Supersonic Man

May 10, 2018

if the solar system fit in a stadium…

Filed under: Hobbyism and Nerdry,science! — Supersonic Man @ 12:00 pm

(I wrote a post about this a few years ago somewhere else, but now I can’t find it, so I am redoing it here, and expanding it.)

How big is the Solar System?

Let’s start by assuming that we have some general idea of how big the Earth is.  If we fly from coast to coast in the United States, we’ve gone one eighth of the way around it.  A long day of driving in a car, say 500 miles, goes about one fiftieth of the way around.  So the Earth is very large compared to your local town or neighborhood, but it’s of a scale that can be grasped and managed with common means of travel, such as cars and planes.  Even preagricultural people sometimes traveled and traded over distances of a thousand miles or more, and that’s not tiny compared to the size of the Earth.

The Moon is a good deal smaller than the Earth, but quite far away from it.  It takes well over one second for a beam of light to travel from the Moon to the Earth.  The distance to the Moon is enough to wrap around the Earth nine or ten times (the Moon’s distance varies over that range during each month).  It’s the sort of distance that a junky old car might accumulate on its odometer after twenty or thirty years of driving — over a quarter million miles when the moon is furthest out.  People are capable of traveling such distances over many years, or in just a few days with our most powerful rockets.

To appreciate the scale of the rest of the solar system in comparison to this, let’s imagine a scale model, sized to fit into a big football stadium.  The scale of this model will be 1/100,000,000,000 of life size.

Let’s look at how each part of the solar system would appear at this scale.  The Sun, which hangs over the middle of the fifty yard line, is a bit over half an inch across — about 14 millimeters, to be more exact.  It’s the size of an olive.  Mercury, the innermost planet, has an eccentric elliptical orbit around it which is eighteen inches (46 cm) from the sun at its closest, and twenty-seven and a half inches (70 cm) at its furthest.  The planet itself is a practically invisible speck, only one five hundredth of an inch across, or a twentieth of a millimeter.  Venus, the second planet, circles our olive-sized sun at a distance of about three and a half feet (108 cm), so its orbit crosses the 49 yard line on each side. The size of the planet is about 1/200 inch, or an eighth of a millimeter, a speck which is probably big enough to see if you get close enough.

The Earth’s orbit is found at a distance of a bit under five feet (150 cm) from the sun.  And the orbit of the Moon makes a little circle around the Earth.  The distance from the Moon to the Earth, which in real life is up to a quarter million miles, and is the farthest distance that any human being has ever voyaged, is only about 5/32 of an inch, or 3.9 mm, in this scale model.  The entire circle traveled by the Moon around the Earth is barely half as big across as the Sun is.  It would fit inside a pea.  The distance to the Sun is almost four hundred times as large.  The diameter of the Earth itself in this model is about 1/200 of an inch, the same as Venus, and likewise would be a barely visible speck.  The Moon, being smaller than Mercury, would be very difficult to see.

Mars circles seven and a half feet out (2.3 meters), and is about 1/400 inch or 1/16 of a millimeter across — a dust speck.  The asteroid belt spreads in a hollow disk around the sun, with the bulk of it starting about ten feet out, and then it thins out at a distance of around eighteen feet (3 to 5.5 meters).  None of the individual asteroids are big enough to see.

Jupiter, the largest planet, sits a little over 25 feet (7.8 meters) out from the Sun.  Its orbit crosses past the 42 yard line on each side of midfield.  The planet itself is plenty big enough to be more than a speck: it’s 1.4 millimeters in diameter, or somewhat under one sixteenth of an inch — the diameter of the head of a pin.  If the Sun is an olive, Jupiter might be a large poppyseed, or a small millet grain.  It has a number of moons, the four large ones being Io, Europa, Ganymede, and Callisto.  The orbit of Io sits about 5/32 inch (4 mm) from Jupiter, and the orbit of Callisto is about 3/4 inch (18 mm) out.

Saturn is 46 feet (14 meters) from the sun.  Its orbit crosses the 35 yard line.  It’s smaller than Jupiter, but if you include its rings, it looks bigger.  You might model it with a small flat sesame seed.  Its major moon Titan sits half an inch (12 mm) out from the planet.  Uranus is much further out, 98 feet (30 meters) from the Sun, so it nearly reaches the 17 yard line, and on the sides it spills over the out-of-bounds line into the sidelines.  Its diameter is half a millimeter, so you might represent it with a grain of fine sand.

In this model, the orbit of Neptune, the most remote true planet, has a span that just about reaches the one yard line, but can’t quite reach the goal lines, orbiting 148 feet (45 meters) from the sun.  Its size is about the same as sand-grain Uranus.

From this you can see that the Solar System is very empty.  Besides the olive-sized sun, everything else on the field is just some specks which, all added together, wouldn’t amount to a grain of wheat.

Now the Sun and all the planets pretty much fit onto the playing field, but that’s not the whole Solar System.  Beyond all the planets are a number of icy bodies, large and small.  They constitute a sort of second asteroid belt.  It’s called the Kuyper belt.  Pluto is one of these icy bodies, and it isn’t even the biggest one.  As far as we presently know, it’s the second biggest.

In our scale model, the Kuyper belt fills the rest of the stadium, beyond the playing field.  Pluto is down in a good low seat right near the sidelines, and some of the others are way up in the cheap seats, hundreds of feet from the field.

The light of the Sun doesn’t reach up there very well.  It casts a good bright illumination in midfield, but the goalposts are pretty dim, and in the top row of the seats you can’t see much when you look away from the sun.  If I have this figured correctly, at this scale, it puts out about five thousand watts of light.  But don’t compare that to a 5000 watt lightbulb — your ordinary traditional bulb puts out mostly heat, so the 100 watt lamp in your living room is only emitting about ten watts of actual light, and if you use a modern bulb such as a compact fluorescent, it will say “100 watts” on the box while only actually using about 25 watts.  The Sun puts out at least three quarters of its energy as visible light.  Think of it more as a 5000 watt welder’s arc than a 5000 watt lamp.

One thing this idea of an arc lamp in a football stadium fails to convey is how slow the light is.  You have to remember that the light from our tiny Sun takes minutes to reach Earth just five feet away, hours to reach Neptune, and most of a day to reach the upper seats.  If there were a snail crawling around on the grass, it might well be moving at several times the speed of light.  And the fastest rockets never approach even a thousandth of that speed.  (The fastest moving objects we’ve ever launched into space, or will launch soon, are solar probes that drop inside the orbit of Mercury.  That inward fall can give them a speed dozens of times faster than, say, the Apollo moon rocket.)

There’s more stuff beyond the Kuyper belt, also consisting mainly of icy bodies.  But I don’t really count this as part of the solar system.  This is where long period comets come from (short comets, such as Halley’s, come from the Kuyper belt).  This zone is called the Oort Cloud.  It’s found out in the stadium’s parking lot, and some thin parts of it probably extend out into the surrounding city, perhaps miles from the stadium.  While the Kuyper belt is similar to the asteroid belt in that it mainly lies in the same plane as the orbits of the planets and rotates in the same direction that they do, the Oort cloud is spread in all directions, and appears to have no net orbital direction shared in common among the various objects.  For all we know this spread of icy bodies may extend throughout the space between the stars, and not constitute a part of our own solar system at all, except to the extent that the Sun’s gravity causes a thickening in nearby parts of it.

Speaking of other stars, how far away is the nearest other solar system?  It would be about 250 miles away at this scale… about the distance you might find between your hometown football stadium and that of a rival team in the next state.  For instance, the distance between Cleveland and Cincinnati, or Green Bay and Minneapolis, or Chicago and Detroit.

As an afterthought…  What if we changed scales in the opposite direction?  What if we magnified everything so that a football stadium engulfed the solar system?  How big would individual atoms be then?

As big as a house, it turns out — unbound hydrogen atoms would be around twelve meters across, carbon atoms about seventeen meters…  Counterintuitively, heavy metals aren’t much bigger than light elements: uranium is just a bit bigger than carbon, and gold is actually smaller.  The stronger the positive charge of the nucleus, the more densely the electrons pull in around it, so the overall size has remarkably little variation.

Green light would have a wavelength of fifty kilometers.  One of your intestinal bacteria would stretch from Columbus to Pittsburgh.  A red blood cell would sprawl over several midwestern states.  If you have a good thick head of hair, your individual hairs might be as big around as the Earth.  A flea would reach halfway to the Moon.  And if you stood on the Sun, your head might reach past the orbit of Earth.


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