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In the ancient times, planets and stars were just thought to be some distant lights; various beliefs and theories ascribed them various properties and meanings, but the concept of planets being spheres of rock of size comparable to Earth, stars being distant Suns, and Sun being as huge as it is, and burning with (at the time unknown) heat and light source, was rather alien.

Obviously, in times of Newton, no enlightened man believed Moon to be an incarnation of Osiris, or anything along these lines. I have some decent estimates on when Earth size (and confirmation of its spherical shape) were found (Herodotus, 431–425 BC), and the geocentric concept was challenged (Copernicus, ~1514), but I can't place in time, when planets and stars were recognized for what they factually are - like when planets were understood to be spheres of rock of size comparable to Earth.

Can you give me preferably a timeline of the discoveries; if that would be too hard, a rough time estimate?

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    Comments are ephemeral, and subject to arbitrary deletion at any time. Please edit clarifications into the question body. – Pieter Geerkens Jul 23 '18 at 11:47
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    @LarsBosteen: How much? Since I know very little on the subject, I don't know how it can be narrowed. I think an overview answer that gives a timeline of the discoveries for an answer would be the optimal solution, but giving any single good key point would suffice. I definitely don't want to force a technically correct but useless answer due to over-constraining the question basing on false assumption - I believe anyone reading it can guess my intent; I want to learn, not obtain a numerical answer to enter into a trivia form. – SF. Jul 23 '18 at 12:52
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    Fair comment. 'Timeline' would be worth editing into your question I think. As @PieterGeerkens said, comments get deleted sometimes. – Lars Bosteen Jul 23 '18 at 13:27
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    You would probably find The Great Ptolemaic Smack-Down to be of interest. In particular, some of the arguments put forth by Tycho Brahe for a geocentric model of the Universe involved estimates of the size of distant stars (see Part I of the series.) These estimates were wrong for interesting & subtle reasons that weren't fully understood until the mid-19th century. – Michael Seifert Jul 23 '18 at 15:38
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    @defaultlocale: Galileo was bad at such "pedestrian" tasks as recording measurements, but the very moment the telescope got popularized (right around that time) a swarm of astronomers began recording and measuring everything, including angular diameters. It would be hard to pinpoint "who first" because it's quite sure there were at least several at about the same time. The date would be somewhere around 1609-1610. A very likely source for the calculation to be used when the unit of 1AU became finally known would be the Rudolphine Tables by Kepler; a defacto standard of astronomy tables then. – SF. Jul 25 '18 at 10:32
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Other people have given some of the history on discovering distances to planets, so I'll focus on the issue of "how did people learn the sizes of planets"?

Though I will point out that accurate distances to planets -- required if you want to estimate their sizes -- didn't come until the late 17th Century. Kepler's Laws provided distances to planets relative to the size of the Earth's orbit (the Astronomical Unit), but you need an independent distance to set the scale. This was first achieved in 1672 with the parallax measurements of the distance between Mars and the Earth by Cassini and Richer (and also by Flamsteed in England using a slightly different method), when the Astronomical Unit was measured to about 7% accuracy; this was refined about a century later to about 2% accuracy using measurements of the transit of Venus across the Sun.

(It's interesting to note that Huygens came up with a similarly accurate estimation of the Astronomical Unit in 1659, by assuming that Venus and Mars had diameters similar to that of the Earth and measuring their apparent angular sizes. This wasn't a direct measurement like the parallax of Mars, but does indicate that astronomers at that time were thinking that the planets could be similar in size to the Earth.)

As far as determining that planets were unlike the stars, and perhaps similar to the Earth in size and composition -- this happened in the 17th Century, almost entirely due to developments in telescopes. Galileo observed that the disk of Jupiter was larger than that of Mars, and that Venus's disk was larger still, changed visibly in size over its orbit, and showed a full range of phases. This was pretty clear evidence that different planets had different sizes and/or distances, and that these in turn were different from the sizes/distances of stars (which showed constant angular sizes, mostly due to the combination of atmospheric turbulence and poor telescope optics, though this wasn't really understood at the time). Galileo also observed sunspots and mountains on the Moon (helping demonstrate that celestial objects could have imperfect surfaces like that of the Earth) and four moons orbiting Jupiter (showing that Jupiter was similar to the Earth in having its own satellites).

Improvements in telescopes enabled later astronomers to more clearly differentiate the observed angular sizes of planets, to find moons around Saturn (Titan, found by Huygens in 1655, and four more found by Cassini in the 1670s and 1680s), to find traces of surface features on Mars and Jupiter, and even to measure their rotation speeds (e.g., Cassini in 1666). The fact that Mars's rotation was only slightly longer than the Earth's undoubtedly helped sell the idea that it was similar to the Earth.

I suspect the default assumption was probably that if the planets were similar to the Earth in these various different ways, then they must be similar in composition as well. I think that by around 1700, however, it was clear that Jupiter, at least, was different. This is because Cassini had observed that Jupiter's polar features rotated more slowly than its lower-latitude features, somewhat that wasn't possible if you were observing a solid surface, and also because once you had the proper size scale, you could use the mass of Jupiter (from using the orbits of its moons and Newton's generalization of Kepler's Laws) and its apparent size to work out that its mean density was closer to that of water than that of rock (see here for a fuller explanation).

  • "Galileo also observed sunspots and mountains on the Moon" I first read that as "on the Moon" applying to "sunspots" and "mountains". – Acccumulation Jun 3 at 20:11
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This was a very slow and gradual process, which still continues, so the question "when" has no meaning here.

Ancient Greeks already knew that "The moon is larger than Peloponnese". But the first scientific measurement of Moon's parallax that we know is recorded in Ptolemy (II cent AD). Parallax gives you the distance to the Moon in terms of the size of the Earth, and the size of Earth was known, about 400 years before, though very approximately.

The correct order of distances (Moon, Venus, Mercury, Sun, Mars, Juliter, Saturn, stars) was known from the times immemorial, except the order of Mercury and Venus).

(Aristarchus made the first attempt to make conclusion of the ratio of the distance to the Sun and the Moon, but his attempt was unsuccessful).

The relative distances of planets were roughly known since the late 16th century, when the correct kinematic model (Copernican) was accepted, and Kepler's laws were discovered. Speaking of the distance to the stars, Copernican model only implies an estimate from below. The parallax of the stars was measured for the first time only in 1838.

Speaking of more remote objects, than the closest stars, no direct measurement of parallax is possible, but there are other methods (I recommend the very clear exposition of this by Hawking, Brief History of Time). The distance to the most remote objects is estimated using the Hubble Law.

Once you know the distance to the object and compare it with the brightness, you can make conclusions about its size.

Literature to begin with: Wikipedia, "Parallax".

  • re "The correct order of distances ... was known": I'd like to see evidence of heliocentric consensus in this time period as support for this statement. – Pieter Geerkens Jul 23 '18 at 18:03
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    @Peter Geerkings: amazingly, the correct order was known long before the heliocentric theory. Already in Ptolemy, a clear distinction is made between lower planets (Mercury and Venus) and upper planets (the rest), and the order is correct. Probably the order was based on periods of revolution. That the Moon is much closer is clear from the parallax. Also Moon obscures all other bodies when it passes between them and us (occultations). – Alex Jul 23 '18 at 18:09
  • @Alex Not according to the Turkish flag. – Acccumulation Jun 3 at 20:13
  • @Acccumulation: I read somewhere that Turkish flag has been modified. The old flag showed an impossible configuration of Moon and a star. The modern flag shows a possible configuration. They moved the star away a little bit, so that it is outside of the Moon disk. – Alex Jun 4 at 1:54
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Aristarchus is the first to measure the relative size of Earth and the Moon in the third century B.C., at a ratio of 8:3. This is a bit lower than the modern calculation at 3.7:1 due to ignorance of the penumbra shadow's narrowing.

Likewise Aristarchus calculates that the Sun's diameter is between 18 and 20 times that of the Moon. We now know that an observational error (due to limits of unaided human vision) results in this value being too small by a factor of about 20, but still clearly extremely massive compared to Earth.

So in answer to your question - since the third century B.C. the Greeks at least were aware that the heavenly bodies in our Solar Systems are of a size comparable to our Earth.

Here are more notes on the History of Geodesy, including for non-European calculations.

Note also that once the sheer scale of inter-planetary distances is known, it becomes self evident that the planets must be of comparable size to the Earth and Moon. That accurate calculations were not always technologically possible is different from understanding the obvious scale of those sizes.

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    Aristarchus's book is really a set of mathematical exercises. It is not clear whether he really measured anything, or even cared about true distances. – Alex Jul 23 '18 at 18:08
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I think, combining answers and comments here, three "milestones" can be established.

  1. Estimate of the size of the Moon and Sun, by Aristarchus, as mentioned by Pieter Geerkens, gave a rough ballpark on the size of the two bodies. Heraclidean system gave the estimate distance to other planets, and by extension, a general clue about their size. (thanks to Pieter Geerkens)

  2. As described in The Great Ptolemaic Smackdown - 1609:

TOF pauses once more to note that the real Scientific Revolution in astronomy was to move astronomy from a branch of mathematics to a branch of physics. Galileo intuited from his study of the Moon that the heavenly bodies were physical places much like Earth, about which physical discoveries could be made.

This was unrelated to size, but a breakthrough in understanding what the celestial bodies are - not some mysterious heavenly spheres of theological nature nature, but places with mountains, geography, etc. (thanks to Michael Seifert)

  1. First rough, in 1639, with about 36% error, then much more precise in 1761 and 1769 - transits of Venus. This is where at long last the distance between the Sun and Earth was measured. Up to that point, astronomy was all about proportions; you could learn how many multiples the size of the Moon the Sun was, and how many Moon diameters was Mars away from the Sun, but the entire domain lacked the singular unit anchoring it in "earthly" units of distance/size. Knowing proportions between Earth orbit and all other celestial bodies, their actual sizes could be finally calculated, not just ballparked basing on very poor quality observations of Earth shadow. (thanks to Pieter Geerkens again)
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As Pieter Geerkens points out, even the very same Greeks and Romans whose original religion defined planets as gods believed that planets were indeed inanimated objects similar to Earth - at least those enlightened enough to study their properties. I would say that, at the very last, the moment christianity took over everybody believed that planets were not gods - or were burnt at the stake.

As for the relative sizes, only Luna and Sol are big enough to determine its angular size without special instruments - and even then you can fail spectaculary like Aristarchus - so you had to wait until the invention of the telescope to get measurable angular sizes for the rest of the planets, and then wait to the transit of Venus of 1769 to get an actual measurement of the Earth-Sun distance to convert relative distances to absolute ones.

  • A reference for "whose original religion defined planets as gods" would refute that this is merely unsupported (and uninformed) opinion. Copernicus already knew the relative orbital sizes for all the visible planets well before 1762. Likewise Kepler, in order to formulate Kepler's Laws 150 years before 1762.. – Pieter Geerkens Jul 23 '18 at 13:38
  • @PieterGeerkens Knowing the size of an orbit and knowing the size of a planet are two questions as apart as they can be without falling out of the same field of study. And you really need a citation to prove that Mars and Jupiter were gods of the greco-roman mythology? – Rekesoft Jul 23 '18 at 13:43
  • First observations of a Venus transit occur in 1639. You have also ignored Tycho Brahe's observations and conclusions. Finally, re gods: Are you really claiming that the civilization that gave us Sophocles was unaware of metaphor.? – Pieter Geerkens Jul 23 '18 at 13:44
  • @PieterGeerkens And it couldn't be measured. Same case as in 1761. – Rekesoft Jul 23 '18 at 13:45
  • @PieterGeerkens Not every greek was Sophocles, though, and many greek philosophers and writers were sentenced to very harsh punishments (including death sentences) for offenses to religion. As with Galileo, you could make research on planetery bodies, but there was a limit to what (and whom) you could preach about. – Rekesoft Jul 23 '18 at 14:06
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The Great Pyramid of of the African Ancient Egyptians embodies an abundance of mathematical measurements related to the sizes and scales of astronomical objects, perhaps far too many to list in a single answer, though we will do so if called upon for further evidence. For example,

The Great Pyramid weighs 6 millions tons More than 2.5 million individual blocks used

Apparently built in 20 years cough (sounds like bullshit and here's why)

For this to be possible the ancients would of had to cut, transport and place 14 stone blocks per hour, 24hrs a day for 7,300 days. There are dozens that weigh at least 70 ton; that's 11% the mass of the Christ the Redeemer Statue in Brazil.

The largest granite stones in the pyramid, found in the "King's" chamber, weigh 25 to 80 tonnes and were transported from Aswan, more than 800 km (500 mi) away.

It's orientated to true north, with the precision of three sixtieths of one single degree.

The average space between each block is 0.5mm

It's height (481ft) x 43,200 = the Polar radius of our planet (in ft).

Measuring the base perimeter and x 43,200 will give you the circumference of our planet (in ft).

43,200 is not a random number. It is derived from the precession of the earths axis. The earth wobbles around it's axis like a spinning top at the rate of one degree every 72 years. 72 x 600 = 43,200.

They have given us the dimensions of our planet on a scale defined by our planet itself, pretty smart right? A scale of 1:43,200. This blows my mind.

See, e.g., The Great Pyramid & The Cardinal Dimensions Of Our Planet: Ancient Egypt Part IV; The Great Pyramid of Giza a mathematically encoded structure; Pi and the Great Pyramid; The Great Pyramid Of Egypt Exactly Marks The Center Of Earth's Landmass

I think it’s also interesting to note that if you multiply the height of the pyramid by a thousand million, you are left with 98,000,000 miles, which corresponds approximately to the distance between the earth and the sun.

At 10,450 BC—and at that date only—we find that the pattern of the pyramids on the ground provides a perfect reflection of the pattern of the stars in the sky. I mean it’s a perfect match—faultless—and it cannot be an accident because the entire arrangement correctly depicts two very unusual celestial events that occurred only at that time.

First, and purely by chance, the Milky Way, as visible from Giza in 10,450 BC, exactly duplicated the meridional course of the Nile Valley; secondly, to the west of the Milky Way, the three stars of Orion’s Belt were at the lowest altitude in their precessional cycle, with Al Nitak, the star represented by the Great Pyramid, crossing the meridian at 11° 08’.8 -Robert Bauval

The Dogon of Mali in Africa, who are direct descendants of the African Ancient Egyptians, have a long history of astronomy, including knowledge of Sirius B, see About the Dogon; Dogon Tribe Nommo; The Dogon, the Nommos and Sirius B; The Pale Fox by Marcel Griaule, Germaine Dierterlen.

Thus, we can trace scientific estimations of sizes and scales of celestial bodies by African Ancient Egyptians to at least 10,450 B.C.E., the Dogon, who are descendants of the African Ancient Egyptians from 3200 B.C.E.; the science, culture, and traditions of the African Ancient Egyptians continuing today within the descendants of the African Ancient Egyptians across the Earth.

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    Most of this answer has nothing to do with the size/scale of celestial bodies. The only relevant part is the estimate of the circumference of Earth, which is based on a highly speculative interpretation of The Great Pyramid measurements. – default locale Jul 25 '18 at 9:47

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