When did realize the scope and scale of the universe?

Factual Questions
21

Not quite. First, you have to get the distance to the Moon from astronomical observations: This can be done either via parallax by observing from different points on the Earth, or by comparing the shadow of the Earth cast during a lunar eclipse to the size of the Moon. Through either or both methods, the distance to the Moon was already known by Newton’s time, and was in fact essential to the development of his theory.

Then, you get Newton who noticed that, given the known distance of the Moon, the motion of the Moon could be explained via the action of the same force as causes an apple to fall from a tree, if you assume that the force falls off as the inverse square of distance. Newton further realized that an inverse square force would result in Kepler’s laws (at least, as a very good approximation). Using either Newton’s work or Kepler’s, you can then determine the relative distances of all of the objects orbiting the Sun (i.e., that Saturn is nearly ten times away from the Sun as the Earth is, and that Mercury is about a third as far away, and so on), but you can’t determine any of those distances absolutely, since you don’t know how much more massive the Sun is than the Earth.

In order to get that scale absolutely, you need to have some other means of measuring either the distance from the Earth to the Sun, or from the Earth to some other body that orbits the Sun. The first person to do this was Aristarchus, but as has already been mentioned, his method (while sound) had unacceptably large errors (though he could at least determine correctly that the Sun must be larger than the Earth). The first reasonably accurate method of measuring any distance was to use the transit of Venus to enable an unusually-precise parallax measurement of the distance to Venus: This method wasn’t even proposed until after Newton’s time, and astronomers didn’t get a chance to put it into practice until 1769. Nowadays, the best measurements come from radar ranging to various other Solar System objects (near-Earth asteroids are probably the best bet).

22

Aristotle knew that, well before Aristarchus’ time. I don’t know how he knew it, though.

23

Eratosthenes measured the size of the earth and did a pretty good job of it. He knew that on midsummer day there was a place in Egypt (currently Aswan but it was called Syene then) where the sun was directly overhead at noon. It shined down to the bottom of a deep well. He then measured how far it was from directly overhead at Alexandria and found it was 7 degrees from vertical. It was also known that Alexandria was due north from Syene. The final measurement (and probably the most difficult) was to find the distance from Alexandria to Syene. It has been conjectured that he measured the circumference of a wagon wheel and counted the number of revolutions needed to go between the two cities. That would accurate if there were straight level roads. Somehow he corrected for this and came up with a number of stadia. Unfortunately, there were several not quite identical stadia in use at the time. For one of them, the Olympic stadium, the figure he stated was amazingly accurate, to within 1% I think.

But no matter, Columbus’s belief that he could sail to China was utterly wrong. It is a source of amusement that when Jacques Cartier sailed up the St. Lawrence River up to the first rapids, he named the landing place Lachine (French for China) and these rapids are still known as the Lachine Rapids.

24

The typical method mentioned to calculate the diameter of the arth was the one with the sun’s shadow mentioned. I imagine in a known world of around maybe 1,000 miles wide before it fades into obscurity, realizing that it was a globe some 24,000 miles in diameter may have been mind-boggling.

IIRC (it’s been a while since I did this stuff) all you need to know is the gravity of the earth - 32ft/sec^2 - to calculate the distance at which a body would orbit at 29 days. That gives the distance to the moon. Then the apparent angle of the moon gives its diameter.

This
http://eaae-astronomy.org/WG3-SS/WorkShops/Triangulation.html
says that parallax triangulation was used - first by Hipparchus, using a solar eclipse to determine the distance to the moon; then in the 1600’s by Cassini using the parallax of Mars to establish the scale of the solar system. Apparently, they were astonished by the scale of the solar system this implied.

25

As I said above, you either need to already know the Earth’s diameter to use this to get the Moon’s distance, or already know the Moon’s distance to get the Earth’s diameter. If the Earth had half the mass, and 71 percent of its radius, it would still have the same surface gravity, but the Moon would have to be closer to still orbit in 29 days.

26

Relevant to this discussion, I’ve always believed that it must have been ULTRA mind-boggling for people to shift from thinking the earth was basically IT, and everything, including the sun, went around it in shells of sorts, to thinking that the whole thing was really big, and out there, and the earth was just a part of it and it moved around the sun, and the planets moved around the sun, too. I think people would have said, “What?!” “What??” Hard to imagine the disorienting sensation, but totally easy to see why the church didn’t really cotton to the idea.

27

Sorry, you’re right - but then, earth diameter ws the first thing they figured out.

28

It seems to have been the fact that he really liked having his mind boggled in this way that led Giordano Bruno to endorse the Copernican theory, and Bruno was the first significant person to endorse it as a literally true model of the universe (as opposed to a mere calculating device to simplify the math). Bruno, who did not even understand the mathematical and empirical basis of Copernicus’ theory, goes out of his way to stress the idea of a much larger universe, something that was a minor side issue for Copernicus himself, and, as I pointed out above, it was Bruno (and Digges), not Copernicus, who introduced the notion of the stars as other suns, scattered through unbounded space. Other early supporters of Copernicanism, very likely Kepler and possibly Galileo, may also have been attracted to it, at least in part, for similar reasons. (It was Galileo and particularly Kepler, of course, who actually provided the arguments and evidence to show that Copernicus was right. Kepler, like Bruno, was strongly influenced by Hermetic mysticism, and I would not be surprised if he was directly influenced by reading Bruno’s work.)

By contrast, although it has become a cliché to say that the Church somehow felt threatened by the idea of a bigger universe, I have never come across any actual evidence to support this: no hand wringing about how this is unchristian, or will cause people to lose faith. In any case, opposition to Copernicanism did not run very deep in Church circles. Such opposition as there was mostly came from academic philosophers and astronomers who were heavily invested in Aristotelian and Ptolemaic astronomical theories. Most Church officials and theologians simply did not give a damn about astronomy. Bruno’s execution had little or nothing to do with his Copernicanism, but resulted from other, very plainly anti-Catholic (and even anti-Christian), Hermetic religious doctrines that he was fervently promoting. Galileo simply got himself caught up in political struggles within the Church hierarchy, and his Copernicanism functioned more as a convenient excuse to shut him up rather than being the real reason for his condemnation.

So, in sum, although you are probably right that the fact that Copernicanism implied a much bigger universe may have been mind boggling for some, this seems to have functioned to hasten the theory’s acceptance, much more than to impede it. The people who turned out to count liked the idea of a much bigger universe (and, in Bruno’s case at least, really liked having their minds boggled).

29

Any and all questions pertaining to the scope and scale of the universe should be directed to Ilya Bryzgalov, goalie for the Philadelphia Flyers.

30

Galileo’s conflict with the Church was very clearly and explicitly about his heliocentric views. If you wish to claim that this was just a cover, then it is you that must provide “actual evidence”.

Bruno’s imprisonment and execution were indeed for more reasons than just his belief in a plurality of worlds, but certainly it was one of the stated reasons. So for a start I would lose the nothing from “little or nothing” to do with his execution.

31

It means that the Earth-radius is to 1 AU (distance Earth-to-Sun) as 1 AU is to the distance of the fixed stars. Actually, Earth’s radius is about 4000 miles (and had been estimated reasonably by that time) and 1 AU = 93 million miles (unknowable to the ancient Greeks), so 1 AU = ~23,250 Earth-radii and Aristarchus is saying the stars are about 23,250 AU away: in more useful units for this scaling-up, 1 AU is about 500 light-seconds and a light-year is 31 1/2 million light-seconds, so Aristarchus is putting the stars a third of a light-year away.

Assuming that Aristarchus was indeed thinking about the parallax problem, we should actually be interpreting this to mean that he is saying, not that the stars are exactly or even approximately that far away, but that they must be at least that far away (the number of AU to the stars must be greater than or equal to the number of Earth-radii per AU) in order to account for the absence of observable stellar parallax. For 23 centuries ago, this is a great result.

32

Yes, the explicit charges against Galileo were about his heliocentric views (or, more accurately, about the insufficiently tentative way in which he presented them), but it is just false that the Church hierarchy at the time was implacably opposed to heliocentrism. The reasons why Galileo eventually came to be put on trial remain obscure, but it was clearly due to contingent factors of his own situation at the time (including his personal relationship with the Pope) and not because the Church was implacably opposed to heliocentrism. Until the moment of his arrest, Galileo did not consider himself to be in conflict with the Church at all. Indeed, he thought the Pope was his good buddy, and probably though that publishing his heliocentric view would please him.

The story, even inasmuch as it is known, is extremely complex and I do not have the time or energy to rehearse it all here (again: I have done so before on these boards). If you don’t believe me I suggest you read a book or two on the subject by any real, professional historian, that has been written in the last 50 years or so.

To the best of my knowledge we do not have very definite evidence of what the exact charges against Bruno were. It is true that Wikipedia (to be taken with the usual grain of salt) lists “claiming the existence of a plurality of worlds and their eternity” as amongst his many heresies, and his belief in a plurality of worlds was related to his belief in heliocentrism. They are not the same thing, however. The connection was one Bruno made for himself. Plurality of worlds (if worlds is understood to mean “solar systems”) is consistent with, but it does not follow from heliocentrism. Bruno did not get it from Copernicus, and other Copernicans did not have to be committed to it. (I am fairly sure Galileo was not; Kepler was tempted by it, but not, so far as I am aware, firmly committed to it). Furthermore, I would guess that the inquisitors would have been much more concerned about claims about the eternity of worlds rather than their plurality, and heliocentrism carries no implications about eternity at all. (Since that time, Christianity has managed to assimilate the possibility of alien life in other solar systems reasonably well, but its eschatology still requires all these worlds to end some day.)

In any case, quite apart from the plurality and eternity of worlds, there is plenty enough in Bruno’s voluminous writings (of which his remarks about heliocentrism and plurality of worlds constitute but a tiny fraction) to convict him of many much more serious heresies many times over. He directly contradicted Catholic doctrines about such central things as the nature of Jesus and of the trinity, the Eucharist, the soul, and the virginity of Mary. Compared to this, the plurality of worlds was peanuts. I stick by my claim that his heliocentrim had “little or nothing” to do with his execution. His heliocentrism was loosely connected (in Bruno’s own mind) with his belief in the plurality of worlds, which may have been one aspect of one of the least important charges made against him.

33

This is completely opposite to the truth. The Church dug in its heels against heliocentric astronomy in an astonishingly stubborn way. To an Index Librorum Prohibitorum banning more heliocentric books, Pope Alexander VII appended a small Bull Speculatores Domus to ensure that all further such books were banned by default: “In our apostolic capacity as the vicar of St. Peter, we enjoin all the faithful to renounce and abjure the pernicious Pythagorean doctrine that the Earth is subject to a double motion, a diurnal rotation about its axis and an annual revolution about the Sun.” Embarrassingly, this language (speaking ex cathedra in his official capacity, and commanding a duty to the whole community of believers) fits the criteria later set in the 1st Vatican Council for an “infallible” statement.

The result was that the study of astronomy practically vanished from Portugal, Spain, Italy, and Poland, all countries which had formerly been rather prominent in the field. In France, although it was a Catholic country, the kings never did take dictates from the church, so astronomy persisted; Descartes’ works on physics and astronomy (as well the works on philosophy and analytic geometry we now know him for) were put on a secondary Index, the list of books prohibitum dum corrigendum, but although they were never “corrected” they remained popular in France. The most prominent Italian astronomer of this period, Cassini (discoverer of Titan and the one who figured out what the rings of Saturn were like-- Galileo thought they were like handles on the sides), had to move to Paris to continue his work.

It was difficult for the Church to walk this back. It was not until 1830 that finally an imprimatur was granted for a science book discussing “What modern astronomers believe…” That is, it was permissible to describe modern theories (it was increasingly embarrassing not to be able to teach Newtonian physics in the schools, and of course Newton’s model of the solar system took heliocentrism as a given), but only on the condition that you do not actually say that those things are true, just that others believe them. Later in the 19th century, this weasel-wording fig-leaf was quietly dropped; Leo XIII built an observatory at the Vatican, implicitly telling astronomers they were acceptable again (he was also the Pope who opened up the Vatican Archives to scholars of all faiths and nationalities). The Bellarmine Catechism, which reaffirmed geocentrism in passing while discussing scriptural inerrance (the author, Cardinal Bellarmine, was Galileo’s prosecutor), was dropped in favor of new catechisms, such as the Baltimore Catechism in the US. This caused an uproar of backlash among conservatives who thought that the church was surrendering to Satan by throwing out the old catechism; the next Pope, Pius X, gave Bellarmine the title “Doctor of the Church” which is held by only a handful of others (Aquinas, Augustine, Chrysostom, a couple more less well-known outside church circles) to placate the diehards.

However, Bellarmine’s strict views on scriptural inerrance were gone from Catholic teachings. Bellarmine was sure that Biblical assertions of material fact, like Joshua stopping the Sun, must be believed as firmly as anything more theological-sounding: “It is as blasphemous to deny that Abraham had two sons as to deny that Christ was born of a virgin, for the selfsame Holy Spirit proclaims both.” (Ironically, the Bible actually says Abraham had eight sons: Bellarmine must not have read that after Sarah and Hagar were dead, Abraham married Keturah.) After the change in catechism, the Catholic church refused to be stuck with the dead-literalist fundamentalism that has plagued many of the Protestant denominations in the United States; Catholic scholars have been much more willing than Protestant scholars to view the Bible as a product of fallible humans, doing their best but inevitably getting some things wrong (though the Holy Spirit will make sure we understand things better before any such mistakes cause real problems). In particular, several Popes have made sure to state that the Church has no conflict with the theory of evolution: no way do they want a repeat of the geocentrist debacle.

34

Even granted that you already know the Earth’s size, this also assumes that you know that the Earth’s gravity falls off as the inverse square. But that was actually determined by knowing the Moon’s distance, not vice-versa.

35

Here are the diameters of the objects in question:

SUN = 1.4 x 10^9 meters
MILKY WAY = 1.2 x 10^21m
VISIBLE UNIVERSE = 9.3 x 10^26m

So you are right about the many orders of magnitude difference S:MW versus MW:VU

However, the distance MW:VU is still so great that the entire “Local Group” of galaxies
of which the MW is a member would be invisible to the unaided eye of an observer on the border of VU.

See these excellent graphics for perspective:

The Scale of the Universe from Strings Up

36

“Don’t worry, be happy.” 'Nuff said. :stuck_out_tongue: It could always be worse.
I once felt sorry for myself because I had no shoes, till I met a man that had no feet. (Confucious?)

37

An interesting popular science book is The Day We Found the Universe:

This covers territory a lot later than some of what’s been discussed, but still fascinating.

38

Oh, by the way, I’m very impressed by that goalie. Sure, he didn’t give much detail, but everything he said was right, and he managed to avoid several common misconceptions along the way. That’s pretty good for a layman, especially one in a field not usually noted for intellectual pursuit.

39

Are you claiming that the consensus view among scholars is now that Galileo’s trial was triggered by political objectives?

40

I just finished reading “A Brief History of the Universe” and enjoyed it very much. It gives a good overview of most of the major advences in our understanding of the universe, along with the related history of the time.