Philosophy 167: Class 5 - Part 12 - Pierre Gassendi and the Transit of Mercury: the Elliptical Orbits, the Sizes of the Planets, and their Heliocentric Distances.
Smith, George E. (George Edwin), 1938-
2014-09-30
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All right, the important one here immediately is Gassendi. Kepler had announced that there would be transits of both Venus and Mercury during I guess it's 1633. 1631, I'm sorry. Yeah, 1631 I should read. It turned out the transit of Venus was visible only in the Western hemisphere. But the transit of Mercury was, many many people attempted to see it, during the time predicted, as I recall it's November of 1631.
Most of them didn't see it for one thing it was a cloudy day in Europe. But more importantly, they didn't use a telescopic sight. So what Gassendi and two others, Kysat and, whoever I'm trying to remember, Remus. Kysat, Remus and Gassendi, were the three people. Gassendi,was in Provence at the time, not in Paris.
They all used camera obscura. That is a small hole with a light coming through but they then magnified it telescopically. And witness, this is Gassendi's publication showing his drawing of Mercury versus the ecliptic moving across the sun. These I have to look at my notes to tell you.
Kepler prediction of when it would occur was off by 13 minutes in arc in longitude. One minute and five seconds in latitude, and in egress, when it left, 14 minutes and 24 seconds. Now that's not four or five minutes of arc, but it's all within 15 minutes of arc.
Longomontanus, or, excuse me. Yeah, Longomontanus was off by more than four degrees. Okay? Not minutes four degrees. And then, Landsberg was more than one degree in longitude and seven minutes in latitude. So, the upshot, and Gassendi simply says this. He's very, very strongly pro Keplerian in announcing this.
Of you can't do Mercury without it being an ellipse. Kepler is exactly right. And from this moment forward from the publication by Gassendi of this result forward. Very few serious astronomers did not use the ellipse. Was the turning point in the acceptance of Keplerian astronomy, not the the area rule nobody almost used the area rule.
They would put an equant at the empty focus was the most common move but that it is an ellipse seems absolutely compelling from this. Now this, of course, just an aside, this is typical of how evidence works in science. This is one piece of evidence, they overreacted as the natural reaction.
No, no, they didn't really overreact, they just saw this was sufficient to adopt a position, pending evidence to the contrary. Why continue to hold on to the circle, if they're so clear that Mercury isn't ellipsed and it looks pretty clear that Mars is an ellipse, too, from Kepler's own work.
Be that as it may, when you ask for really compelling evidence in science, you usually are asking for something a generation or two down the line from when it first becomes accepted. Because it takes the community a long while to actually develop Comprehensive evidence rather than initial strong evidence.
I'll give you just one other example, this Higgs boson got announced. They finally have confirmed it's existence after all these years. What are they doing now? They're trying to measure its mass precisely and until they do that, they really haven't got nearly as solid grounds as they would like to have.
So it's the same thing. It's always the same thing. Scientists are so desperate for evidence and when they get something really strong they very legitimately say they jump you know it's a big deal. The other thing that shocked people on this and that's the thing on the bottom you can't see it but I think you can see it in your handouts.
Is Mercury was so much smaller than they expected it to be from looking at it through a telescope. When it went across the sun. How much smaller? Somewhere I have in my notes. It was around 20 arc seconds in diameter, and they expected it to be two minutes.
So that's a factor of ten smaller than they expected. I think that's right, no, it's not right. 20 seconds is a third of a degree, six, it's a factor of six difference. And that left them wondering what in the world's going on here? Why is it so much smaller than it appears in the telescope?
Now we know the reason, and I've already told you. Chromatic aberration puts a nice circle around those things, making them appear larger than they actually are, and Galileo had warned of that. Galileo had actually said that he thought the appearance of these things in telescopes was being exaggerated.
But once you had this it became very clear that it was not easy to trust the telescope. And now the issue became, and it's a twofold issue, what's the actual sizes of the planets and how far away are they really? Those two are hand in hand. Because if I can see the disk and I want to know its size relative to the Earth.
If I know how far away it is and I know how much it subtends. I can draw that conclusion I can even adjust it for the chromatic aberrations surrounding it etc. If I don't know how far away it is, it's very problematic to draw any conclusions. And to see how problematic, Hortensius here concludes, on the basis of telescopic observations, that Jupiter is smaller than the Earth.
Okay, it's not a trivial thing to work out. I mean, Jupiter is immense side-by-side with the Earth. I think the mass ratio is about, it's 100. A little over 100. Earth is one hundred thousandths of the moon and Jupiter is one thousandth of the moon. So we are talking about very, very different sizes needless to say.
But strikingly Saturn is much larger. Of course, he can't really see what's going on with Saturn, with the protuberances on the side. So there's confusion there. But the point I'm making with Hortensia's planetary table sizes, and that comes out of a very useful book, by Albert Van Helden.
It's the whole history of sorting out two things. The sizes and the distances. And we'll come back to this. You'll read part of this later in the course when it gets past the point of conjecture. He compares it in that book and also in, what do I want?
This book, which reminds me, I'll say something in a moment. These are the ones from the medieval times. It's striking, the ones from the medieval times, which were done entirely on guesses about the relative size of the Earth, Moon, and Sun, based on the sun being 1,000 Earth radii away.
It's 22,000 Earth radii away so you can see how useless all this is. Based on that, some of these are actually better values than the ones in Hortensia's. The main point though is they didn't have a real clue of either what the sizes were or the distances were.
They had raised the issue and started worrying about it a good deal. And now I wanna remind you. Tycho, excuse me, Colomy had said the Earth is about 1100 Earth radii away from the sun. Copernicus had reduced it a little, Tycho had increased it a little. Kepler, in reviewing observations, decided Tycho was three times two small in terms of the distance.
That is, he went from three minutes of arc horizontal parallax down to one minute of arc horizontal parallax, but didn't do anything to correct anything. He had just decided it can't be as big as Tycho. So the issue now becomes a very significant question. What's the right distance to the Sun?
And we need it for parallax corrections. And we need it to figure out what the correct atmospheric corrections are, atmospheric refraction corrections. So this becomes the observation of Mercury being so small going across the face of the Sun. That's a very big moment in all of this because it's saying we're way, way off on sizes and distances.
The question is now thrown quite wide open.
