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I hope this isn't too off-topic. Someone showed me a reference to a French, 11th century biblical commentator who implied that there were over 600,000 stars. This got me thinking, how many stars did people/astronomers think there were back then? As I understand it

For the actual reference, it is Rashi on Deut. 1:10:

The Lord, your God, has multiplied you, and behold, you are today as the stars of the heavens in abundance. (Deut 1:10)

And, behold, you are today as the stars of the heavens: But were they [the Israelites] on that day as [many as] the stars of the heavens? Were they not only six hundred thousand?

Assuming they only counted stars they could see, how many stars can a sharp-eyed person see with the naked eye, assuming ideal observing conditions of course? On top of that, were there any theories in ancient astronomy that extrapolated the number of stars to include ones that couldn't be seen?

Other links:

Wikipedia on Astronomy in Medieval Islam

Wikipedia on Astronomy in Medieval Europe

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I don't think this belongs here... This isn't a question about physics. –  Will Jul 9 '13 at 4:11
@will The astronomy and the physics stack exchange sites were merged. And I'll tell you that my astronomy textbook gets a lot closer to answering this question than my history textbook. Do you have a better place where I should ask this? –  A L Jul 9 '13 at 4:25
Meta post left open and undecided: meta.physics.stackexchange.com/q/156 –  tpg2114 Jul 9 '13 at 4:28
@AL with the changes made my Chris White, I am happy with the question. Your original question was: "This got me thinking, how many stars did people/astronomers think there were back then?" This is a history question, not a question about physics. –  Will Jul 9 '13 at 4:30
This is the physics and astronomy stack exchange. The history of astronomy is part of the subject of astronomy. Voting to leave open. Please do the same. –  Nathaniel Jul 9 '13 at 14:59
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2 Answers

The number of stars that are visible depends heavily on local conditions. Under perfect conditions (e.g. a mountain area with minimal atmospheric turbulence) and with perfect eyesight, one would be able see stars as faint as magnitude 6.5. Of course, conditions are usually not ideal. According to this site, there are

1500 stars brighter than mag 5.0
4800 stars brighter than mag 6.0
6000 stars brighter than mag 6.3
8000 stars brighter than mag 6.5

in the entire night sky. Of course, at any given moment you can only see half of the celestial sphere. But as the Earth rotates, you can observe a larger portion of the night sky from a given location: for example, someone on the equator can in fact observe the entire night sky. It's easy to show that someone on a latitude $\varphi$ can observe a fraction $\frac{1}{2}(1 + \cos\varphi)$ of the celestial sphere. Someone in the Mediterranean can see ~90%, while someone in central Europe can see ~80% over the course of a year.

However, there are a few factors that limit the number of stars that we can actually see with the naked eye. First, it's more difficult to see stars near the horizon than stars near the zenith, because the former have to pass through more air mass. So the threshold magnitude depends on the altitude above the horizon. Second, many stars are components of binary systems (or multiple star systems). Of course, to the naked eye these systems appear as single stars.

So how many stars were known prior to the invention of the telescope? The standard star catalogue in the Middle Ages was the one published by Ptolemy in the 2nd century (part of his Almagest), which in turn was based on Hipparchus' work. Ptolemy's Almagest contains 1022 stars. In the Arab world, Ptolemy's work was updated by Al-Ṣūfī, who published his Book of the Fixed Stars in 964.

The first real improvement, particularly in positional accuracy, was made by Tycho Brahe, who completed his ”thousand-star” catalogue in 1598. His catalogue contains 965 stars. Finally, Johannes Hevelius published the last major catalogue based on naked eye observations in 1687, the Catalogus Stellarum Fixarum, which contains 1,564 stars. The gaps in the southern sky were filled by Louis de Lacaille, who sailed to South Africa in 1750, but his work is based on telescope observations.

It would be interesting to know how many stars were catalogued by Indian and Chinese astronomers, but I haven't found info on that.

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Thank you for a well-written and researched answer. Do you happen to know whether the understanding was that there were only as many stars as they saw, or whether there were any theories or considerations for a very large number of unseen stars? –  A L Jul 10 '13 at 2:37
I think the dominant view was that the universe was finite, with the stars fixed on a celestial sphere (the geocentric model of Plato, Aristotle and Ptolemy). But some Greek philosophers thought that the universe was infinite (Anaximander, Democritus, Lucretius,...) - see cosmic pluralism. In the 15th and 16th century, people like Nicholas of Cusa and Giordano Bruno supported this view on religious grounds ("an infinite God necessarily created an infinite universe"). –  Pulsar Jul 10 '13 at 3:02
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There are about 6000 stars brighter than 6mag visible in the Northern hemisphere.

Before streelights and pollution people would have been much more aware of the stars and so there would seem to be a huge number - while to a modern observer (at least near a city) there appear to be only a handful.

Were there any accurate counts is probably a history question, but it would certainly have been withing the ability of a Roger Bacon to count a sample area and estimate the total

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Request for clarification: 6000 stars within some DEC range (what is the southern limit)? or 6000 on a given night? or 6000 over the whole sphere (which I don't think you mean)? –  Chris White Jul 9 '13 at 4:21
@MartinBeckett Are you recommending that the history.SE site would be a good resource for what was popularly thought of as the number of stars/what theories there were as to how many "unseen" stars there were? –  A L Jul 9 '13 at 4:29
@AL It's hard to say if they have the answer there or not, but whether another site can answer the question is tangential to whether it's on topic here... I can't speak for the answerer of course as to what recommendations are being made or not –  tpg2114 Jul 9 '13 at 4:33
@ChrisWhite - "6000" is just one of those numbers that everyone uses as "visible stars" it's surprisingly hard to find a reference. The northern hemi is a qualifier because there are a lot more stars in the southern hemisphere since the galaxy plane is visible. –  Martin Beckett Jul 9 '13 at 18:23
@AL - Id meant I don't know of any books with specific counts of stars by actual medieval astronomers. There were lots of people (Arabic, European and Indian) who were technically able to do this. –  Martin Beckett Jul 9 '13 at 18:28
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