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.That would have to be modeled too.
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.And what's stopping you...
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....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...
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....These little particles collide (point masses don't collide),..
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.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.
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.Modeling protoplanetary systems requires a lot of coupled, high powered computers because one needs to model millions of tiny particles.
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.Well don't forget Newton's law of gravity only makes sense for point masses.
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.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.
We're talking about Newton's law of gravity, not Newton's laws of motion.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.
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)But there's no reason you can't integrate an ellipsoid, or any other shape, without going beyond Newton's laws.
That is because what you wrote is wrong.You said "wrong" below this:Well don't forget Newton's law of gravity only makes sense for point masses.Wrong.
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?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)
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?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?
Not in the context of dust forming proto-planets in order to test Titius bode.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.
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.Not in the context of dust forming proto-planets in order to test Titius bode.
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.Objects need to be a few km wide before their gravity is significant enough to consider.