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Wrapping our head around proportions August 24, 2009

Posted by Jorge Candeias in Planets.
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4 comments

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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On placemats and other mostly cultural stuff August 24, 2009

Posted by Jorge Candeias in Definition of planet.
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4 comments

Today, Mike Brown (I keep talking about this guy, for some reason) decided to post about placemats. I agree, they’re evil, and promote a very erroneous picture of the planetary fauna that exists out there and of the distances between the large and small chunks of rock, ice, gas and a few liquids that circle the sun. They are far from being unique in that, though. More often than not, even scientific illustrations fall prey to the same kind of reality-bending depictions most solar system skematics show. That’s actually part of the reason why I posted those two size comparisons below, and why I may follow with some more. Thanks to all those non-accurate renditions of planets’ sizes and distances, people are very often left with distorted notions about space. They think they know stuff, but they really don’t.

So he’s right. Mostly. Where he really gets it wrong is in thinking his version of placemat could really make a difference in the public perception of the solar system. People want simplicity: that’s why so many of the people complaining about the notion that evertything in hydrostatic equilibrium should be called a planet did it while brandishing the probable number of planets that would ensue. 200 planets? What an absurd, they said. Eight is much better: kids can learn their names by heart, they said. And, of course, have placemats with eight very incorrectly rendered planets instead of nine, much less 200.

That’s one of the cultural consequences of reducing the number of planets to 8. Instead of learning about the real solar system out there, about the various classes of planets that circle the sun, about how they interact with eachother, people will satisfy themselves with parroting some kind of mnemonic and end up knowing less about the solar system than they did when they thought the planets were 9, and much, much less than they could know with the term planet defined as a vast umbrella where every gravitational ball has its place.

And there’s another, recurrent, error 8-planet advocates fall into: to speak of these things as if the Solar System was the only planetary system of the universe. It most definitely is not.

Size comparisons, take two August 14, 2009

Posted by Jorge Candeias in Ceres, Mercury, Neptune.
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I’ve already shown you a comparison between the largest Solar System planets in each category, and then I thought, heck, for the sake of completeness let’s do the same with the smallest ones, also with the help of Celestia. So here you go:

Size comparison between Neptune and Mercury

Size comparison between Neptune and Mercury

Size comparison between Mercury and Ceres

Size comparison between Mercury and Ceres

Isn’t this cute? The proportions look very much like those of the largest planets in each group, and if you prefer some numbers here they are: Neptune is 10 times larger than Mercury, wereas Mercury is nearly 5 times larger than Ceres. If you go check the masses, you’ll find that Neptune is almost 290 times heavier that Mercury, and Mercury 375 times heavier than Ceres. Everything very similar to the proportions between the biggest planets in each class. It should be noted, though, that Neptune may be the smallest of the giants but is not the lightest; that is Uranus’ claim to fame. Or one of them, anyway.

And, again, there isn’t much of a point in this. It’s just a visual reminder that if you look at the objects without taking into consideration their positions relative to eachother, the differences between giant and terrestrial planets tend to be larger than the difference between the terrestrials and the dwarfs.

Some size comparisons August 7, 2009

Posted by Jorge Candeias in Earth, Eris, Jupiter.
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2 comments

Well, I think it’s about time this blog includes a few pictures. And, since posts with pictures tend to require less words, it’s also a great way to give it content without spending in it too much time. So here are two quick renditions I made with Celestia, showing side by side the largest of the Solar System’s giant, terrestrial and dwarf planets:

Size comparison of Jupiter and the Earth

Size comparison of Jupiter and the Earth

Size comparison of the Earth and Eris

Size comparison of the Earth and Eris

The Earth in the bottom image is slightly larger than Jupiter in the top image (it isn’t easy to get this just right in Celestia without doing some math, which I didn’t), but I think the comparisons are effective even so. Eris (which doesn’t look like that, by the way; since we’ve never seen its surface, Celestia uses by default a generic texture, the same for all bodies in the same situation) is closer to the size of the Earth than the Earth is to the size of Jupiter. If you need numbers, then they are approximately as follows: the diameter of Jupiter is 11 times that of Earth. The diamater of the Earth is 5 times that of Eris (and no, the rather large uncertainties in Eris data don’t change this by much; at most they may drop that number to 4). More interestingly, if you compare not sizes but masses, which are actually more relevant, you get a couple of very similar numbers: Jupiter is about 320 times more massive than the Earth; the Earth is approximately 360 times more massive than Eris.

And the point is?

There isn’t much of a point, really. This just goes to show you that when it comes to compare sizes we’re not all that gifted. The big boys in the block are really big. And if you look at them from this perspective, the dwarfs don’t seem all that insignificant anymore.

And remember: if you look beyond the Solar System you’ll find other big boys that are even bigger than the big boy from our own neighbourhood, making our planet seem even more puny and helpless. HD 139357 b, for instance, is a behemoth 9.76 times more massive than Jupiter, which is to say 3100 times more massive than the Earth. Yes, that’s three thousand Earths needed to make only one gas giant.

Good thing that it strolls around almost 400 light years away, huh?