Inside the Solar System
     The distances in astronomy are so vast that they are difficult to comprehend. The Earth seems very large to us, but even on the scale of our Solar System, it is an infinitesimal speck, its 8,000 mile diameter paling in comparison to the tens of billions of miles required to encompass our planetary system; and when we leave the Solar System, and wander among the stars, the scale of things beggars the imagination.

     The first stop in a tour of our Solar System is the Moon, which lies about a quarter million miles from the Earth, or about thirty Earth diameters away. If we were to use a miniature model of the Solar System, in which the Earth is only about an inch across (about 500 million times smaller than its actual size), the Moon would be a quarter-inch diameter ball, only about two and a half feet away.

     On this scale, the Sun, which is around 93 million miles from the Earth-Moon system, or about four hundred times further than the Moon, would be a ball approximately ten feet in diameter, a thousand feet away from the inch and quarter-inch balls which represent the Earth and Moon.
     Lying somewhere within the thousand foot radius circle which approximates the orbit of the Earth would be another one-inch ball, representing Venus, and another ball, a little less than half an inch in size, representing Mercury. Mercury's half-inch model would be three to five hundred feet from the Sun, depending upon where it was in its somewhat eccentric orbit, while Venus would be about seven hundred feet from the Sun. If passing between the Earth and Sun, it would be three hundred feet from us, but if on the other side of the Sun, it would be seventeen hundred feet away.
     Now think about what these objects would look like, as seen from the inch-wide Earth. The Moon, although only a quarter-inch across, is only two and a half feet away, and as a result, would be seen as a small ball, about half a degree in size. The Sun, although much further away, is much larger than the Moon, and would appear to be about the same half degree in size. (Which is, of course, the way they look in our sky.)
     Mercury and Venus, however, being not much larger than the Moon and smaller than the Earth, would be so tiny, given their huge distances from us, that they would only be dots as seen from the Earth, unless viewed with some kind of magnifying device (e.g., a telescope). And when we look at the night sky, that is exactly how we see them and every other individual object in the Universe, save for the Moon and Sun. Only the planet we live on, its satellite, and the star it orbits are big enough or close enough for us to see them as anything other than infinitesimal dots, without optical aid.
     Beyond the Earth's orbit the Solar System stretches out, ever emptier, as we move through the vast spaces between the outer planets. In our half-billionth scale model, Mars, the next planet outward from the Sun, would be a half-inch ball located fifteen hundred feet -- nearly a third of a mile -- from the Sun. Jupiter, the next planet, is considerably larger, and in this model would be a ball nearly a foot in diameter, but at a full mile's distance from the Sun, and over four thousand feet from the Earth, would still be merely a dot (albeit a bright dot) in the night sky.
     Saturn, the next planet, would also be a ball nearly a foot across, surrounded by an almost infinitely thin disk-like structure -- its ring system -- nearly double the width of the planet. But at a distance of two miles, it would also be a dot, as would Uranus and Neptune, four-inch diameter balls four and six miles from the Sun in this model, and billions of miles out, in actual space.

The Edge of the Solar System
     This ends the count of the major planets, but not the inventory of our solar system. Slightly beyond the orbit of Neptune, hundreds of thousands or millions of small chips of ice, less than a fifth of an inch in diameter in every case, and mostly smaller than snowflakes in our model, slowly move in vast orbits, as much as two hundred miles in radius on our half-billionth scale model, or a hundred million million miles in actual radius. These are the Kuiper Belt Objects (KBOs), of which the first discovered, Pluto, is the only one currently accorded planetary status, although its status as a planet, and that of other objects of similar size, are hotly debated now that we know that Pluto is not the sole occupant of this outermost part of the planetary system.
     Two centuries ago, a similar question existed in the inner Solar System. Between the orbits of Mars and Jupiter lie hundreds of thousands of small bodies, the asteroids, which would be mere grains of sand, or more commonly microscopic specks of dust, in our model. When Ceres, the first to be discovered, was found, it was presumed to be a planet. But soon Pallas and then Vesta were found, and within a few more years, several more, and it very quickly became obvious that it might not be reasonable to call all these objects planets; so they were demoted to planetoids, meaning objects similar to planets (but of sufficiently small size that their planetary status was in doubt), or asteroids, meaning objects so small that, at planetary distances, they look like stars, even through a telescope; whereas the "real" planets, although mere dots when viewed without a telescope, exhibit small disks, when viewed with one.
     If Pluto's discovery had been as quickly followed by the discovery of similar objects as Ceres' discovery was, we might have early on decided to demote Pluto from planetary status. But more than fifty years passed between the discovery of Pluto and the next-discovered KBO, during which time Pluto's status as a planet became more or less firmly entrenched in the mind of astronomers and the general public, and so the question of its status is still a matter of very varied opinion.
     Most of the KBOs move around the Sun in orbits that are more circular than not, in the same direction as as planets, and in nearly the same plane. But there are tens or hundreds of billions of other objects moving around the Sun, far beyond the disk-like structure that contains most of the KBOs. The vast majority of these bodies are only a few miles across, and would be represented by microscopic specks of ice in our model; but despite their small size, they can occasionally appear larger, in our night-time sky, than the Sun or Moon! This occurs when one of these bits of space fluff moves from its normal position, well beyond the orbit of Pluto, to well inside the orbit of Jupiter As the icy object nears the Sun, its heat vaporizes some of its ices, and the resulting gases stream into space in all directions, forming a rarefied ball of gas tens of thousands of miles in diameter -- the "head" or "coma" of the "comet". At the same time the Solar Wind, an incredibly thin breeze (too evanescent to represent in any way in our model) blowing away from the Sun at hundreds of miles per second pushes on the gases streaming away from the icy bodies, moving the gases outward, faster and faster, until they form a glowing streamer, stretching away from the Sun, toward interstellar space. It is this "tail" that gives comets their name ("comet" is based on a Greek term meaning "hairy star"), and their large apparent size; for even though the speck of ice that is the actual physical body moving around the Sun is far too small to see, the tail may stretch tens or hundreds of millions of miles, and if the comet passes near the Earth, the tail may stretch as much as halfway across the sky, under exceptional circumstances.
     For a long time, the origin of the comets was a mystery; but we are now virtually certain that they represent left-over bits from the formation of the outer Solar System, cast into the vastness of space by gravitational interactions with the large planets that lie there, until they fill a region nearly ten to twenty percent of the way from the Sun to the nearby stars with a spherical distribution of incredibly tiny, but incredibly numerous bodies, each revolving around the Sun in an orbit that is perfectly stable, in the absence of outside influences, but so many of them, with so many different types of orbits, that the numbers used to describe the orbits can be almost any collection of random numbers that do not violate the laws of orbital motion.
     Now, it was just stated that these bodies "fill" a region nearly ten to twenty percent of the way from teh Sun to the nearby stars. But just how big is that region, and how well do they fill it? The answer is, very very big, and not very much at all. For the distances to the nearest stars are measured in tens of millions of millions of miles, and even in a model that is half a billion times smaller than reality, the nearest stars would be more than fifty thousand miles away. So the Oort Cloud region, as it is called, is perhaps ten to twenty thousand miles in diameter, in our model, and even hundreds of billions of microscopic bits of ice would be spread so thinly that it would be virtually impossible to see them, even if they were considerably larger. As a result, this outer edge of the Solar System, although almost certainly as described here, has never been observed, and it is hard to imagine any way to ever observe it, save for the fact that its existence is almost certainly required, to explain what we observe, when one of the denizens of that vast region happens to pass near us, and the star that binds us all to it with its gravitational influence, the Sun.

The Realm of the Stars
     Beyond the Solar System, tens of thousands and more miles from us, in our model, and hundreds of millions of millions of miles in the vastness of real space, lie the stars. Each of the stars that we see in our skies is a Sun, like ours. Most are smaller and fainter than our Sun, but almost all seen without optical aid are larger and brighter, and in some cases, much larger and brighter than the Sun. Polaris, for instance, appears as a very faint star to those who live in brightly-lit city skies (which is, of course, most of the people in the world). This is partly because it is relatively far away, compared to the closest stars, and partly because all stars are far away, in any normal conception of distance. The nearest star we know of, Proxima Centauri, is two hundred fifty thousand times further than the Sun, or in our scale model, fifty thousand miles. Other stars are scattered through the vastness of space at similar or larger distances from each other, so that each star's nearest neighbors are tens of thousands of miles away in our model, and hundreds of millions of millions of miles away, in space.

     Since the distances of the stars are so vast, we cannot expect to use miles to describe them; and for quite a long time, a light year -- the distance that light, traveling at 186,400 miles or 300,000 kilometers per second passes through in one year -- has been considered a convenient unit of distance.
     Within the Solar System, we do not usually bother with "light units" to measure distances, as the large speed of light allows it to cross the distances between the planets, vast though they are, in relatively short times. It takes only a second or so for light to reach the Earth from the Moon, only a few minutes to reach us from the Sun and nearer planets, and only a few hours for it to reach us from the furthest planets. But when we take truly giant steps outward and lose ourselves in the vastness of stellar space, light travel times become years, then decades, then centuries, and millennia, for there are stars, such as Rigel in Orion, and Canopus in Carina, whose light takes thousands of years to reach us. Such stars are among the brightest stars we know, tens and hundreds of thousands of times brighter than the Sun, but they lie so far away that in our night-time sky, they are mere specks, faintly glittering in the blackness of the empty spaces which lie between them and the Sun.
     For hundreds of light years in all directions, and thousands of light years in other directions, stars are scattered, almost at random, through stellar space. Even though several light years apart, the vast distances they are scattered through allows their total numbers to swell, as we move further and further out into space, until tens or hundreds of millions of faint specks of light fill long exposure images of the sky.

Remnants of the original lecture notes, to be replaced by discussion, as time permits --

      Because the stars are so far away, using AU's, or miles, or kilometers, is ridiculous. Instead, we invent new units. The first such unit was the Light Year (LY).
      Light goes 186,400 mi/sec, or 300,000 km/sec, or, since there are 31,000,000 sec/yr, about 6 trillion miles, or 10 trillion km, in one year. That makes it a good yard-stick for stars.
      The nearest star, other than the Sun, is alpha Centauri, which is a little over 4 light years away. Polaris is about 1000 light years away. Rigel, in Orion, about 2000 light years away. Most of the stars in the night-time sky are a few tens or hundreds of light-years away, and a very few are just a few LY away, or thousands of LY away.
      LIGHT YEARS are nice, because they are easy to understand. AND, because when you look out into space, you are looking back into time. We see the Sun as it was, 8 minutes and 20 seconds ago. We see Jupiter as it was, somewhere between 35 minutes and 50 minutes ago.
      If you look at a star, you see it as it was, as many years ago, as its distance in LY. NORMALLY, this makes no difference. Stars don't change much, in times that are short compared to millions or billions of years. But occasionally, it can make a difference.
      THIS IS PARTICULARLY TRUE, if we look at things that are VERY far away, such as GALAXIES. However, we also use a different unit, the PARSEC, to measure large distances, for reasons we'll discuss later in the semester.