Create an Orbital Simulator

That would have to be modeled too.
And what's stopping you from imagining a handful of planets made up from 100 particles each, rotating in a cloud of 500 other particles, and this occuring automatically starting from an initial cloud. I only want to test Titius Bode as a mathematical property that should originate from the inverse square law in any scale, atomic or galactic. Not confine it to the actual masses, distances, etc of a solar system.

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tony873004
Gold Member
And what's stopping you...
A lack of interest in Titus-Bode prevents me from trying to verify it through simulations. But if it interests you, that doesn't need to stop you. Anyone with a Windows computer can run my simulator.

...I only want to test Titius Bode as a mathematical property that should originate from the inverse square law in any scale, atomic or galactic...
There are 6 opportunities in our solar system for Titus-Bode to be revealed: the planetary system, and 5 moon systems (>2 moons: Jupiter, Saturn, Uranus, Neptune, Pluto), none of which demonstrate Titus-Bode. The planetary system fails because there's no major planet between Mars and Jupiter, and Neptune is out of place.

D H
Staff Emeritus
Modeling the formation of planetary system is a vastly more complex task than a simple orbital simulator. Planetary growth is a complex and not yet fully understood process. I assume Tony's simulator treats the planets as point masses. This is a good assumption for a stabilized system with only a small number of orbiting objects. It is not a good assumption for modeling planet growth. Tony's simulator runs on a single off-the-shelf computer. Modeling protoplanetary systems requires a lot of coupled, high powered computers because one needs to model millions of tiny particles. These little particles collide (point masses don't collide), have angular momentum due to rotation (point masses don't have angular momentum due to rotation) and exchange angular momentum with the Sun and each other. Once again, point masses don't do this.

tony873004
Gold Member
...I assume Tony's simulator treats the planets as point masses....These little particles collide (point masses don't collide),..
They're treated as point masses for the sake of computing acceleration, but they do have size, so they can collide and stick. But every collision simply combines their mass and momentum into a new object if their distance is less than their combined radii. But the points you make are what I was getting at a few posts ago (#48). The real system has lots of stuff going on besides point mass interactions. There are more types of collisions than the simple one my code models. And the real system has gas that behaves differently than solid matter. So I can only agree with you that this type of a simulator is too simple for task. It doesn't mean than you can't make some assumptions and generate simplified models to explore various aspects. But to build a solar system from scratch, which you can draw confident conclusions about, is well beyond its capabilities.

I assume Tony's simulator treats the planets as point masses. This is a good assumption for a stabilized system with only a small number of orbiting objects. It is not a good assumption for modeling planet growth.
Well don't forget Newton's law of gravity only makes sense for point masses. Everything else is approximated by point masses, for the purposes of this law. Conglomerates of point masses can have angular momentum but there is no need to introduce angular momentum in the model. Just point masses connected with breakable and rejoinable spring-damper links, should be enough to model just about anything we might be interested in gravity-wise, and I think Tony is not far from this. The difficulty is with the estimation of suitable parameters for something that matches the real thing, but then we are not always interested in matching the real thing but just want to explore possibilities.

Regarding Titius-Bode that I am interested in testing, there is no reason to assume it applies exclusively to the scale of our solar system. I would expect it to also apply to much bigger and much smaller systems, because it seems to be a statistical result, like Gaussian distributions that appear in nature.

By the way, Titius-Bode -like equations predict a planet between Mars and Jupiter, and indeed there is the asteroid belt there, ie a planet that failed to form or a planet that formed and was later broken apart somehow, perhaps in a collision with a large object like the one that hit the earth when the moon was formed.

Modeling protoplanetary systems requires a lot of coupled, high powered computers because one needs to model millions of tiny particles.
There's a simulation of the collision of the Mars sized object with the earth when the moon was formed. Judging from the number of particles, it seems able to run on todays pc's. It ends up with the moon at the right distance from earth, and the right masses for the earth and moon.

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D H
Staff Emeritus
Well don't forget Newton's law of gravity only makes sense for point masses.
Wrong. It is an trivial matter to compute the gravitational influence of a non-point mass body that has spherical shape and a uniform density on some object. An ellipsoidal body is not too much harder. We use complex mathematical models such spherical harmonics to describe real body such as the Earth. Some spherical harmonics models of the Earth's gravity field include http://cddis.nasa.gov/926/egm96/egm96.html" [Broken] and more recent ones based on Lunar Prospector data. JPL has developed spherical harmonics models for Venus, Mars, and even some asteroids.

Regarding Titius-Bode that I am interested in testing, there is no reason to assume it applies exclusively to the scale of our solar system.
One of the cornerstones of the scientific method is the concept of falsification. Neptune falsifies the Titus-Bode law. Most astronomers view the Titus-Bode law as mere numerology. I suggest you post your concepts on this law in the scepticism and debunking forum at PF.

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Newtons law of gravity does not apply to ellipsoid shapes last time I checked, only spherical shells are equivalent to point masses, and only on the outside (shell theorem).

But if you have proof that ellipsoid shapes are equivalent to point masses too, as required by Newton's law, I'd like to see it.

Or if you have proof that ALL spherical harmonics are equivalent to point masses for Newton's law to apply, I'd like to see it.

Cause what I have seen from my numerical calculations (in thread
Numerical integration of gravity at surface of an object
), Newton's law of gravity only matches spherical shells. And therefore it can only be used exactly for spherically symmetrical distributions of matter like an onion, everything else is by appoximation.

D H
Staff Emeritus
I never said ellipsoidal shapes are equivalent to point masses. I said one can compute the gravitational attraction toward an ellipsoidal body. The gravitational attraction at some point $\mathbf x$ outside some body is volume integral

$$\mathbf a(\mathbf x) = G\int_V \frac{\rho(\mathbf {\xi})}{||\mathbf {\xi}-\mathbf x||^3}(\mathbf {\xi}-\mathbf x)\,d{\mathbf {\xi}$$

where the integration is taken over the massive body in question.

tony873004
Gold Member
Newton's Laws: (from memory)
1. An object at rest remains at rest, or an object in motion stays in linear constant motion unless acted upon by a force.

2. F=ma
3. For every action, there is an equal but opposite reaction.

There's nothing here that excludes ellipsoids. Newton spent a lot of time developing Calculus simply so he could mathamatically justify his assumption that a sphere simplifies into a point mass. He did this by integrating the volume of a sphere. Now we can save a lot of time by using this nice shortcut. But there's no reason you can't integrate an ellipsoid, or any other shape, without going beyond Newton's laws. And if you wanted to do it numerically, if I created an ellipsoid from a collection of 1 million point masses, and then simulated a particle orbiting the ellipsoid, using Newton's laws, I imagine it would work quite nicely, showing the proper orbital precession that gives us "walking" orbits and "sun synchronous" orbits.

I never said ellipsoidal shapes are equivalent to point masses.
You said "wrong" below this:

Well don't forget Newton's law of gravity only makes sense for point masses.
Wrong.

Newton's Laws: (from memory)
1. An object at rest remains at rest, or an object in motion stays in linear constant motion unless acted upon by a force.

2. F=ma
3. For every action, there is an equal but opposite reaction.
We're talking about Newton's law of gravity, not Newton's laws of motion.

But there's no reason you can't integrate an ellipsoid, or any other shape, without going beyond Newton's laws.
I've done this for a living. It's another thing we're talking about here (whether Newton's law can be used exactly in anything but point masses and equivalent spherical shells)

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D H
Staff Emeritus
You said "wrong" below this:
Well don't forget Newton's law of gravity only makes sense for point masses.
Wrong.
That is because what you wrote is wrong.

I've done this for a living. It's another thing we're talking about here (whether Newton's law can be used exactly in anything but point masses and equivalent spherical shells)
I gave the exact answer in post #58. Whether that integral is computable in closed form or has to be approximated numerically is a different question. The integral is the exact answer to the acceleration due to gravity. BTW, this is exactly what I do for a living (one of the things I do for a living). Moreover, NASA has many people at JPL and Goddard working on developing high-precision gravity models. Until recently they used ephemeris data from satellites that had some other primary objective as the basis for these gravity models. NASA and ESA together are now flying an expensive pair of satellites whose sole objective is developing even higher-precision gravity models of the Earth. Do you think they would this just for fun?

tony873004
Gold Member
If you're referring to F=GMm/d^2, then yes, this works only for point masses. But throw a double integral symbol in front of it, with the limits of integration describing your desired shape, and you can do any shape you want. You're still applying the point mass formula GMm / d^2 (or one M for acceleration) to each differential element. And if you want something that is not uniform in density, and you have your density function, then write it the way DH did.

NASA and ESA together are now flying an expensive pair of satellites whose sole objective is developing even higher-precision gravity models of the Earth. Do you think they would this just for fun?
Certainly not, but we were talking about the formation of a solar system from dust, and you are introducing ellipsoids. Don't you think they're from another application?

throw a double integral symbol in front of it, with the limits of integration describing your desired shape, and you can do any shape you want.
Not in the context of dust forming proto-planets in order to test Titius bode.

Even if an analytical formula came out from integration, you still can't use it in this context.

tony873004
Gold Member
Not in the context of dust forming proto-planets in order to test Titius bode.
I agree with you. You're not going to be using Newton's laws of gravity for dust. Objects need to be a few km wide before their gravity is significant enough to consider. I don't think it's fully understood yet, what happens prior to this point.

And that's one of many reasons why my program will have a difficult time helping you verify TB. My program is GM/d^2 inserted into an endless loop.

Why don't you post a copy of your program in case anyone wants to play with it. Or have you already?

Objects need to be a few km wide before their gravity is significant enough to consider.
Well you'd start with thick "dust" then, wouldn't you. Like that simulation of the formation of the moon from a collision of a large object with Earth: both objects turn into thick "dust" at places.

D H
Staff Emeritus
Ulysses, please stop with the Titus-Bode law. It is numerology. No causal mechanism, and debunked by Neptune.

Red cars cost more to insure in the UK. Insurance companies do not seek a cause why red cars have higher statistics for accidents. They just use the result and charge more.

So if you do not know a cause for an observed statistical trend, that does not mean no cause exists. It just means you don't know a cause yet. In trials of new drugs they give a license if the drug gives results that are "statistically significant", and they have equations for deciding if a result is

a. statistically significant (and therefore caused by the drug) or

b. not significant (and therefore just chance), and the drug is rejected.

So refusing to even simulate the formation of planets roughly in search of ANY statistical pattern (if it exists it should appear after many repeats), refusing to even test is not a scientific approach, it is dogmatic thinking that has no place in science.

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D H
Staff Emeritus