On our ancestors

“If I have seen far, it is because I have stood on the shoulders of giants”

– Isaac Newton (apocryphally, making fun of Robert Hooke, a hunchback- but that’s irrelevant)

I’m sure every scientist (or writer, for that matter) wishes they could travel back in their time machine and go to some bygone age before some important discovery was made.  Go back to 1900 and discover Cepheids and the true size of the Universe… eat that, Hubble!  Go back to 1820 and beat Bram Stoker to the publication of a vampire novel, or pre-empt Shakespeare.  It’s a pretty rosy picture- things were so much easier then, before all this extra work was done and it became so hard to get your voice heard.

Recently, I was researching the history of nearby young stars for my thesis, and decided to track back the knowledge of the Pleiades as far back as I could go  The SEDS page for M45 mentions that a Rev. John Michell mathematically proved the Pleiades were a cluster in 1767, and since the paper was available on JSTOR I had a look.

What was idle curiosity caught my attention.  Apart from the mathematical proof I was looking for(which is both brilliant and simple- given the number of stars of that magnitude in the sky, what is the probability that so many of them are clustered in Taurus?), Michell goes on to theoretically determine all the basics of stellar astrophysics I was taught as an undergraduate, with an impressive success rate.

Though no man can at present doubt, that the want of a sensible parallax in the fixed stars, is owing to the immense distance…

This is exactly right, although vague.  Parallax is best described as the apparent motion of another object as you move.  As you drive down a road, the tree by the side of the road seems to move a lot, the mountains barely move at all; therefore the mountains are more distant.   By this point in history, it had already been realized that if the Earth orbited the Sun, a star at a non-infinite distance should seem trace out a corresponding “orbit” of its own in response, of a size inversely proportional to its distance.  As of 1767, no one had managed to measure that.

In order to do this with accuracy, it would be proper to compare the quantity of light; which we at present receive from [the sun], with that of the fixed stars… I shall assume Saturn then in opposition, exclusively of his ring (and when the earth and he are at their mean distances from the Sun) as equal or nearly equal in light to the most luminous fixed star… [some math determining how much of the Sun’s light falls on Saturn, assuming Saturn is 1/10 the Sun’s diameter]… and removing the Sun to 220000 times his present distance, he would still appear at least as bright as Saturn, and his whole parallax upon the diameter of the Earth’s orbit would be less than two seconds.  This must consequently be assumed for the parallax of the brightest of the fixed stars…

Saturn isn’t 1/10 the Sun’s diameter… but the resulting general scale is right: The closest “fixed” star, Alpha Centauri C, is 268300 times farther away from the Sun, and has a “whole parallax upon the diameter of the Earth’s orbit” of 1.5 seconds of arc.  Of course, it’d be more than 70 years before the parallax to Alpha Centauri AB (together, the third brightest “star” in the sky) was actually measured, and another 70 years before Alpha Centauri C was even known.  Then again, Alpha Centauri C is not one of the brightest of the fixed stars- but Michel was aware of that too:

“Upon supposition then, that the fixed stars are of the same magnitude and brightness with the Sun, it is no wonder that their parallax should have hitherto escaped observation, since, if this is the case, it could hardly amount to two seconds, and probably not more than one in Sirius himself…”

(For the record, the parallax of Sirius, as Michell would report it, is 0.76 seconds, a distance of 2.6 parsecs or 8.6 light years.)

We have assumed the magnitude of the stars, as well as their brightness, to be equal to that of the sun; it is however probable, that there be a very great difference amongst them in these respects… perhaps the consideration, that a star must be a thousand times as great, caeteris paribus, to appear equally bright, if it is placed at ten times the distance, may serve to make it probable, that the limits of the errors, which we are likely to commit, in judging by such a rule, are not so great as we might otherwise imagine them to be.

This guess is dead wrong.  Stars vary in intrinsic brightness by factors of BILLIONS.

In other instances, we may perhaps judge some degree of the native brightness of different stars with respect to one another by their colour; those, which afford the whitest light, being probably the most luminous [according to a footnote, this is derived from observations of terrestrial fires and smithys- red being cool, white being hot]

Conceptually, Michell has invented the photometric distance estimates my PhD thesis are built on.

If however it should hereafter be found, that if any of the stars have others revolving about them (for no satellites shining by a borrowed light could possibly be visible) we should then have a means of discovering the proportion between the light of the Sun, and the light of those stars, relatively to their respective quantities of matter,

Here we have a mass-luminosity relation, a cornerstone of my thesis adviser’s career…

for in this case, the times of the revolutions, and the greatest apparent elongations of those stars, that revolved about the other as satellites, being known, the relation between the apparent diameters and the densities of the central stars would be given…

… and the way angular diameters of (binary) stars were measured prior to interferometry.

..at the same time it seems probable, that we shall never be able to discover any sensible magnitude in their apparent diameters, which in Sirius himself, if he is not of less native brightness than the Sun, must be considerably less, whatever be his parallax, than the hundredth, probably than the two hundredth part of a second… Nor can we well expect to find their apparent diameters from any occultation of the moon, since a diameter… would be covered…in less than the fiftieth part of a second of time.

Actually, lunar occultation studies are now possible thanks to high-speed photometers, and long-baseline interferometry makes it possible to measure the diameters of stars like Sirius, which is 1/170 of an arcsecond in angular diameter.  But that result was only obtained 200 years later.

There are some other worthy mentions in there- statistical analysis of the Pleiades of course, but also mention of the probable albedo of Saturn, measuring the densities of stars, kinematics of stars based on proper motions…  but I think I’ve given altogether too many examples.

Now, don’t get me wrong- I don’t think it’s really fair to claim Democritus invented the concept of the atom when it bears NO resemblance to what Bohr and Rutherford were playing around with- Michell is very vague in the paper, but it’s clear that scientists of his day had a MUCH better idea of the science than I thought.

Point being, were I to be dropped back in 1767, I would not stand out any more than I could today.  These scientists understood the basic physical principles, had the mathematical tools to use them, but were limited by the available technology, just as I (hypothetically) would be.

It’s very easy to think of our ancestors as backward, or fools because they didn’t know what we know now.  Fact is… that’s completely wrong.  And that’s where the quote at the beginning comes in.


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