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ANALOGY TO HELP APPRECIATE ASTRONOMICAL DISTANCES AND TIME

G. Wyckliffe Hoffler, M. D.  --  14 July, 2001

Begin with our SOLAR SYSTEM.

Start with the Earth where we are. It is 12,740 km in diameter (almost 8000 miles, and I will hereafter stay with our customary units with which we are more familiar).  We understand this as an enormous dimension when we walk across its surface, or drive great distances, or even fly between continents.  The British-French Concorde, traveling at twice the speed of sound can cross the Atlantic Ocean in about 3.5 hours.  However, the Space Shuttle, traveling over 17,000 miles per hour, requires only 90 minutes to circle the Earth.  And the Apollo space craft, ejected from Earth orbit at 25,000 miles per hour (escape velocity) took 3 days to reach the Moon.

Now our Moon is about 2160 miles in diameter (1/4 Earth's) and lies on average about 240,000 miles away. When we deal with just these nearby distances, we need some kind of model to appreciate them.

Imagine with me our Sun (886,000 miles in diameter, 3 1/2 times the distance to the Moon) represented by a basket ball (this arbitrary scale is thus 1 foot equals 1,000,000 miles, or a 1:5.28 billion spatial compression) placed along the central Florida coast line.  Mercury , its first planet out, would be represented by a small seed (1/16 inch) located 38 feet from the Sun.  Then at 67 feet a small pea (smaller than a BB shot) would represent Venus. A similar pea at 93 feet is our Earth; but here, if we looked very carefully, we would see a peculiar double planet system, with a small seed (1/32 inch), our Moon, circling the Earth 3 inches away.  Farther out at 152 feet, but with highly varying distance depending on its orbital position, a red seed somewhat larger than Mercury would represent Mars.  It would take high magnification to detect its two tiny orbiting moons, Deimos and Phobos.

Over a span of several tens of feet outward from our centered basket ball-Sun, with a radius averaging almost the distance of a football field (276 feet), we would encounter many sand grains and countless more microscopic particles orbiting the Sun as what we call Asteroids or, more correctly, Planetoids. The largest of this solar system debris is Ceres, less than 600 miles in diameter and a sand grain less than a hundredth inch in diameter on our arbitrary scale.

Continuing out from the Sun, at 520 feet, we would come upon a golf ball sized object. It is Jupiter, the king of the planets, a gas giant comprising more mass than all the other planets combined.  Indeed, some astronomers opine that if Jupiter had perhaps ten times its current mass, it might be a double star with the Sun.  In fact, it actually does emit more energy (not at visible wave lengths) than it receives from the Sun. And we are just on the verge of a quantum gain in our knowledge of Jupiter and its miniature planetary system. The space craft Galileo has made exhaustive close orbital study of the planet and many of its 18 known moons.

Wandering farther down the beach, at 954 feet, we come upon a most unusual sight.  There is a Ping-Pong ball sized sphere with a thin ring of material encircling it. And like its larger compatriot, Jupiter, Saturn has a veritable swarm of tiny moons about it.  Titan, appropriately named, is the second largest moon of the solar system and the only one known to date to possess a significant atmosphere. The Cassini mission, scheduled to reach Saturn in 2004, much as Galileo is now studying Jupiter, should send a probe into the atmosphere of Titan.

At more than double Saturn's distance from the Sun (1918 feet—0.4 mile) we find a pale blue-green sphere about the size of an English walnut.  Uranus (the first planet discovered by scientific processes and whose name derives from the Greek word for Heavens () has five known moons and a ring system of its own. This multi-ring system was discovered by the earth-based flying observatory (the Kuiper Airborne Observatory) timing the occultation of a star by Uranus before Voyager confirmed its presence visually. Incidentally, Uranus can achieve naked eye visibility, but it was never detected by the ancients.

At some 3006 feet a slightly larger, and more subdued blue-green English walnut is our Neptune.  Not to be outdone, it sports several moons, rings, and surface features not unlike Saturn and Jupiter.  While Voyager first revealed surface features, the HST can now also show them from its unobscured vantage point in earth orbit.

Now we are approaching the realm of the Oort cloud of cometary masses hovering at the far periphery of our Solar System. At an average of 3944 feet (but in a highly elliptical orbit, and at this very time actually closer to the Sun than Neptune), we find a little object (discovered in 1930, slightly more than double the size of Ceres) never visited by a space craft, and until recently with the HST, never seen as a disk with surface features, nor with an atmosphere and a companion, Charon, discretely resolved.  Much scientific conjecture prevails now:  Is Pluto a planet or a comet? And are some asteroids merely spent comets?

After such a casual saunter down the beach, we must realize that the plane of the beach may well represent the rather flat layout of the Solar System, although we must have full orbital dimensions in all directions within that plane. Curiously, all the planets but Mercury and Pluto revolve around the Sun within 2.5 degrees of a common plane (which we call the Ecliptic—the projected path of the Sun in the sky from our earth perspective) and in a counterclockwise direction as viewed from the Earth's northern hemisphere. This seems to be a common phenomenon seen throughout the universe, namely of flattened, circular organization of groupings of matter.  There are renegades and exceptions, however.  Asteroids and comets may be found in virtually any orbital definition.

We could carry our analogy also into the time dimension. For instance, suppose we arbitrarily scaled time such that one second represented a day (a 1:86 ,400 compression). The little seed we chose for Mercury would zip around its 37-foot radius (232-foot circumference) orbit in 88 seconds (that equals about 1.8 mph), Venus, in 167 seconds, and Earth, of course, would complete its orbital year in 365.25 seconds A person carrying that small seed pea would have six minutes to make Earth's orbital circuit of 584 feet, a linear distance of about two foot ball fields in a leisurely saunter of 1.1 mph. Similarly, the times for the other planets would find their equivalent representations. And our most distant planet, Pluto, would require for its real 250-year orbital period over 25 hours to go once around its circumference, a nearly 5-mile compressed, elliptical path.

Please note carefully, however, that, if we had kept our time compression at the same ratio (1:1,000,000) as that for the distances above, our day would be represented by 16 microseconds instead of 1 second, and Mercury would be blazing around its 232-foot orbital circumference in 1.4 milliseconds.  You could entertain many exercises in time and space compression or expansion and gain some real insights into the reality of our microcosm, the solar system, or of the enormous universe whose mysteries we are continuing to unfold.

Perhaps now we can better appreciate that this little retinue of orderly, though sometimes appearing chaotic, mass we call the Solar System is an infinitesimal in the scheme of the Cosmos. From the Greek, Cosmos (order) is the antonym of chaos.  Our solar system, with a sort or run-of-the-mill star, is a tightly knit grouping incomprehensibly distant from the nearest next stellar system. On our previous beach scale for the Solar System the nearest star from Earth (Sun) is the Alpha Centauri group (really Proxima Centauri). Its sentinel of light would shine on our Florida beach mini-scaled solar system from somewhere in California (2500 miles).  The real distance is nearly inconceivable, 25 trillion (25,000,000,000,000) miles.  Hence we have devised other units for measuring distance:  the astronomical unit (AU), the LIGHT YEAR (LY), and the parsec (PC). The astronomical unit (AU) is the average radius of Earth's orbit (roughly 93 million miles), but that is also quite inappropriate for recording stellar distances; it takes light only about 8 minutes to reach Earth from the Sun. In perspective, light from the Moon takes only 1.25 sec, from the Galileo space craft at Jupiter (remember that radio waves, like light, are part of the electromagnetic spectrum and travel at the same speed) 43 minutes, and from Pluto 5.5 hours. Yet at this great speed  (300,000 kilometers or 186,00 miles per second), it requires 4 1/3 years for light to reach us from Alpha Centauri.  The parsec is a yet longer unit of distance, that distance from which the semi -major axis of Earth's orbit subtends an angle of one arcsecond (in the sky our Moon is about 1800 arcseconds or one-half degree). The parsec is accorded the usual metric prefixes, such as kiloparsecs (1,000 PC) and megaparsecs (1,000,000 PC), much more convenient terms when we get out to galactic distances.

So we see, in the greater perspective of the universe, that nearest star is still figuratively in our back yard. The distance across our Milky Way galaxy, containing maybe 140 billion stars, is more like 100,000 light years (or 30 kiloparsecs), and the very closest next galaxy to our Milky Way is the Andromeda galaxy (Messier 31), some 2.2 million light years (about 660 kiloparsecs) away.  Incidentally, that feeble light can be glimpsed easily in a dark sky setting with the unaided eye.  In some of the recent images from HST, taken deliberately in areas of sparse star density, there are visually hundreds of more and more distant galaxies, out toward the presently reachable limits of 12-14 billion light years (on the order of 6 or more megaparsecs).  So far we do not seem to have appreciated an edge or terminus of the observable universe. Our human cerebral capacities cannot grasp the implications.

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