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Wrapping our head around proportions August 24, 2009

Posted by Jorge Candeias in Planets.
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After writing the previous post, I was left with this uneasy feeling of not having been entirely fair towards not only placemats, but Solar System skematics in general. The truth is, it’s impossible to draw the Solar System to scale. The distances between the various bodies are so mind-boggingly vast, that something just has to be distorted, usually planet sizes. The only way to actually have everything to scale and to convey a real sense of sizes and distances is to scatter planet models over vast areas, and travel around the Solar System model thus created. Never in a skematic to be found online, in publications or in placemats.

We can also, of course, use numbers that are closer to our day-to-day experience. Inches, feet and miles for the americans; centimeters, meters and kilometers for the rest of the world. Shrink everything to fit into something a bit more palpable than thousands of kilometers and astronomical units. We all know what a meter is, more or less; we can stand up, put a hand somewhere along our torso and say “it’s about this high”, and we shouldn’t be wrong by much. So, if we divide all the true Solar System numbers by the same constant, we can provide a much more palpable notion of the real proportions out there. For instance…

Say the Sun’s diameter is not more than a million km (1 392 000 km, to be exact), but 100 meters. That’s still a pretty big ball: higher than the first level of the Eiffel Tower, in Paris, and wider than the tower, too. Still, if the Sun is that big, the first of the planets is another ball… with a diameter of 35 centimeters. That’s not even twice the size of a football ball (americans: I’m referring to soccer here). And to find that 35-centimeter ball called Mercury, you’d have to walk more than 8 kilometers!

Next is Venus. To find it, you’d have to travel another 7 km, and when you finally do, you’d see a largeish 87 cm wide ball. You are now 15.5 km from your starting point already and your trek is just beginning. Next, the Earth, another largeish 92 cm-wide ball, is found 6 km further along the road, 21.5 km from your starting point. See a pattern here? Centimeter-wide balls separated by kilometers? Yeah, that’s how things will be till the end. Only more so.

Next: Mars. Mars is, of course, smaller, only 49 centimeters in diameter, and to reach it from the Earth you have to travel 11 km more, away from your 100 m Sun ball. You are now 32 km from it, and unless you have been climbing a mountain of some sort, you probably won’t be able to see it anymore. And you’re still in the inner Solar System.

The next planet, Ceres, is also the smallest. At only 7 centimeters in diameter, you can pick it up with ease, but you’ll probably have a real hard time finding it, after travelling almost 27 km from your last stop. The Sun, almost 60 km away, is nowhere to be spotted already.

Now you have a long travel to make: 52 km. That’s about half an hour if you have a car and a highway handy, but a neverending hike if you try to go on foot. At the end, you’ll find the second largest ball of all, a 10 meter wide cliff of a thing, which dwarfs you for the first time since you left the sun behind. That was, remember, almost 112 km ago.

Hop on the car, go back to the highway: you’ll be driving for almost an hour to cover the 93 km that separates you from your next destination: a more than 8 meter wide ball called Saturn. 8 meters would seem a lot, if you weren’t 205 km from your starting point already. That far from the Sun, it strikes you as a positively lonely chunk of planetary real estate. But hey, it’s a beautiful one, with all those rings and stuff, and with many other centimeter-wide balls hundreds of meters distant, in all directions. So it’s fine, kinda. But you have to keep going, so you return to the car, stop at the next gas station and fill your tank, because your next travel is long.

208 km long to be exact. There are capitals in Europe separated by less than that. And yet, it’s simply the distance between Saturn and Uranus in our model. The Sun is 413 km away. And when this long voyage finally ends, what you find is a blue ball with a diameter of three meters and 64 centimeters. You’re tired. But you’re stubborn and you want to reach the end of this, so you go find Neptune. To do it, you’ll have to travel 233 km more, and when you finally reach your destination, you find another blue, 3-meter wide ball. For a moment you may think you went in a circle and returned to Uranus, but when you measure the ball you discover that it’s 10 cm smaller than the previous, so you’re really where you should be. Phew! But where is that? That’s 646 km away from your starting point. In Europe, you’d probably be in another country already. In the Americas, in another state or province.

Now, you know that whoever made the model you’re travelling through didn’t bother with orbits and actual positions in space, only with the average distance to the Sun. Had he taken orbits into the model, you’d be now in big trouble, because the next planet, Pluto, actually gets closer to Uranus than to Neptune due to its orbital resonance with the latter planet. You’d have to make a really long travel to find it. But since the model creator didn’t bother with that, you can go on in a somewhat straight line, and after travelling another 202 km, you’ll find a 17-cm wide ball waiting for you with a slightly smaller one right next to it. You try to get your bearings from the Sun, but it’s no use. It’s now almost 850 km away.

Next stop: Haumea. To reach it, you have to travel another 78 kilometers, and once you do you find a weird ellipsoid some 8-10 cm in diameter. You’ve travelled for so long and so far, that your vision has become blurry, and you begin to have a real hard time seing the planets you’re trying to find. But you push on, travel for another 57 kilometers, and find another ball around 11 centimeters in diameter: Makemake. You think this has to stop somewhere, but you know you’re still to find Eris, so you get back to the car, and start driving.

This time it’s the largest travel of all: 470 km, no less, and when you finally stop, after almost falling asleep during the long hours of driving, you’re a whooping 1455 km from your startng point. You pick up the Eris ball. 19 centimeters in diameter. A foot ball is 22. And it’s cold, oh, so, so cold. You know there’s more. Orcus, Ixion, Varuna, Sedna, Quaoar. But you’re so tired you thank the IAU for its slowness in making officially new dwarf planets. Only one more stop and that’s a wrap. You’ve heard so much about the Oort cloud that you’d like to pay a visit. But when you ckeck your map, you have a surprise: it ain’t there. In fact, you find out you’d have to leave the Earth and almost Earth’s orbit to reach it, for its outer edge is supposedly more than a million km away, almost three times the distance to the Moon. You swear profusely, and all we can hear is a succession of beeps, but you finally give up and go find a hotel. You’ll have a very long way to go back tomorrow. A very long way indeed.

And remember: the Earth is not even one meter wide at this scale.

That’s how huge the Solar System is.

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