| Further Considerations: Planets and Stars.
The Relative Distances of the Planets.
At this writing (late September 2004), you can see Venus as a bright starlike object, high in the Eastern twilight shortly after dawn. In other years and at other times, you will sometimes see Jupiter spectacularly bright in the Southern sky, or reddish Mars (which was particularly conspicuous in the summer months of 2003). But how, I wonder, would you set about deducing which of these objects is farther away, and on what basis? This is really difficult, especially if you are not allowed the use of telescopes or modern instruments of any kind.
First, you would have to recognize that planets are something distinct from stars! Of course, their motion hints at this, but tells you little else because, to the unaided eye, they appear merely as dots of light. None of the detailed structure we know of now -- not even the prominent rings of Saturn -- can be discerned without a telescope. On the other end of the scale of distance, it is not obvious that Mars, a reddish dot of light, is comparable in many respects to our own moon, an object so nearby that even the unaided eye can see some of the larger structural features, such as the dark 'seas' (maria) and lighter 'highlands.'
Suppose, therefore, that we restrict ourselves to an intercomparison of the planets alone -- that is, leave the remote, unmoving stars and the nearby, resolved moon out of the discussion. What, if anything, can we infer?
Here are a couple of possibilities:
Is it possible to argue that the brighter planets, like Venus and Jupiter, are in general closer than the fainter planets, like Saturn? In fact, this argument doesn't work very well, for two reasons.
1 The brightness of each individual planet changes with time. Venus, for instance, is sometimes very bright, sometimes quite a bit fainter, because of its variable distance from us and the sun, and the changing angle at which we see it.
2 Even if you were to compare the planets at their very brightest (say), this still does not work. Jupiter, for instance, is much farther from the Earth than Mars is, but it can get quite a bit brighter because
it is bigger, so intercepts much more sunlight (it is a `bigger mirror'); and
it is covered with clouds which reflect a lot of light, whereas Mars's rocky surface is not so reflective. (Jupiter is also a `shinier mirror').
We could try parallax measurements (triangulation) in the way we discussed for
For instance, we could arrange to have two people in widely separated locations simultaneously determine the position of Mars relative to the field of remote background stars. This is much more difficult than the exercise involving the moon, since Mars and the other planets are so much farther away, and would in fact have been quite impractical.
In short, before the advent of the telescope, or at least the careful measurements made by Tycho Brahe and interpreted by Keper, there was no really practical way of determining the planetary distances directly, or being absolutely certain about their relative positions. In developing their cosmology, therefore, the Greeks relied on the qualitative argument mentioned earlier: they assumed that the fastest moving things (like the moon) are closer to us than those which appear to move more slowly relative to the stars (like Jupiter). This turned out to yield the correct order of distances, although the actual distances, in units like kilometers or miles, were still quite unknown.
The Relative Distances of the Sun and Stars.You might think it fairly straightforward to work out how far away a star is -- after all, can't we just assume that it is "just another object like the sun?" We would deduce that it looks terribly faint because of its much greater distance, and then simply take that geometric factor into account in working out how much farther away it must be. Unfortunately, it is not quite that simple. First of all, consider the very large mental leap required in making the assumption that the sun is a star! Since you have been told this from childhood, it seems natural to you; but their visible manifestations and importance to us on Earth are really rather different. It is not at all clear that ancient people would have found this a straightforward assumption to make! But let us assume that this obstacle has been successfully overcome. What do the numbers now tell us? Modern measurements reveal that we receive about one trillion times as much light from the sun as we do from a typical nearby star. This is almost entirely attributable to the fact that the stars are about a million times farther away. (This is a consequence of the inverse-square law of brightness. See the figure on page 523 of your text, and remember that one million times one million = one trillion.) But imagine making this measurement in the days before precise instruments were available! You would have to look at the stars at night and say "Well, I estimate that the stars tonight look about one trillion times fainter than the sun does in the day." This is clearly hopeless. Or is it? Surprisingly, there are clever ways to make some progress on this. For instance, you could build a completely dark shed, and then make pinpricks in one wall so that, when you were inside the shed in the daytime, it looked like the stars at night. With a bit of calculation, you could then work out roughly how much sunlight is getting through. Of course, this is still very much up to one's subjective judgement -- can you, in the day, remember how bright a star looks at night? -- but the idea is not completely impractical, and you might be able to at least crudely estimate the relative distances. Forget the sun! It might be more straightforward to intercompare stars with stars. You could, for instance, assume that the stars are all identical in intrinsic brightness, and that their different apparent brightnesses stem from the fact that they are at a variety of distances. You would then conclude, for instance, that Sirius -- a conspicuously bright star -- is closer to us than Polaris, which looks quite a bit fainter. Although this sounds promising, it turns out to be wrong for most stars! They differ greatly in their intrinsic properties. Some of the very closest stars glow so feebly that they can't even be seen, while some of the conspicuous stars are quite far away but extremely luminous -- literally millions of times brighter than the sun itself. The sun, of course, looks very bright because of its proximity. It is, however, a middle-of-the-road star, neither very bright nor very faint.
The Composition and Nature of the Stars and Planets.While there was much speculation on such topics, it is clear that no insight whatever could have led to a reasonable "modern" understanding of the nature of the sun, stars, and planets. We will chart the developments which led to a real understanding as we progress through the course. Note for instance that even in the 1600s Galileo thought there were seas on the moon, and in the 1700s Herschel believed it possible that the sun itself might be inhabited! Very simple physical arguments show that these ideas are completely untenable, but that is a modern perspective, and we should not fault these early astronomers for their imaginative speculations.
Where Do We Stand Now? Keeping Things in Perspective.We have been celebrating some of the achievements of the ancients, and I have occasionally made specific reference to the Greek astronomers in particular. Indeed, your textbook, like many, gives a strong emphasis to the development of astronomical and scientific thinking in the Mediterranean (in ancient times) and Europe (in the last few centuries). To their credit, however, the authors correctly draw your attention to some developments in other societies, a point I would like to stress. Please remember that important and continuous observational records were kept in the Orient (China, Korea, Japan) for millennia; that the Mayans had a very sophisticated calendar, based upon the periodic appearance of the planet Venus; and so forth. Do not make the mistake of assuming that only Europe and the Near East contributed or had independent profound, and often correct, ideas of the nature of the universe. For example, we will see later in the course that modern astronomy is now benefitting in unexpected ways from the rich history of astronomical observations recorded at many of the oriental courts, millennia ago. That having been said, for the moment I still want to summarize the amazing list of achievements of just this one set of thinkers as exemplary of the kinds of intellectual developments made even thousands of years ago. Here is a small tabulation (please do not memorize the dates and details!): 570-500 BC: Pythagoras describes a round Earth 500-400 BC: Philolaus describes the Earth orbiting a `central fire' (not the sun; his model was more obscure than that, but did imply an Earth moving freely through space) 500-428 BC: Anaxagoras speculates that the moon is seen by reflected sunlight, and he correctly explains eclipses 384-322 BC: Aristotle presents various proofs that the Earth is round 310-230 BC: Aristarchus derives the relative sizes and distances of the Sun and Moon 273-? BC: Eratosthenes accurately determines the size of the Earth These were not insubstantial achievements! There were, of course, occasional absurdities (as seen from a modern perspective) in some of these arguments and conclusions, and alongside these successes one could equally write down a series of irrelevant and erroneous conclusions drawn by other thinkers of the time. But in general one cannot help but be impressed by the intellectual achievements, especially in contrast to what one is so often led to believe about the primitive thinking of early civilizations. It is all the more remarkable that so much was accomplished before the development of any systematic understanding of the laws of physics and in the absence of instruments such as telescopes. The challenges facing the ancient astronomers were many. Interestingly, the first of them is a challenge which you too will have to face - one of visualising the geometry of the solar system, and trying to unscramble its structure and nature, from the confusing perspective of a rapidly moving platform: the Earth. In short, it is time for us to add the complication of our orbital motion to our analysis of the sun, moon, Earth and planets. That is the subject of the next section of the notes. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Tuesday, 20 October, 2020.)