I need some help conceptualizing this (Ptolmey's model of the solar system)

I got into a discussion with someone who earnestly and honestly believes that the sun revolves around the earth (yes, folks, they’re out there).

When I asked him how he could believe such a thing despite all the evidence that is available to the contrary, he gave me an answer which, down to the core of me I know is wrong, but I have trouble with spatial conceptualization, and so, can’t quite wrap my head around how it is wrong.

His answer was that because of relativity, it was just as equally valid to state that the sun was going around the earth as vice-versa. Since one can view the earth-sun system with either body “at rest” relative to the other, either view is perfectly plausable, he maintained.

Now, I know that that is wrong. I can take a piece of paper, put a dot in the center of it (to represent the sun) and draw an “orbit” around it. My pen moves along the orbit around and around the dot. But when I try to stop my pen, I can’t figure out how the earth should continue to appear to revolve around the sun.

I figure that the answer lies in one of two things: (1) My disputant has the wrong idea of relativity or (2) I’m lousy at spatial puzzles. My guess is #2, but I wouldn’t be surprised if it were a bit of each.

I did throw my disputant a bone, however. I told him that, in fact, the earth and the sun do, in fact, revolve around each other (in a sense). I am aware that the sun and earth actually revolve around the center of the earth-sun system (ignoring, for the moment, the gravitational effects of the other planets on the sun), which is actually not too far from the center of the sun.

So, please help me out here. It really bothers me that this kind of ignorance is running around out there and it bothers me even more that I can’t seem to grasp this simple idea.

Zev Steinhardt

Your bone is spot on the money. You should have asked him if the moon orbits the Earth, and when he said yes, stated that the the Earth orbits the Sun in the same way.

Could you also not point out that more massive objects orbit cannot less massive ones by the law of gravity?

I suppose that’s true as well.

I’m not really looking for proofs, as I already believe that the earth revolves around the sun. What I’m really looking for is a disproof (one that I could draw, preferrably) to the notion that one can view the earth as “at rest” and have the sun go around it.

Zev Steinhardt

Here’s a really simplified version of Ptolemy’s model.


I’d help you more if I can, and I think I know how to illustrate what your friend is trying to say, but I have terrible spatial skills, so I can’t be of much help.

As you say “In a sense” of some sort.
Geometrical relationships, and Astro-Geometry are not Classical Relativity.

What does removing the pen have to do with the path around the dot? Same path, same dot, an imaginary dot will continue around the path will it not?

#2, You guessed it right!
BTW he is also confused.

For an interesting exercise draw a schematic of the solar system with several planets orbiting the sun. Plot the eliptical paths of the planets for a full year of twelve months.

OK here it comes:
Draw anothe solar system with the earth as the center of rotation and plot the planets as before but in their epicyclic orbits for a full twelve months.

If he’s really basing his opinions on relativity, then general realtivity indicates that massive objects bend space-time around them in a way that alters the path of other moving objects. The sun bends a lot more space-time than the earth does, so it has a much larger effect on earth’s orbit than vice versa.

The biggest problem with Ptolemy’s system, even if you just look from a relative observer’s standpoint, is that he also had the planets going around the earth. Takes some real geometric gymnastics to explain things like retrograde motion.

Is your friend really supporting the Ptolemaic system of the cosmos or is he just saying “The sun goes around the earth?” In other words, do all the planets go around the earth or just the sun? Does he believe in elliptical orbits or (as both Ptolemy and Copernicus did) circular ones?

If he really buys the Ptolemaic theory he should buy into Aristotelian physics as well. In brief he should believe that terrestrial matter (earth air fire water) are fundamentally different from heavenly matter (the aether, or quintessence). He should reject any theory of gravity, as Quartz said, since it’s pretty much impossible to explain a geocentric solar system using either Newton’s or Einstein’s physics. Also he’ll have to believe in all the epicycles, equants, and eccentricities that Ptolemy used to explain retrograde motion, which Twoflower brought up.

I suspect that your friend came accross a bit of relativity. Specifically the bit that says “Their is no privileged reference frame.” Then your friend says “Hey according to this it’s just as valid to say the sun goes around the earth as vice versa! I’m Clever!!” However it’s quite a leap to get from the first thought to the second. To get a geocentric universe out of modern physics you’d have to invent all sorts of pseudo-forces to account for planetary (and Solar!) motion. When Einstein said “The laws of physics are the same in any coordinate system” he didn’t mean that all bodies are equally massive, or that heavier bodies won’t attract lighter bodies and fix them into elliptical orbits.

Reminds me of the old (almost certainly apocryphal) story about Einstein. Travelling by rail, he once asked the ticket inspector “What time does Zurich stop at this train?”

Well, that was your first mistake.

Bzzzt! Objects in orbit are under acceleration, and are therefore not equally “relative to the other”. In an rotating system, there is a definite coordinate system (or at least an axis) about which things can reference. Technically, the common center of reference for the Earth-Sol system is not about Sol but about the common center of gravity between them. In practice, this lies near enough (well within the photosphere of the sun) for us to just consider the earth rotating about the sun.

Ach, you haven’t even seen ignorance yet. Wait until you run into those people who think that Social Security can be saved without raising taxes. :dubious:

Seriously, the first point I’d bring up is the Ptolemy’s whole “epicycles within epicycles” deal, which attempts to explain the apparent retrograde motion of the planets (actually due to the offset axis of their orbit with respect to the earth). You’d have to have some pretty serious cam or oblong gear sets to make that model run. Then there’s the whole sending probes to other planets…but no doubt he doesn’t believe in that, anyway.

Some people are beyond help, like flat earthers, rail gin drinkers, and Senator William Proxmire. The best you can do is just outlive them. :wink:


That, my friend, is all too true. :slight_smile:

Well, hold on a minute. Pioneer 10 is under acceleration, moving away from the Sun. But one can say that Pioneer 10 is “at rest” and the Sun is moving away from P10, no? Or is that totally wrong?

Which is exactly what I told him!

I suppose what I’m hoping to get out of this thread is the answer to this question:

If the earth would be viewed as stationary (as my disputant claims), what path would the sun take? I can draw an orbit of the earth going around the sun, but if I were to view the earth as a stationary object, then what “path” would the sun take. Surely not revolving around the earth? Or is my question somehow meaningless because I’m failing to grasp something here?

Zev Steinhardt

What you are failing to grasp (and don’t feel bad, as it took a few excommunications from the Church and the revelations of an obscure German patent clerk to make clear) is that an object revolving around another is under acceleration. This is clearer if you understand that acceleration isn’t just a change in speed (the magnitude of velocity) but a change in direction, irrespective of the actual speed of the object. In other words, if you are driving your car, in order to go around a curve and come out at the same speed you have to give it some gas. (Try it if you don’t believe me.) In the case of the Earth, that “gas” is provided by the gravitational field of the sun. It is conservative because the energy (potential and kinetic) remains constant, but the energy in any given direction changes as the planet goes through its orbit.

Although, from a casual observational point of view it may not make any difference which revolves around the other, if you measured accelerations at both bodies with an inertial potentiometer it would be obvious, although we don’t notice because the centrifugal accelerations are both tiny and mostly balanced out by the gravitational attraction of our bodies to the sun.

But the most damning evidence comes from observing other bodies. The heliocentric model leads to very simple results as defined by Kepler’s Laws of planetary motion, whereas the Ptolemy epicyclic model requires the kind of machinery that would cause Rube Goldburg to throw up his hands in frustration. In short, your correspondent is an idiot. But it’s okay, nothing to be ashamed of; the same is true for many Presidents and literary figures. (Yes, Susan Sontag, I’m talking about you.)

Now, if only I could get a job explaining this sort of thing; it’s far more fun than making PowerPoint presentations for Mittlewerks California. How do I apply for Carl Sagan’s job, anyway? Ah, heck with it; I still have two fingers of Bushmills and three chapters of Orwell to get through before I turn in.


Relativity, eh?

Take your friend aside. Throw a bowling ball on a trampoline. When it settles down, roll a ping-pong ball onto the trampoline such that it spirals around the depression caused by the weight of the bowling ball. Exclaim, “Look, the bowling ball is going around the ping-pong ball!”

IANAPhysicist, but I think the answer might go like this

  1. If Pioneer 10 is moving away from the Sun at a constant speed, then, yes, it is equally valid to say that the Pioneer 10 is at rest and the Sun is moving away from Pioneer 10.

  2. If Pioneer 10 is accelerating away from the Sun, then it would be a bit difficult to say that Pioneer 10 is at rest and the Sun is moving away from Pioneer 10 because it is Pioneer 10 who is expending a lot of energy to accelerate, so under what physical laws would you have one object expending a lot of energy in terms of rocket thrusters only to have it remain stationary while another object accelerates whenever your rocket thrusters are turned on?

Quick answer:
If you are standing still and your friend is running around you in a clockwise fashion, from your friend’s perspective, you are moving around him in a clockwise fashion.

With math:
Let (x_e, y_e) be the coordinates of the Earth and (x_s, y_s) be the coordinates of the Sun.

In the frame of reference where the Sun is stationary, while the Earth revolves around the Sun in an elliptical orbit, we could write
x_s = 0;
y_s = 0;
x_e = Asin(wt) + a;
y_e = Bcos(wt) + b;

where t denotes time.

If we change our frame of reference to put the Earth in the center, we will have
xPrime_e = 0;
yPrime_e = 0;
xPrime_s = x_s - x_e = -Asin(wt) - a;
yPrime_s = y_s - y_e = -Bcos(wt) - b;

xPrime_e = 0;
yPrime_e = 0;
xPrime_s = Asin(wt+pi) - a;
yPrime_s = Bcos(wt+pi) - b;

which means that the Sun will also be following an elliptical path around the Earth.

Of course, the above does not take into account any physics; it is just a consideration of how the path of the Sun might look if we have a frame of reference with the Earth stationary at its center.

Actually, the earth does not revolve around the sun. Neither does the sun revolve around the earth. They both revolve (in different sized orbits) around a common point. It’s just that the sun is so much bigger than the earth that the common point might as well be the center of the sun.
I think that in a universe with only the earth and the sun, it wouldn’t matter who revolved around whom from an astronomical point of view - it would look/behave exactly the same. The problem that Ptolemy (or rather his disciples) ran into is that trying to describe all of the apparent motion of the planets (retrograde motion, etc) recourse to epicycles, epi-epicycles, epi-epi-epicycles, ad nauseum, if not ad infinitum - which gets both complex and aesthetically displeasing, to say the least (as Twoflower notes). And thats merely to describe the problem. Developing some sort of coherent theory of gravity or even something like Kepler’s laws would be frightfully complex.

In any case I thought that Galileo’s discovery of the Jovian moons (or any other celestial body which visibly orbits something other than earth) had finally put the Ptolemaic theory to rest.

Nope. It might look, superficially, the same–it’s true that from a POV on Planet Earth it appears that the Sun is in orbit–but the dynamics of the system are different.

Imagine this; take two solid brass balls, one large and one small and put them on each end of a long, massless rod. (Get your mind out of the gutter, you perverts!) Mount the large ball on a pivot (so the large ball is just spinning on its own axis) and spin the contraption. Now reverse the positions, so the small ball is rotating and the large ball is swinging. The second configuration will have a much higher rotational inertia and will take much more force for the same angular velocity.

As you pointed out, the Earth-Sun system are actually orbiting about a common center of mass, but that center of mass is a fixed frame of reference with respect to either body. You can’t place it at any arbitrary distance between them without getting some very odd, non-linear kinematics. Mathematically, this would be very inconvenient to explain without invoking some kind of cosmological gear-works.

Ptolemy’s epicycles of epicycles are an approximation which becomes more and more difficult to maintain as observational accuracy increases. It’s similar to using polynomial approximation to map an arbitrary function; using enough powers and don’t look to closely will give you a reasonable fit, but if you start looking at small regions you’ll find big perturbations.


What the sun would do if it revolved around the earth is what it appears to do every day. It revolves around the earth, rising in the east, and setting in the west. And it’s path fluctuates from low in the sky in the winter, and high in the sky in the summer.

It is the advent of systematic observation, and eventually the telescope that makes it all complicated, with retrograde motions, and such.

If you don’t keep track all that closely, it all just flows by, up in the sky, round and round.

I wouldn’t bother distressing your friend. He probably doesn’t actually believe that crap, and just wants to piss you off.


Easy. Keep the pen in one place, and move the paper around in a circle. The problem is, for a workable model of the universe, you’d need one gigantic piece of paper. And you’d need to spin it around 365 times while simultaneously moving it a larger circle. You can draw the same pattern much easier with a Spirograph.

And as others have pointed out, this model isn’t wrong, relativistically speaking. One only need look up at the night sky to verify it.

It’s just when you have to model all the other bodies of the universe that it becomes terribly unwieldly.

So in a twisted and sick sort of way, your friend is right. But you might not want to tell him that. :wink:

SoaT: It might look, superficially, the same–it’s true that from a POV on Planet Earth it appears that the Sun is in orbit–but the dynamics of the system are different.

Right. Kinematically—that is, in terms of the geometrical pattern of motion—it doesn’t make a difference which is revolving around which. (Just as the sun and the moon both appear to revolve around the earth over the course of the year and the month, respectively: they change their position on a more or less circular path against the background of fixed stars in just the same way, although at different speeds. The moon is revolving about the earth, while the earth is revolving about the sun, but we perceive the same sort of relative motion in both cases.)

But dynamically—that is, with respect to the physical forces involved—it makes a big difference who’s revolving around whom, as Stranger explained.