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A Sense of Scale - the first lab assignment:

Our solar system consists of the Sun surrounded by nine planets, dozens of moons, hundreds of comets and thousands of asteroids. It is likely that many millions more comets lurk at the edge of our solar system, tens of thousands of astronomical units away. We measure distances in the solar system in terms of the astronomical unit (AU), which is the distance from the Sun to Earth, about 93 million miles (150 million kilometers). Distances are so vast beyond the solar system that other units of measure become useful. Light travels at 186,000 miles per second (3x108 meters per second), so in a year light travels about 6 trillion miles. Even at that great speed the images we see of the nearest stars takes over four years to reach us. We call the distance light travels in a year a light year (LY). In terms of this unit of measure, our Milky Way galaxy, with its hundreds of billions of stars, slowly spins as a flattened spiral disk about 80,000 LY across.

The Milky Way is one of about a score of galaxies we call the Local Group, which are gravitationally linked to each other. The local group spans a region about 3 million LY in extent. Our group (or cluster) of galaxies is part of one of many superclusters of galaxies. Our supercluster extends some 150 to 200 million LY. 

A Scale Model

If you're asked what the universe is made of, the most accurate answer may well be "nothing". Although there are uncountable galaxies, each made of billions of stars, the extent of the universe is so vast that the matter of which it is made occupies only an infinitesimal fraction of its volume. Our solar system, consisting of the Sun, the planets and their moons, the asteroids, comets and meteors is a comparatively densely populated region of space, yet it too is mostly empty. It is difficult to get a feeling for the scale of the solar system, much less the universe, but here is a model you can build that may help. You will model the Sun, Earth and the nearest neighbor star to the solar system in this simple experiment. I'll show the calculations so you can see how it comes about. You will make similar calculations to complete lab #1

First we need to set the size of our model. I choose an orange to represent the Sun - it's the right color, a convenient size, and when you're done you can eat it - you can start with the Sun as I did, or any of the planets, and choose any starting size. To be specific, I choose an orange with diameter 4 inches, a fairly average size. This sets my scale: The actual diameter of the Sun is 1.4x109 meters or, since I used inches to measure the orange, 5.5x1010 inches. (You can find data on the size of the Sun and planets in the back of most astronomy text books). Our scale then, is 4 inches divided by 5.5x1010 inches, or about 7.3x10-11 to 1. The rest is easy. The diameter of the Earth is 1.27x107 meters, or 5.02x108 inches, so we multiply this diameter times our scale factor. The result is 0.04 inches. Where do you find something this size? Actually, it's sort of difficult, but a fair, although somewhat oversized, approximation is the ball in a fine tipped ball point pen. So sacrifice a pen to science and find an orange, and you have the makings of the model. Next, the two components of our solar system model (the Sun and Earth) need to be properly located. Call the location of the orange the center and place the ball from the pen one (scaled) astronomical unit away. Again, we establish the scale by multiplying the astronomical unit (93 million miles) by our scale factor, after converting miles to inches. The result is 430 inches, or about 35.8 feet (about 15 paces). So now we have it (it's not very impressive unless actually do it!). Find a big room, or your yard, set down the orange, walk away 15 paces and set down the ball from the pen. Now make believe the rest of the scenery is empty space! Next, make similar calculations for the rest of the planets (don't worry about the various moons, asteroids, etc.). Actually, I converted the distances into inches to match the 4 inch orange. You will find it easier to convert the size of your defining object (I used an orange to represent the Sun) into meters - all the measurements of planetary sizes and distances are given in meters or kilometers.

What about the neighbor star? Find another orange for the star alpha centuri - it's about the same size as the Sun, and 4.38 light years away. A light year is 3.7x1017 inches, so 4.38 light years, when scaled using our scale factor becomes 1.2x108 inches, or about 1,876 miles. So to complete this part of the model, pack a lunch (don't eat the orange), jump in your car and drive 1,876 miles to where the orange is to be placed. (Depending on your direction - and choice of transportation - you could choose Chetumal, Helena, Nuuk or Pointe-Noire, to name a few.)

All in all, its futile to try to build such models, and its about as difficult to get a "feel" for the scale of such things - but without actually trying you really won't understand why. If ever the expression "boggles the mind" comes into play, this is the place. By the way, in the calculations above, some convenient conversion factors are 1 inch = 2.54 centimeters, 1 mile = 5280 feet (Do you know why there's such a wierd number of feet in a mile?), 1 meter = 100 centimeters, and 1 year = 3.16x107 seconds.

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