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How do we know, without using modern equipment, that the stars are further away than the moon in the night sky? Further, is there a simple and actionable argument to prove that this is indeed the case? Additionally, I would like to know how people in earlier times knew this fact without having access to modern equipment, including telescopes.

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    $\begingroup$ Do you need something more sophisticated than "When a star is behind the moon, we can't see the star"? When we can't see Bob because Alice is blocking our view of him, we readily deduce that Alice is closer to us than Bob. $\endgroup$ – Boluc Papuccuoglu Mar 14 '20 at 20:28
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    $\begingroup$ I agree with your observation about the simplicity of the proof using occlusion, @BolucPapuccuoglu. However, if there is no valid counter- argument, a simpler argument is perhaps more desirable than a complex one. On the other hand, I am very much interested in all possible answers and invite you to add any answers (or the related question here) which might require sophisticated argumentation or ones that may involve the use of modern equipment. $\endgroup$ – kbakshi314 Mar 14 '20 at 21:28
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    $\begingroup$ We went to the moon without stopping at any stars on the way? (OK, I guess Saturn V + Apollo still counts as "modern" ;-).) $\endgroup$ – Peter - Reinstate Monica Mar 15 '20 at 23:33
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    $\begingroup$ Would a telescope and a diffraction grating qualify as "modern equipment"? If not, you can use the Balmer lines to make a strong argument that the stars and the sun must be pretty similar. Since stars appear much smaller than the sun, they must be further away. $\endgroup$ – craq Mar 16 '20 at 0:05
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    $\begingroup$ Meta post about the closing of this question $\endgroup$ – BioPhysicist Mar 17 '20 at 1:23
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If you don't mind modern equipment, there are some arguments. For example, we have sent spacecraft out well past the moon to get to other planets. As you approach a planet, the direction to it changes. Eventually, there it is beside you instead of in front. But the stars have mostly not changed their apparent direction at all.

Every year, the Earth goes around in an enormous circle. The size is something like the distance to the nearer planets. You would expect to see nearer stars move past the more distant stars. Something like the nearby trees appear to move past distant mountains when you drive on the freeway. And this has been seen. But the motion is tiny. It takes extremely careful measurements to see it. The biggest shift is less than 1 arc second = $1/3600$ degree. Given the size of Earth's orbit, this puts the nearest star at about 4 light years away, much much farther than the moon and planets. Most stars are so far away that no change can be seen.

Modern research has shown that stars are bright like the sun. Given that they appear to be faint little dots, they must be far away. First because something so bright appears to be so faint. And second, something so big looks like a point, not a disk.


Edit - Measurements with early telescopes in the 1600s

As Charles Francis' answer says, the Hipparchus calculated the distance to the moon is $60$ $1/2$ Earth radii, and the distance to the Sun is $2550$ Earth radii. More measurements became possible after the invention of the telescope. For example, Galileo discovered 4 moons of Jupiter in 1609 or 1610.

Wikipedia article on Romer's determination of the speed of light says that in 1671 - 1676, Romer made the first crude measurements of the speed of light, and used it to find some distances. Predicted times of eclipses of the moons of Jupiter were off by up to 15 minutes. He attributed this to the time it takes light to travel from Jupiter to Earth. The time varies as the orbits of Earth and Jupiter bring them closer together or farther apart.

He found light takes much less that 1 sec to travel an Earth diameter. The time to travel from the Sun to the Earth was 10 - 11 minutes. This confirms the Sun-Earth distance is much bigger than the distance to the moon.

The distance from the Sun to Jupiter was part of the calculation. Romer only had crude Earth-Sun distances, so his Earth-Jupiter distances were also crude. This website gives the Earth-Jupiter distances used by Romer as 3.95 to 5.75 Earth-Sun distances. Again, much bigger than Earth-moon distances.

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The fact of parallax in the observed position of the moon was known in ancient times. This makes possible a calculation of the distance of the moon in terms of Earth radii. No parallax was then observed for the Sun. The first known calculation of the distance to the moon is generally attributed to Hipparchus of Nicaea

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    $\begingroup$ Thanks for the answer and the explanation. If possible, please elaborate on or pass any references on how, if possible, one can know relative distances of celestial objects without using multiple observations related to positions, that is, by using a snapshot of the night-sky which can contain information about the intensity, wavelengths and other information related to the celestial objects. $\endgroup$ – kbakshi314 Mar 14 '20 at 19:53
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    $\begingroup$ This is a different question, and it would have to be asked as such. It occupies a chapter of my book, troubador.co.uk/bookshop/computing-science-education/…. A snapshot contains very little information. For near planets, we can use radar. Beyond the range of parallax measurements, we use standard candles - the luminosity of objects whose absolute luminosity is known from studies of near (almost) identical objects. For the furthest galaxies, we can only use red shift. $\endgroup$ – Charles Francis Mar 14 '20 at 20:05
  • $\begingroup$ I have posted the extended probing into this topic as a separate question. Thanks for the reference, which I will read at leisure, but it will be great to have a concise answer summarizing the general nature of the ideas which are used to calculate distance of such objects, using snapshot-like information. $\endgroup$ – kbakshi314 Mar 14 '20 at 20:26
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    $\begingroup$ @kb314 Re, "Thanks for the answer and the explanation, but I need to know how to defeat the balrog with one hand tied behind my back." Why? Science is not a sport with sporting rules and level playing fields. Science is an all-in quest for knowledge, and scientists consider all of the available facts when constructing their theories. $\endgroup$ – Solomon Slow Mar 15 '20 at 17:57
  • $\begingroup$ @SolomonSlow, I agree with you. However, my formal training in orbital mechanics has, it is clear now, not exposed me to several methods for determining orbital positions other than using position (or velocity) data at several time steps. My comment was intended to express my curiosity about those methods. $\endgroup$ – kbakshi314 Mar 16 '20 at 1:55
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Lunar occultations. Just missed the moon block Mars last month. Not sure when Mars will block a star, thereby proving the stars are further than the moon.

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  • $\begingroup$ Ok! Simple enough. But is there no other argument than occlusion? There could be a counter-argument that the star is becoming less visible because of lower intensity compared to that of the moon. $\endgroup$ – kbakshi314 Mar 14 '20 at 3:55
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    $\begingroup$ The moon occasionally occults Aldeberan, the red star which is one eye of Taurus the Bull. Unless it's full at the occultation, the star either vanishes behind or reappears from behind the dark limb of the moon. It's a naked-eye event, but you have to know where to be and when to look. A rabbit hole: occultations.org $\endgroup$ – rob Mar 14 '20 at 4:31
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    $\begingroup$ @kb314 not when it goes behind (reappear from) the dark limb for a waxing (waning) moon. Moreover, multiple observers can verify that the occultation is not visible from all latitudes. $\endgroup$ – JEB Mar 14 '20 at 4:43
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    $\begingroup$ @rob according to Sky magazine, they come in groups of 49, and the last one was Sept 2018. But: "The moon will reach a northern extreme in the constellation Taurus in the year 2025. At that juncture, the moon will be occulting Alcyone, brightest star in the Pleiades star cluster. That’ll happen on a monthly basis from September 5, 2023 to July 7, 2029. " $\endgroup$ – JEB Mar 14 '20 at 4:47
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    $\begingroup$ Occultations are the simplest and most directly observable fact, but the two stage process (observe the moon occult mars, then watch mars occult a star) seems complex. You can directly observe lunar occultation of stars, simply demonstrating that stars are more distant. $\endgroup$ – James K Mar 15 '20 at 6:55
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the occlusion of stars by the moon is a simple and easy way to prove your point.

the one being occluded (blocked from view) must be behind the object obstructing the view, therefore further away from the observer.

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  • $\begingroup$ This is a simplest answer. The moon is in front of the stars - you can tell this because the moon covers over the stars it passes over. $\endgroup$ – nick012000 Mar 16 '20 at 9:04
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We have used radar ranging to determine the distance to the Moon, the Sun, Mercury, Venus, Mars, Jupiter, the Galilean satellites, Saturn, the rings of Saturn, and Titan. We have fired radio signals at stars and have not observed a return signal. Either stars are closer than the moon and somehow invisible to radar (which would be very surprising for a ball of plasma having the blackbody radiation spectra we observe from stars), or stars are much further away.

Passing back in time a bit... Hipparchus (ca. 140 BCE) used the shadow of the Moon on the Earth during a solar eclipse to estimate that the Sun is about 2500 Earth radii (getting the ratio of Moon distance to Earth radius within about 10% and getting the ratio of Sun distance to Moon distance 10-times too small).

Ptolemy (ca. 150 AD) used an epicyclic model of planetary motion to lower bound the distance to the celestial spheres to more than 20,000 Earth radii (which is bazillions of times too small).

So the stars are at least 8-times further away than the Moon.

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    $\begingroup$ Did the radar measuring worked with the sun? $\endgroup$ – Paŭlo Ebermann Mar 15 '20 at 2:22
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    $\begingroup$ @PaŭloEbermann : Yes: adsabs.harvard.edu/full/1966ApJ...146..356J . Technically, that article ranges the solar corona, but in the context of this question, that should be "close enough". $\endgroup$ – Eric Towers Mar 15 '20 at 15:26
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Compare angular sizes of stars and sun. Sun has angular size of $\approx 32 \,'$ and our closest star Alpha Centauri A has angular diameter of $0.007\,''$. This gives of angular size ratio between them as about $270\,000$ times, which correlates very well with real distance ratio between them and Earth. You don't need a measurement device for this. You can see sun's visual diameter by putting some dark black glass in front of eyes. And stars are merely like "dots" when we look at them at night. Because sun is just an ordinary G-type main-sequence star, it's not that hard to conclude that other stars in a night sky is far far more distant than our sun.

Now moon has comparable angular diameter with that of sun. It would be unwise to expect that moon mass would be greater or comparable to that of sun, thus it's natural to conclude that moon can only be at a distance closer to Earth than that of our sun. So by concluding it we imply that stars are also a lot more distant than moon.

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    $\begingroup$ Most of this already pre-supposes things like "stars are similar objects to our sun". Also why would the moon-sun expectation "unwise"? $\endgroup$ – Paŭlo Ebermann Mar 15 '20 at 2:21
  • $\begingroup$ @PaŭloEbermann Yes, there is such assumption. We need to start from something. Why moon radius can't be comparable to sun ? Well, unless you live in a binary star system, it's unnatural. Hypothetically if you would live in a binary star system, moon should shine like a star, but now it has very low intensity of light, meaning it's not a star. However I agree that second paragraph is not a firm proof. $\endgroup$ – Agnius Vasiliauskas Mar 15 '20 at 10:05
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If you take it as a given that the Earth is revolving around its axis once per day than you could make the argument that anything that does not move (after subtracting the apparent movement due to the Earth's rotation) must be far away, or it would fall down.

Satellites have a short orbital period, the Moon a longer one, everything else must be "very very far away". Of course things are complicated by Earth's orbit around the Sun; if that's not a given then one is stuck with Ptolemy's curly trajectories for the planets, but the general idea still holds.

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