The Modern View of the Universe

Astronomy has pervaded popular culture to such an extent that we accept many of the difficult concepts almost instinctively, although it may be that the suspension of disbelief that we naturally invoke when watching film or television (or when reading books) probably keeps us from realizing the extent of the transformation in our view of the universe. We are comfortable with the picture of starships plying the mains between the stars of our galaxy in films and TV shows such as "Star Trek" and "Star Wars". Even more difficult concepts such as "Black Holes" and the theory of Relativity also figure in our popular culture, at least in word if not idea. Perhaps this is not so surprising. Astronomy is the science that has the most to do with our world view, and therefore as this world view progresses it is natural that astronomy feeds our mythology. Q: Can you identify other names and terms that are derived from astronomy? (Hint: Car names are a good place to start.)

The traditional method for the teaching of the basics of astronomy begins with the view of the Universe as painted upon the inside of the Celestial Sphere. This toy model for looking at the sky is simple, and has its uses, but we should no more think about the stars in this way than we would think that when in standing downtown Philadelphia that the skyscrapers are painted on a shell surrounding our priveleged selves! It is much easier to think this way about the stars, however, because we lack the visual cues that allow us to "sense" distance and make the third dimension appear. Q: How do our eyes give us a sense of depth? (Hint: think in stereo).

The Scale of the Universe

It is also true that the compression of time and space that necessarily occurs in the transference to one to a few hours on the screen does not properly convey the vast scale and age of the Universe. After all, as it says in the Hitchhiker's Guide to the Galaxy, "Space is Big. Really Big." It takes light, which after all is as fast as you can go, nearly 4 hours to reach the planet Neptune, currently the most distant planet from the Sun in our solar system.

Because of the vast distances involved, and the extremely wide range of scales of importance (from the atomic, to the human, to the reaches of the Universe), it is important to understand and feel comfortable with the powers of ten, scientific notation, and orders of magnitude. Powers of ten simply refers to the sequence of numbers formed by taking the base 10 to different integer powers, for example 1,10,100,1000,..., as well as 0.1,0.01,0.001, etc. Rather than writing out all those digits and zeros, scientist use what is called scientific notation, where the implicit powers of ten are designated, for example 10^2 (this is supposed to be 10 with a superscript 2, which I can't do in the HTML 2.0 language of the Web), sometimes written as 10E2, or "10 to the power 2", equals 100 of course. Then, 10^3 is a thousand, 10^6 a million, 10^0=1, 10^-2=0.01. For a review of scientific notation, see the beginning of Appendix C in the text (p.A11). Note that we can express any number in scientific notation by pulling out the factors of ten as a multiplier: 12000 = 1.2x10^4. It is traditional to use a mantissa, the number out front, between 1 and 10. Q:Express the equatorial radius of Saturn, 60300 km, in scientific notation.

The idea behind orders of magnitude is the same, since 1 order of magnitude means a factor of 10 (so 2 orders of magnitude equal 100, etc.). Thus, the numbers 0.003 and 30 are separated by 4 orders of magnitude, or 10000. It is easiest to see this by writing these out in scientific notation, 0.003=3x10^-3 and 30=3x10^1, and noting the difference in the exponents 1 minus -3 is 4. Because quantities in astronomy, such as distances or masses or luminosities, span such a large range, it is often very useful to do rough calculations to find out the value of something to the nearest order of magnitude (is it 10? 1000? 10^8? 10^-4?) to see if it make sense. This sort of calculation called order of magnitude estimation is an artform in itself. We will be using this to get the idea of relevant quantities.

WARNING! Order of magnitude is not the same as magnitude (of a star, for example) which denotes the brightness. We will come across this term next lecture when we discuss star brightnesses. The magnitude system was invented by the Greek Hipparchus over 2100 years ago, and although it is a logarithmic system, it is not based on factors of 10! Oh well, this is not the only confusing antiquated system that we will encounter in astronomy. Think of it like the difference between the English system (inches, feet, miles) and the metric system. Just remember, when I say "order of magnitude" I mean factors of 10, and when I say just "magnitude" I mean those funny units of relative brightness.

As an aid to visualizing the scale of the Universe, I have devised "Steve's Handy Manual Scale of the Universe", based on the size of your (or my) fist. I have a small hand, so my fist is about 10cm across, when scrunched roughly into a ball. Let that represent the Earth. Look at the table of Physical Properties of the Planets in the back of the Seeds text (p.A18) and find the Equatorial Radius of the Earth, 6378 km. This means the diameter is twice that, or about 12800 km (rounded off, as I will tend to do to make the calculations easier). The moon (see the Satellites table, p.A19) is 1738 km in radius (about 3500 km in diameter), or 27% of the Earth's diameter. This makes it 2.7cm on our scale, or about the size of my thumb! So far, so good. Oh yeah, its 384000 km from the Earth, or 30 Earth Diameters (E.D.) (=384000/12800). Thus, we would place the Moon (thumb) 30x10cm=300cm=3m away. My arms aren't long enough, so I'll have a friend do the moon. Try it yourself with a friend. Then picture a tiny, tiny Apollo spacecraft (on our scale, actually, about 0.002mm or 2 microns, a tiny dust grain!) shooting from your fist, then heading across the 3 meters to the thumb!

The Sun is around 1.4x10^6 km (Constants Table p.A12, convert meters to km, then radius to diameter) in diameter, or nearly 110 E.D., so on our Manual Scale the Sun is 11 meters across (a big room, 36ft across). The average distance from the earth to the Sun is around 150x10^6 km, or nearly 12000 E.D., so it would be placed 1.2 km from our Earth-fist. This is just short of a mile --- if we hold up our Earth in DRL, then the Sun is in the center of the city! Q: Find a map of the city and use the scale to locate an appropriate landmark 1.2km from the DRL.

The average distance from the Earth to the Sun, which is 149.6 million km, is known as the Astronomical Unit, or AU. It is a convenient unit for measuring the orbits of the planets in our solar system (as we will find when we study Kepler's Laws and orbits). We just showed on our manual scale that 1 AU = 1.2km.

We can now consult the Orbital Properties Table (p.A19) to place the planets in our Solar System. Our nearest neighbor planet, Venus, has an orbital "semimajor axis", or radius, of 0.72 AU, or = 8640 E.D. (we round to 8600). Therefore, Venus circles our Sun at a distance of 860m. Venus is about the same size as the Earth (0.95 E.D.), so we can use a friend's fist to represent it. Q: What is the closest distance Venus approaches to the Earth (assume circular orbits)? What is this on our Manual scale?

Jupiter is 11.2 times the E.D., so we make it 1.12 m across (slightly larger than if you make a circle with your arms). Its orbital "semimajor axis" from the Sun is 5.2AU, which places it 6.2km from the Center City Sun. Q: If we locate the Sun in Center City, and hold up our fist for Earth in DRL, then where should our friend holding their arms in a circle stand to represent Jupiter at its closest approach to Earth?

Here is a summary of our Manual Scale of the planets so far.

Planet	Diameter	Distance	Scaled Dia.	Scaled Dist.
Sun	1.4x10^6 km	0	11 m	0
Venus	12200 km	0.72 AU	9.5 cm	860 m
Earth	12800 km	1 AU	10 cm	1.2 km
Jupiter	143000 km	5.2 AU	1.12 m	6.2 km

Note that I have adopted a heliocentric, or sun-centered, system (the distances are referred to the Sun at 0). All values have been rounded to two significant figures (three if the first digit is a 1). Q: Can you fill in this table for the other planets? (Use the tables in the back of the Seeds textbook.)

Astronomy as Archaeology

Astronomy as a science is in many ways like archaeology or paleontology. And I don't mean this just because the finite speed of light causes more distant object to appear as they were in the past. What I mean is that what we know about the Universe outside our solar system we have found out from the study of relics - in this case the light that comes to us from the stars and galaxies. Just as the archeologists cannot travel to ancient Egypt, or paleontologist do not have the luxury of travelling back to the Jurassic period, we lack the means to travel out many light years into space and visit those stars that we want to understand. We can't really even visit our Sun because of the extreme conditions. We must deduce what the stars are made of, what the Universe is made of, by what we happen to see.

We are under even more disadvantages than the archaeologist. We are unable to even look at one of our relics from more than one direction. This is similar, I guess, to the plight of the paleontologist, who must take the fossil as it is, and hope to find many different fossils of the same creature preserved in a variety of positions and circumstances, so as to be able to reconstruct the animal or plant as it truly was. So must we sort through the many fossils of the Universe to find order and pattern, and thereby learn what it is that we are seeing. And to find out the nature of this Universe that we are inhabiting.

Construction of the Astrophysical Model

It used to be that models of the Universe, the solar system at least, were constructed of brass. David Rittenhouse, the nation's, and Penn's, first astronomer and contemporary of Ben Franklin, painstakingly constructed such models, called orreries. In the west wing of the first floor of Penn's main library there is a display of a large orrery. I urge you to visit it.

The modern astrophysical model is constructed of mathematics, not metal. Our goal is to build quantitative models, with predictive power. We wish to be able to calculate the positions of the planets in the coming years, of the stars in the coming centuries, of the galaxies in the coming millenia and longer. We wish to know the fate of our Sun, and what its history was also. The science of physics, to which astronomy has contributed greatly, has laid down the physical "laws" or rules by which the Universe is seen to run. Mathematics is the language in which the physical law is written. By building a model out of equations, insubstantial as they are, we can fathom the workings of the Universe. This is a tricky business, with many obstacles and false roads followed. Yet we have been remarkably successful in our endeavor.

The Role of Observation

Because the light that we see is the fossil relic which we are able to study, astronomical observations are our prime tool to explore the universe. Ancient astronomers used their eyes to look upon the heavens. It wasn't until the time of Galileo that telescopes were devised to enhance our view of the sky. It was at this time that the great discoveries of astronomy began, spurred on by the amazing new observations and measurements that were made with these ever improving instruments. It is still true today, in astronomy as in other sciences, that new instrumentation is the fuel for discovery. New telescopes equals new discoveries equals more information equals better theories equals (hopefully) better understanding of the true nature of the Universe and the physical laws that govern it.

Astronomy and Other Disciplines

Besides the obvious connections to physics and mathematics, astronomy borrows tools and ideas from all the other sciences. This is not surprising, given that astronomy is the science of the Universe. Planets are made of rock and gas, and one must know Geology and Chemistry to study them in detail. The Earth is teeming with life, and the possibility of finding life elsewhere brings Biology into the picture.

The astronomer, when wearing the mantle of observer and instrument builder, is a jack-of-all-trades. Engineering, optics, cryogenics, electronics, machine fabrication all have their place in the astronomer's repetoire.

It is perhaps appropriate that you have chosen Astronomy as the science to explore, as it encompasses all sciences.

Steven T. Myers - Last revised 16Jan96