2voyage
CC BY-SA 4.0
2020-11-10T18:08:38.673Z
Is it be possible for Pluto's and Neptune's orbits to get close enough that we get an eclipse? I know their orbits are in some type of sync, but wondering how close they get.
ypercubeᵀᴹ
CC BY-SA 4.0
2020-11-10T18:18:17.693Z
No, because of the 3:2 gravitational resonance, Pluto and Neptune never get closer than 16 AU.
Connor Garcia
CC BY-SA 4.0
2020-11-10T18:20:47.840Z
I see, thank you!
ypercubeᵀᴹ
CC BY-SA 4.0
2020-11-11T18:54:20.557Z
_"As expected, the transit of Uranus from Neptune is the rarest, occurring next in October, 38172 CE."_ Can't wait!
Asteroids With Wings
CC BY-SA 4.0
2020-11-11T18:55:31.553Z
_"Since, if the nth planet can't fully eclipse the sun from the n+1th planet than it certainly won't be able to do so from any other planet. For example, if Jupiter can't eclipse the sun from Saturn, it certainly won't be able to from Neptune."_ Can you expand on this? Why is this a given?
Asteroids With Wings
CC BY-SA 4.0
2020-11-11T20:37:58.953Z
@AsteroidsWithWings Certainly! From Saturn, Jupiter appears smaller in the sky than the sun.  From Neptune, the sun only appears slightly smaller than from on Saturn, since the sun is so far away from both.  But Jupiter appears much smaller from Neptune than it does from Saturn, because Jupiter is much closer to them both.  So, since, Jupiter can't eclipse the sun from Saturn, it certainly can't from further planets.  This example, of course, applies not only to Jupiter, but the rest of the planets as well!
Connor Garcia
CC BY-SA 4.0
2020-11-11T21:12:03.773Z
@ConnorGarcia Doesn't that assume the only criteria is apparent size in the sky? Aren't there orbital factors to consider? Surely you could have a pair of planets that will never eclipse in this fashion, despite the size not being a disqualifying factor, simply due to their orbital arrangement; then the next pair out would still potentially be candidates. Granted, the statement I quoted seems to hold as long as we only consider planetary size (and distance) as a factor... or if orbital arrangement is not a problem for any Solar System object pair and we are only considering the Solar System.
Asteroids With Wings
CC BY-SA 4.0
2020-11-11T21:32:40.143Z
@AsteroidsWithWings My answer is restricted to our solar system, in which the variations of the orbits never change the order of planets by distance from the sun.  My choice of use of aphelion for the inner planet and perihelion for the outer planet pairwise handle all remaining orbital factors.
Connor Garcia
CC BY-SA 4.0
2020-11-11T21:42:37.920Z
@ConnorGarcia I didn't mean changing the order of planets, merely whether the positions ever lined up to create an eclipse. But that's fine, thanks :)
Asteroids With Wings
CC BY-SA 4.0
2020-11-11T22:21:26.677Z
@AsteroidsWithWings You are certainly correct that there could be a solar system in which the first planet never eclipses the sun from the second due to resonance, but does eclipse the sun from the third.  However, for any system, if you calculate that the first planet's apparent size would be too small to block the sun from the second even without the orbital resonance, than you can reasonably conclude that the first will never be able to eclipse the sun from the third.
Connor Garcia
CC BY-SA 4.0
2020-11-11T23:52:52.113Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/116123/discussion-between-connor-garcia-and-asteroids-with-wings).
Connor Garcia
CC BY-SA 4.0
2020-11-09T03:02:31.717Z
2020-11-09T19:16:25.403Z
2020-11-09T19:16:25.403Z
Connor Garcia
<p>When the Sun, Earth and Moon get properly aligned, we get eclipses, where the Sun is partially or totally hidden by the Moon when seen from Earth.</p>
<p>Is it possible for one planet of the solar system to produce an eclipse on another one?</p>
<p>There are two underlying questions in this:</p>
<ul>
<li><p>are alignments of the Sun and two planets actually possible (and if so, how frequent)? Given the slightly different orbital planes of the planets, this seems difficult?</p>
</li>
<li><p>even though planets are much smaller than the Sun, with appropriate distances between the three bodies considered, is it actually possible for one planet to partially or completely hide the Sun like we see in the Sun-Moon-Earth case, or does it only happen for planet-satellite combinations given the relative distances (i.e. in all other cases if would just be a tiny point transiting across the Sun)?</p>
</li>
</ul>
<p>I understand that the Earth would not be able to project a shadow far enough to get such a phenomenon on other planets, but are there other combinations where it’s possible/did happen?</p>

CC BY-SA 4.0
2020-11-09T03:56:37.043Z
Does that include "transit" and "occultation"? https://en.wikipedia.org/wiki/Planetary_transits_and_occultations
Nilay Ghosh
CC BY-SA 4.0
2020-11-09T10:19:34.403Z
@NilayGhosh I'm interested in any case where one planet is clearly visible as covering partially or totally the Sun. So occultations, definitely. Transits, the goal is to determine if they are really visible or if that's just at best a tiny speck.
jcaron
CC BY-SA 4.0
2020-11-09T14:31:26.303Z
_"are alignements of the Sun and two planets actually possible"_ Alignment isn't just possible, it's a given for any two planets orbiting the Sun (or any two satellites orbiting the same parent). There is no way to draw two orbits around the same body (Sun) in such a way that the two ellipses don't either cross or completely overlap. You'd need two parallel ellipses to keep them separate, which is impossible since every orbit's plane _must_ intersect the parent body's center of mass. That automatically means that two orbits will always cross one another, no matter how varied they are.
Flater
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2020-11-09T14:41:04.340Z
@Flater I suppose you mean the planes containing the ellipses, rather than the ellipses themselves. Indeed there is necessarily an intersection between the planes, but that does not mean the two planets will be at that intersection **at the same time**. I suppose it is bound to happen at some point (unless they are in orbital resonance), but probably with very very infrequently for some combinations, especially in the outer planets?
jcaron
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2020-11-09T14:43:05.380Z
@Flater this is almost true.  If two planets are in orbital resonance, than they may never be colinear with their star,
Connor Garcia
CC BY-SA 4.0
2020-11-09T14:55:27.387Z
@Flater the links posted by Michael Seifert in his comment on the answer below have timescales. So definitely not frequent, but definitely not impossible either, with a few millennia on average between such events.
jcaron
CC BY-SA 4.0
2020-11-09T15:11:37.930Z
@ConnorGarcia: Correct, but this is not the case for any of the planets in our solar system, which the question focuses on. I skipped the edge case because of the character count in the comment, since it was irrelevant for our solar system. But you are indeed correct :)
Flater
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2020-11-09T15:21:51.920Z
@Flater, agreed
Connor Garcia
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2020-11-10T13:17:28.387Z
@Flater Some of the dwarf planets are in orbital resonance with some outer planets, aren't they?
Hearth
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2020-11-10T13:21:59.017Z
@Hearth: Be careful with naming here. A dwarf planet is not considered a planet in the commonly used sense of the word. Otherwise Pluto would still be considered a planet, since it is in fact a dwarf planet. But this is not the case. Since it has been classified as a dwarf planet, Pluto has _ceased to be_ a planet, since the two don't overlap. A "dwarf planet" is not a subset of "planet", it's a sibling group. The names just happen to both contain "planet", which in English often means a filtered subset, but in this case it doesn't. In the same vein, jellyfish and crayfish aren't fish either.
Flater
CC BY-SA 4.0
2020-11-10T13:35:18.340Z
@Flater Yes, I meant that as an additional thing, not a correction.
Hearth
<solar-system><solar-eclipse><planetary-transits><eclipse-non-earth-related>
Can a planet in our system eclipse the sun as seen from another one?
jcaron
# Can a planet in our system eclipse the sun as seen from another one?

(Asked by: username_0 on 2020-11-08)

When the Sun, Earth and Moon get properly aligned, we get eclipses, where the Sun is partially or totally hidden by the Moon when seen from Earth.

Is it possible for one planet of the solar system to produce an eclipse on another one?

There are two underlying questions in this:

* are alignments of the Sun and two planets actually possible (and if so, how frequent)? Given the slightly different orbital planes of the planets, this seems difficult?
* even though planets are much smaller than the Sun, with appropriate distances between the three bodies considered, is it actually possible for one planet to partially or completely hide the Sun like we see in the Sun-Moon-Earth case, or does it only happen for planet-satellite combinations given the relative distances (i.e. in all other cases if would just be a tiny point transiting across the Sun)?

I understand that the Earth would not be able to project a shadow far enough to get such a phenomenon on other planets, but are there other combinations where it’s possible/did happen?

**Tags:** solar-system, solar-eclipse, planetary-transits, eclipse-non-earth-related

> **Comments:**
> **username_1**: Does that include "transit" and "occultation"? https://en.wikipedia.org/wiki/Planetary_transits_and_occultations  
> **username_0**: @username_1 I'm interested in any case where one planet is clearly visible as covering partially or totally the Sun. So occultations, definitely. Transits, the goal is to determine if they are really visible or if that's just at best a tiny speck.  
> **username_2**: _"are alignements of the Sun and two planets actually possible"_ Alignment isn't just possible, it's a given for any two planets orbiting the Sun (or any two satellites orbiting the same parent). There is no way to draw two orbits around the same body (Sun) in such a way that the two ellipses don't either cross or completely overlap. You'd need two parallel ellipses to keep them separate, which is impossible since every orbit's plane _must_ intersect the parent body's center of mass. That automatically means that two orbits will always cross one another, no matter how varied they are.  
> **username_0**: @username_2 I suppose you mean the planes containing the ellipses, rather than the ellipses themselves. Indeed there is necessarily an intersection between the planes, but that does not mean the two planets will be at that intersection **at the same time**. I suppose it is bound to happen at some point (unless they are in orbital resonance), but probably with very very infrequently for some combinations, especially in the outer planets?  
> **username_3**: @username_2 this is almost true.  If two planets are in orbital resonance, than they may never be colinear with their star,  
> **username_0**: @username_2 the links posted by Michael Seifert in his comment on the answer below have timescales. So definitely not frequent, but definitely not impossible either, with a few millennia on average between such events.  
> **username_2**: @username_3: Correct, but this is not the case for any of the planets in our solar system, which the question focuses on. I skipped the edge case because of the character count in the comment, since it was irrelevant for our solar system. But you are indeed correct :)  
> **username_3**: @username_2, agreed  
> **username_4**: @username_2 Some of the dwarf planets are in orbital resonance with some outer planets, aren't they?  
> **username_2**: @username_4: Be careful with naming here. A dwarf planet is not considered a planet in the commonly used sense of the word. Otherwise Pluto would still be considered a planet, since it is in fact a dwarf planet. But this is not the case. Since it has been classified as a dwarf planet, Pluto has _ceased to be_ a planet, since the two don't overlap. A "dwarf planet" is not a subset of "planet", it's a sibling group. The names just happen to both contain "planet", which in English often means a filtered subset, but in this case it doesn't. In the same vein, jellyfish and crayfish aren't fish either.  
> **username_4**: @username_2 Yes, I meant that as an additional thing, not a correction.  

---

## 2 answers

### Answer by username_3 on 2020-11-09. Score: 39

In our solar system, it is possible for one planet to partially eclipse the sun, but it is not possible for any planet to cause a full solar eclipse as seen from another planet.

The sun is too big and the planets are too small and too far apart. Transits occur, and can occur for any pair of planets, but they are very rare. As seen from earth, Mercury only transits a dozen or so times per century, and before 2004, the last time Venus had transited the sun was 1882. <http://www.eclipsewise.com/transit/transit.html> Orbital periods increase for the planets further away from the sun, so transits across the sun by the outer planets (while possible since no planets are in orbital resonance since Pluto got kicked out) are increasingly rare. Michael Seifert dug up these treasures, documenting transits of the outer planets: [Jupiter](https://web.archive.org/web/20120609103443/https://en.wikipedia.org/wiki/Transit_of_Jupiter_from_outer_planets), [Saturn](https://web.archive.org/web/20120605054027/https://en.wikipedia.org/wiki/Transit_of_Saturn_from_outer_planets), [Uranus](https://web.archive.org/web/20120605054035/https://en.wikipedia.org/wiki/Transit_of_Uranus_from_Neptune). As expected, the transit of Uranus from Neptune is the rarest, occurring next in October, 38172 CE.

**Proof that no planets could fully eclipse the sun from another planet:**
To rule out the possibility that any eclipses are possible, We only have to verify orbits pairwise in order of increasing distance from the sun. Since, if the $nth$ planet can't fully eclipse the sun from the $n+1\_{th}$ planet than it certainly won't be able to do so from any other planet. For example, if Jupiter can't eclipse the sun from Saturn, it certainly won't be able to from Neptune.

As seen from a planet, if the apparent size of the sun in the sky is smaller than the apparent size of the next inner planet, then a full eclipse is possible. The largest an inner planet can appear from an outer planet is when the inner planet is at aphelion and the outer planet is at perihelion and the pass is directly overhead of the observer.

The formula for angular radius of a sphere is $\delta = \arcsin (d/2D)$ where d is the diameter of the sphere and D is the distance between the observer and the center of the sphere.

I ran these calculations using matlab and data from NASA. <https://nssdc.gsfc.nasa.gov/planetary/factsheet/>
For my input data, the rows are planets, and the columns are diameter (km), perihelion (e6km), and aphelion (e6km).

Here are my results. Since the values in the second column are smaller than the first for each row, no inter-planetary solar eclipse is possible. As an example of how to read this table, an observer on Venus will see an angular radius of 6.48e-3 radians for the sun in the sky, but an angular radius of only 6.47e-5 radians for the next inner planet, which is Mercury.

[![enter image description here](https://i.sstatic.net/5lGfg.png)](https://i.sstatic.net/5lGfg.png)

Here is my matlab code for posterity:

```
sunDiameter = 1.3927e6;
planetVals = [4879,12104,12756,6792,142984,120536,51118,49528;...
46.0,107.5,147.1,206.6,740.5,1352.6,2741.3,4444.5;...
69.8,108.9,152.1,249.2,816.6,1514.5,3003.6,4545.7];
results = zeros(2,7);
for i=1:7
  innerPlanetDiam = planetVals(1,i);
  innerPlanetApogee = planetVals(3,i)*1e6;
  outerPlanetPerigee = planetVals(2,i+1)*1e6;
  outerPlanetDiam = planetVals(1,i+1);
  sunApparentSize =
    asin(sunDiameter/(2*(outerPlanetPerigee-outerPlanetDiam/2)));
  innerPlanetApparentSize =
    asin(innerPlanetDiam/(2*(outerPlanetPerigee-outerPlanetDiam/2-innerPlanetApogee)));
  results(1,i) = sunApparentSize;
  results(2,i) = innerPlanetApparentSize;
end
results'

```

> **Comments:**
> **username_5**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/116056/discussion-on-answer-by-username_3-username_3-can-one-planet-in-our-system-eclipse-anoth).  
> **username_6**: Is it be possible for Pluto's and Neptune's orbits to get close enough that we get an eclipse? I know their orbits are in some type of sync, but wondering how close they get.  
> **username_3**: No, because of the 3:2 gravitational resonance, Pluto and Neptune never get closer than 16 AU.  
> **username_6**: I see, thank you!  
> **username_7**: _"As expected, the transit of Uranus from Neptune is the rarest, occurring next in October, 38172 CE."_ Can't wait!  
> **username_7**: _"Since, if the nth planet can't fully eclipse the sun from the n+1th planet than it certainly won't be able to do so from any other planet. For example, if Jupiter can't eclipse the sun from Saturn, it certainly won't be able to from Neptune."_ Can you expand on this? Why is this a given?  
> **username_3**: @username_7 Certainly! From Saturn, Jupiter appears smaller in the sky than the sun.  From Neptune, the sun only appears slightly smaller than from on Saturn, since the sun is so far away from both.  But Jupiter appears much smaller from Neptune than it does from Saturn, because Jupiter is much closer to them both.  So, since, Jupiter can't eclipse the sun from Saturn, it certainly can't from further planets.  This example, of course, applies not only to Jupiter, but the rest of the planets as well!  
> **username_7**: @username_3 Doesn't that assume the only criteria is apparent size in the sky? Aren't there orbital factors to consider? Surely you could have a pair of planets that will never eclipse in this fashion, despite the size not being a disqualifying factor, simply due to their orbital arrangement; then the next pair out would still potentially be candidates. Granted, the statement I quoted seems to hold as long as we only consider planetary size (and distance) as a factor... or if orbital arrangement is not a problem for any Solar System object pair and we are only considering the Solar System.  
> **username_3**: @username_7 My answer is restricted to our solar system, in which the variations of the orbits never change the order of planets by distance from the sun.  My choice of use of aphelion for the inner planet and perihelion for the outer planet pairwise handle all remaining orbital factors.  
> **username_7**: @username_3 I didn't mean changing the order of planets, merely whether the positions ever lined up to create an eclipse. But that's fine, thanks :)  
> **username_3**: @username_7 You are certainly correct that there could be a solar system in which the first planet never eclipses the sun from the second due to resonance, but does eclipse the sun from the third.  However, for any system, if you calculate that the first planet's apparent size would be too small to block the sun from the second even without the orbital resonance, than you can reasonably conclude that the first will never be able to eclipse the sun from the third.  
> **username_3**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/116123/discussion-between-username_3-username_3-and-username_7).  

---

### Answer by username_2 on 2020-11-09. Score: 22

The short answer is no. The alignment occurs, but the eclipse does not, due to the distances and size differences involved.

There are a few things to consider here. You already mentioned a lot of them, I'll address those considerations separately.

---

## Alignment

> are alignements of the Sun and two planets actually possible (and if so, how frequent)?

We can intuitively gauge this, as we've seen this happen during the transit of Venus:

[![enter image description here](https://i.sstatic.net/tnQddm.jpg)](https://i.sstatic.net/tnQddm.jpg)

This situation describes your scenario. The sun, Venus and the Earth are aligned (within some reasonable range).

But, in fairness, you're asking about any of the planets, not just Earth and Venus. So is this possible for any other (or possible even all) combinations of two planets?

This is two questions in one: Do two planets' orbits overlap, and do these planets ever find themselves at this overlap point at the same time?

**Do two planets' orbits overlap?**

Quite interestingly, not only can they overlap, they *must* do so. The only way for two orbits to never overlap would be if they were parallel to each other (e.g. one orbit around the equator and one orbit around the tropic of cancer), but that second orbit is impossible.

All orbital planes must intersect with the parent body's center of mass. It's not possible to have an orbit that does not. To put it into visual terms:

[![enter image description here](https://i.sstatic.net/uaMkZ.png)](https://i.sstatic.net/uaMkZ.png)

There is no way to position these two orbits in a way that they (a) are physically valid and (b) not have any overlap.

**Do these planets ever find themselves at this overlap point at the same time?**

The only way for them to *not* find themselves at this overlap point would be if their orbits were periodic. I would argue that *perfect* periodicity is unlikely to occur in nature, but that's an intuitive argument.

Looking at [the planets' orbital periods](https://space-facts.com/orbital-periods-planets/), none stand out as being particularly periodic. I'm unsure if we can ever prove that our measurements or orbital period at any given time have perfect precision to conclude that perfect periodicity exists.

Other answers have already indicated the frequency with which such overlaps could occur. I'm mostly interested in whether they can occur or not, to see if we can conclude that your idea is *possible* or not.

---

## Casting a shadow

So far, we haven't actually disproven the theory. Orbital planes will overlap, and our planetal orbits are not periodic so they will eventually overlap. But now we get to the other part: the shadow. Will the shadow of the nearest planest reach the furthest planet?

Let's look at the expected size of the shadow. Do you think it will be larger or smaller than the planet who casts it?

The simple rule of thumb here is that if a shadow is larger than the object itself, then the object itself must be larger than the light source. If instead the light source is significantly bigger, then the object's shadow will shrink, and effectively disappear past its focal point.

*Note: I call it a "focal point" because of what it looks like on a diagram, and for lack of a better name. If anyone has a more official term, I'd be happy to hear it.*

To put it in visual terms:

[![enter image description here](https://i.sstatic.net/iQ4KZ.png)](https://i.sstatic.net/iQ4KZ.png)

I don't think we need to explain how much bigger the Sun is compared to any of the planets.

The relative size of the Sun vs any planet renders the penumbra negligible. It could possible be perceived by lightsensitive equipment (edit: I don't know if it can be perceived, I just can't prove that it can't be perceived), but not by a human who observes this while standing on the further planet. It won't look like an eclipse. I refer back to the transit of Venus:

[![enter image description here](https://i.sstatic.net/tnQddm.jpg)](https://i.sstatic.net/tnQddm.jpg)

Given the significant size difference between the Sun and planet, and the massive distances between the planets themselves, it doesn't seem feasible for the umbra to even reach the next planet's orbit before it hits its focal point, which is why we don't describe such a transit as an eclipse.

NASA explains this on [their website](https://www.nasa.gov/content/eclipses-and-transits-overview):

> Like an eclipse, a transit occurs when one object appears to pass in front of another object. **But in a transit, the apparent size of the first object is not large enough to cast the second into complete shadow**. Instead a much smaller dark shadow makes its way across the face of the further planet or star. Perhaps the most famous recent transit was that of Venus across the face of the sun in 2012.

---

## Casting a shadow - intuitive explanation

There's a more intuitive way to express this. If a certain object (nearest planet) can block a light source (Sun), that means that from the point of view of the observer (on the furthest planet), the object must appear to be bigger than the light source. There's a quite well-known scene from Apollo 13 that showcases this:

[![enter image description here](https://i.sstatic.net/PfbiE.jpg)](https://i.sstatic.net/PfbiE.jpg)

Tom Hanks (as Jim Lovell) is blocking out the moon using his thumb. Even though the moon is much bigger than Tom Hanks' thumb (citation needed), the relative closeness of his thumb to his eye (compared to that of the moon) makes the thumb *appear* bigger than the moon.

Let's say that Tom Hanks puts down his hand, and Chris Hadfield sticks his thumb out of the window of the ISS. His thumb is perfectly aligned between the moon and Tom Hanks' eye. We assume his thumb is the same size as Tom Hanks' (citation needed).  
This wouldn't block out the moon anymore from Tom. But why is that?

Very simply put, even though the thumb is the same size, the relative distances between the eye, thumb and moon have changed. And now, Chris Hadfield's thumb does not *appear* to be bigger than the moon, when observed by Tom Hanks. And therefore, it can no longer block the moon from Tom Hanks' view.

So, we can reformulate your eclipse question: **Is there any planet which *appears* to be bigger than the Sun, when observed from another planet?**

The answer is no.

*Edit: I've decided to make the below text easier to parse, by talking about the Earth and Venus. These are just examples, the same applies to any combination of planets, where Earth = furthest and Venus = nearest.*

If you assume that the Sun is `X` times larger (in diameter!) than Venus, and the sun is `Y` times further from Earth than Venus is from Earth, then Venus will appear to be bigger than the sun (when standing on Earth) when `X < Y`.

In other words, when measuring the distance from Earth, the sun needs to be *further away* than Venus, by a larger factor than the sun is *bigger* than Venus.  
As a simple example, if the sun were exactly 5 times bigger than Venus, it would have to be >5 times as far from Earth as Venus is, for it to appear to be smaller than Venus.

If you look up the numbers for planet diameters and orbital radii, you'll notice that this doesn't happen in our solar system. Not even close. This is because the sun is simply too big relative to any ratio of two planetary orbits.


---

