Edit, 19 March 2012–added some images.
You can find any level of anti-science idiocy on the internet, especially from some of the really nutty fundamentalists.
Here for example is someone named MegaSage007 and he issues the following challenge to “atheists” (though perhaps he really ought to issue challenges like this to astrophysicists).
challenging Atheists to produce a working model in its own gravitational field of the solar system to prove they and their godless minded scientists really do know what they are talking about when they say they understand the functionality of the Universe. We will not accept computer simulations nor charts on paper nor any further nonsense about a self creating big bang universe from anyone without proving first they have the ability to do what we say God did in supremely intelligently designing the universe and the finite solar system we were born into without knowing we were coming here. Insofar as producing a working model of the solar system in its own gravitational environment suitable to it, of course Atheists are welcome to use their computers and anything else needed to produce a working model functioning in the air without strings. God has provided mankind with materials and with the intelligence to work them. We are not asking Atheists to create the materials necessary for the functioning project to work, but since the solar system is supremely intelligently designed we know mankind cannot produce such multiple motions of orbital bodies in the air of any space. Mankind is extremely limited in their design capabilities and likewise is also extremely limited in theorizing on paper how a self creating universe could come into being ~ leaving Atheists with blind faith to believe their vain attempts to prove such a thing possible.
OK so he wants a “working model in its own gravitational field of the solar system…” Hanging in the air. And ixnay on it being a computer model, he wants a physical model.
Of course anyone with a passing familiarity with physics knows this is just absurd.
I’ll show just how absurd with a bunch of full frontal but fairly accessible math and physics, then give a properly snarky response. If you just want the snarky response, skip ahead.
Just for Grins
Let’s just play along with this and see where it leads.
MegaSage quite generously allows us to not have to leave the confines of our own solar system to make the model (at 4:06). All we have to do is generate our own gravity field and put our model in it. How massively (pun intended) generous of him. All we need to do is figure out how to generate artificial gravity! I tell you what, it’s probably easier to leave the solar system. And so:
I am going to have to assume one change in condition right up front. This model cannot be “in the air,” atmospheric drag will mess it up. Also, having the earth’s gravity pull on the entire model from below will mess it up. We cannot even put it in orbit because tidal effects will also serve to mess it up. Though I imagine MegaSage doesn’t understand such issues. The model must be isolated from aerodynamic drag and from outside gravity, so imagine it will be put way out in deep space, not in Low Earth Orbit. Like maybe halfway out to Mars, though beyond Jupiter’s orbit might be better. I don’t think this is a weaseling out though, and perhaps MegaSage is honest enough to accept it. For it to be good model, it has to not have to deal with extraneous factors that the real solar system doesn’t have to deal with.
[Unless MegaSage thinks the solar system has atmosphere throughout its entire volume? That would be news to the astronauts aboard the ISS. And surely the Apollo astronauts will be mad as Hell once they realize they really could have done the whole moon mission without having to wear those clunky space suits.]
I am going to assume a scale model is acceptable, if not preferred; it doesn’t have to be a full size model. I am pretty sure MegaSage wants a model he can walk up to and look at and take in easily.
Also, I am going to call this a feasibility study. I am only going to do the Sun and Earth. If I cannot do that, then surely I cannot throw in the other seven planets and their moons!
Defining the Problem
The first thing to do is to understand the system you are modeling. We want a gravitational model of the solar system, and the theory says that force is dependent on both mass and distance. The concept of force in turn involves mass, distance and time. So we need to work with mass, distance and time. OK, so what do the real Sun and Earth look like?
The Sun masses about 1.989 × 1030 kilograms. We’ll round a tiny bit and call it a 2 with thirty zeros behind it. Its radius is 696,000 km, let’s round that to 700,000 km, for a diameter of 1.4 million km.
Orbiting the Sun at a distance of 149,598,000 km (average) is the Earth. We’ll round that distance to 150,000,000 km. The earth weighs in at 5.977 × 1024 kilograms, again a readily roundable number, call it 6 with 24 zeros after it. And the earth’s radius is 6378–about 6400 km, so the diameter is 12.8 thousand kilometers.
The earth makes one orbit of the sun in one year (by definition). That’s 31.557 million seconds. Astrodynamicists call that the “orbital period” and since I actually have done classwork in astrodynamics, I will too.
So that’s what we have to model. We have masses, distances and times defined. Now if we want to scale it down to something that we can handle, the question becomes: How?
One Trillionth Scale
Should we reduce everything down to 1 trillionth (10-12th) of its actual value? Doing so lops twelve zeros off of everything. This has a lot of appeal. Reducing our distances by a factor of a trillion gives us a sun-earth distance of .15 meters, or 15 centimeters, basically six inches. The earth’s orbital diameter is a foot. Nice and compact! That will help when we eventually add the outer planets; the thing will still be less than 100 feet across. The sun ends up being 1.4 millimeters across, while the earth is 12.8 micrometers. That’s not too good, because you will need a microscope to see the earth. C’est la vie.
But things get a little funky when we look at our masses. Dividing by a trillion, the model sun ends up weighing 2 × 1018 kilograms or 2 quadrillion metric tons (Americans will need to know that a thousand kilograms is a metric ton, or “tonne.” The model earth’s mass is now 6 trillion kilograms or 6 billion tonnes.
This is ridiculous! (And no doubt some of my readers saw it coming! I don’t doubt it because the one I had proof read it read me the riot act.) But before we do something about it, I want to try something just for fun. Bear with me while I indulge my curiousity. What’s the orbital period of such a model?
I looked up the formula for orbital period, based on distance and the mass of whatever it is you are orbiting. It looks like this:
P = 2πr3/2 / sqrt(μ)
(Alas the limitations of HTML dictate that I use “sqrt(x)” to mean “square root of x”.)
What do the symbols mean? P is obviously the period, and r is the radius of the orbit. But what is μ? That, it turns out, is the mass of the body being orbited, multiplied by the gravitational constant G. (When you work over and over with satellites orbiting a body of a certain mass, it’s easier to calculate μ once and use it over and over again, rather than multiplying the same two numbers again and again.) G is (when working with metric units) 6.67 × 10-11. And the mass of our model sun is 2 × 1018 kilograms. So μ is 133,400,000.
Plugging everything in:
P = 2π(0.15)3/2 / sqrt(133,400,000) = 31.6 × 10-6
Almost 32 microseconds. Well, that’s interesting. That turns out to be a trillionth of a year! So if we are so silly as to divide distances, radii, and masses all by the same factor, we will also divide the period by that factor. Of course this too is quite absurd, because our two billion tonne, dust speck sized earth model is moving at 30 kilometers a second!
Too bad that packing that much mass into such small spaces is impossible. Because of that, even though this model is consistent, it’s beyond absurd because of the incredibly dense matter you’d need to make the model planets. Neutron star matter, anyone? Well MegaSage did say god had made the materials for us, but I don’t think MegaSage realized how far we’d have to travel to get them!
What went wrong? We scaled all distances by a factor of a trillion, but in doing so we scaled volumes by a the cube of a trillion, or 1036. Now the mass of something is going to double when the volume doubles, or halve when the volume doubles, usually. But when we developed this model, we cut the masses of everything by a trillion also, not by 1036. So now, proportionally speaking, we have masses that are 1024 times too high for the volumes we are using.
Let’s try reducing the masses to match how much we reduced the volumes of the model sun and model earth. In other words, instead of reducing masses by a factor of 1012 let’s reduce them by a factor of 1036. By doing this we will end up with a Sun model and an Earth model of the same density as the real ones, because we have reduced both volume and mass by 1036. This “feels” right in a way the last model didn’t.
If we do that, we will also increase our orbital period, because reducing the mass increases the period. We’ll see soon by how much, but we can see it won’t be directly proportional or inversely proportional, because the mass is under a square root sign.
So now our model sun, rather than weighing 2 quadrillion tons, now weighs 2×1030 kg divided by 1036, or a whopping 2 milligrams! Well we can certainly stuff that into a 1.4 millimeter sphere.
The earth model now weighs 6×1024 kilograms / 1036, or 6 billionths of a gram, easily stuffable into a 12.8 micrometer diameter sphere.
So now we have decided to scale distances by a trillion, and masses by a trillion trillion trillion. What’s the orbital period now? Going back to that formula, μ is now 133.4×10-18. Plugging in:
P = 2π(0.15)3/2 / sqrt(133.4×10-18) = 31.6 × 106
Which is the actual period of the real earth. So if you scale distances by a trillion, and masses by a trillion trillion trillion, you don’t have to scale times at all! And the velocity of our model earth now becomes 32 nanometers (billionths of a meter) a second.
Well this model certainly seems like one that could theoretically be built! But think about it. You are proposing to put something weighing 6 billionths of a gram into a precise location, moving at a very precise but small speed (about 32 nanometers a second) and going in exactly the right direction. If you don’t have the earth move in the right direction, your model will end up with the earth in some sort of highly elliptical orbit (but that orbit will still have a one year period).
How are you going to keep air currents from wrecking your model? Even one stray collision with a molecule would probably wreck it. I wouldn’t even want to shine a beam of light on my little model earth. And if there is any comparatively massive body near by (like, say, you, or even your remote camera you are using to record the experiment, since both you and your camera will be far more massive than the model sun) the orbit will be wrecked as well by the gravitational perturbations.
(You could increase the size of the model by a thousandfold (and the masses by a billionfold) and still have these difficulties; you have an earth model weighing six grams, 150 meters away. Now where are you going to find a vacuum chamber that big?)
This is almost as big an engineering difficulty as the simplistic trillionth scale model I started out with. Even though you don’t need to go to a neutron star to get your building materials.
My response to MegaSage
For you to make this demand is to demand an engineering impossibility. And saying that does not in any way disprove our understanding of the universe; in fact it shows that we have a better grasp on it than you do, because you are ignorant enough to think this is a reasonable demand. Anyone with a smidgen of scientific and engineering knowledge can see it’s silly, and can do a bit of simple math and back it up. But I guess if you are too incompetent at math and science, you can instead take refuge in the rantings of bronze age goat and sheep herders. You get the confidence without having to do arithmetic.
But it’s not necessary to go to the effort of constructing your model. Because we have your model. It’s a full scale model, and you are standing in it right now.
Want to see? Find a telescope. Just about any telescope will do, you don’t need the Hubble space telescope.
That second-brightest “star” in the west right after sunset (as of mid March, 2012) is the “Jupiter” part of our model. It’s full scale, of course.
Now when you look at it in the telescope, you will see three or four little dots in a line either side (or maybe all on one side; it changes night to night) of Jupiter. Those are the four Galilean moons (Io, Callisto, Europa, Ganymede); if you only see three, well maybe one is in front of or behind Jupiter right now. If you look at them over several days, you will see them orbit Jupiter, in complete accordance with Kepler’s laws, which happen to work because the theory of gravitation is correct. Astronomers can use the theory of gravitation, that you like to claim we don’t really understand and is worthless, to flawlessly predict where these moons will be at any time in the future, and they publish charts in advance showing you where you will see them when you look at them through the telescope. They’ve been doing this for hundreds of years now, and the theory of gravitation has worked perfectly.
Jupiter and the Galilean moons as seen through a small telescope (from Wikipedia)
And just incidentally, the instant Galileo realized that these little dots were undeniably orbiting Jupiter and not the earth, the geocentric model of the universe was toast, and the Catholic Church (your church, I am told) that pushed it on people and persecuted those who dared disagree with it ended up looking like shitheads. It only took those shitheads well over three centuries to get around to pardoning Galileo, by the way. Hmmm, come to think of it some Catholics still look like shitheads today.
If that was not enough to crush geocentrism, there’s more. Look at the brightest “star” in the west, right after sunset. It’s just to the right of Jupiter. It’s the “Venus” part of our full scale model. Using the telescope, you will see that tonight (12 March 2012–which happens to be the night Jupiter and Venus got quite close together in the night sky–I hope you didn’t miss it) it looks like a half moon, or in a few days or weeks perhaps more like a white crescent with the horns of the crescent pointing away from the Sun. Follow Venus over the course of a couple of years, and you will see it not only exhibits phases, but the apparent size of the planet shrinks when it’s in a gibbous phase (more than half), and grows when it is a crescent.
The phases of Venus (from Wikipedia)
That means of course that Venus is closer to us in the crescent phase, when we cannot see most of the lit side, and farther away from us in the gibbous phase, when we can. And what is lighting it? The sun. When we see most of the lit side, Venus is farther away from us than the sun is–it’s being front lit–and when it’s crescent, it’s backlit by the sun and it’s closer to us. And it never goes that far away from the sun in the sky, maybe about 60 degrees or so–and it goes from one side of the sun (visible in the evening sky) to the other (visible in the morning sky).
Venus orbiting the sun (not the earth) results in the phases shown in the previous diagram.
What’s the obvious conclusion? Venus is orbiting the sun, and by the way it is doing so in perfect agreement with the useless law of gravitation, again. Galileo saw this too, four hundred years ago. And made the Catholic Church and anyone else who was a geocentrist, look like shitheads.
I suppose you can excuse them for thinking so before Galileo turned his telescope to the sky, but there is no excuse now for doubting the planets orbit the sun and that moons orbit planets, in accordance with the law of gravitation. But hey, there are still shitheads out there who think all our theories are worth even less than the match it would take to burn the paper they are written on, right?
You shouldn’t need us to build a model of the solar system to prove to you we have a handle on gravitation, when any cheap-ass “trash telescope” from a department store will be enough to tell you the story. But maybe you shouldn’t bother. You might find yourself getting interested in science and learning something. And realizing what a shithead you have been. Far better for you to be stubborn about it and rest on your laurels as an oblivious shithead. And blithely regard science as uninteresting.