multibody gravity question

Good luck with your simulation of the Universe. ;)

Cheers

Phil Hobbs

Why one earth do you think that? The only thing they have in common is that both gravity and electrostatic charge obey an inverse square law and so obey Gauss's Theorem which can short cut some solutions. The big difference is that gravitation is always attractive.

sci.astro or sci.physics would have got you a few more people who are working on numerical gravitational dynamics problems.

EE's tend to have some very strange ideas about science. I knew one who worshipped a megohmeter through his total lack of understanding. The same guy also believed he had a proof that pi = sqrt(10) and was annoyed that no journal would publish it so he self published instead.

Every good physicist or engineer knows that pi^2 = g

- an allowable approximation in the days of slide rules!

No, pi = sqrt(1/g) which is why a 1 metre long pendulum has a half period of 1 second.

Cheers

Absolutely. A good sleazy approximation is better than an unintelligible exact result any day.

Cheers

Phil Hobbs

D'oh. I mean pi * sqrt(1/g) = 1 which the same as Martin's.

Cheers

My other favourite is pi x 10^7 seconds in a year. (slightly short measure)

Specializing in one field doesn't necessarily preclude interest or ability in one or more other fields, especially when you can port math from one to another.

(snip)

I'll just point out that three points define a plane, so there's no point in posing a 3D case with less than four masses.

Um. Points where forces balance are where the field intensity vanishes.

As for calculating the field at any given point due to the presence of arbitrarily many masses:

"The field around multiple particles is simply the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would feel in these individual fields."

Equation follows that bit.

Mark L. Fergerson

Our physics degree included a fairly comprehensive electronics course in the second year and several of us were already advanced hobbyists before going to university. Quite a few ended up designing electronics.

Just plot the potential in Excel and you can see graphically where the minimum is (BTW putting the middle mass at 0 simplifies the algebra).

Hint: the solutions to the 1D problem above are close to 4 and 6.5. (the latter being at lower energy)

Sketch the potential due to each mass and then add them up to see why.

That is still a 2D problem. 3 points define a plane.

Why? What *ARE* you trying to do?

It makes no physical sense to have gravitating masses that are unable to move in response to the forces acting on them.

A quick and dirty approach is to consider the two masses that are closest together and then correct for the more distant masses. It won't always work but it is a half decent starting heuristic.

Also if the masses are randomly positioned then appeals to symmetry can allow you to make a sensible starting guess to begin your search.

Yeah, but the number of seconds in a year is like the number of arc seconds in a radian--one of those numbers that every astronomy undergrad memorizes, and even old guys like us remember to at least single precision. ;)

Cheers

Phil Hobbs

There are a certain number of top electronics designers who never got an EE degree. Besides Jim Williams, there's Errol Dietz, who sterted out as Bob Pease's technician and wound up as CTO of National, and Jan Hall of JILA (2

IIRC our very own Win Hill is mostly an autodidact as well. Talent and a f ire in the belly will get you most of the way there, but you have to acquir e enough math at some point or your growth will be stunted.

Cheers

Phil

OTOH, what does the man in the street care about universe simulations. His problems are a tad more, um, down to Earth. ;-)

It is based on the notion that God has a sense of humour and appreciates sarcasm :D

Hi,

Here is a spreadsheet I made for a 1dimensional gravitational field and space time curvature plotter for three masses:

screenshot of the spreadsheet:

screenshot of output graphs of gravitational field intensity and gravitational induced spacetime curvature from the three masses:

Basic analysis:

For three masses there are two spots where the gravitational force == 0 (horizontal slope on graphs) and the gravitational field intensity (or gravitational potential depth) is different at these two points.

The fixed point singularity masses have infinite gravitational field intensity, their exact locations aren't plotted to avoid an excel error from this (#DIV/0!). This brings me to the next section:

Very extended analysis: (a shiny new theory to consider)

Integrated gravity over spacetime:

A singularity has an infinite gravitational field, but if integrated gravity is a repulsive force over spacetime, then when a singularity (blackhole or fundamental particle) approaches a singularity in size, the gravitational field integrated over the very near spacetime will become so high that the spacetime expansion force (of integrated gravity as a repulsive force) will cause spacetime to expand and stretch the fundamental particle into a non-singularity.

This can also explain fundamental quantum oscillations at a fundamental level too I think, since any mass that approaches a point size, will create a gravitational field approaching infinity, which will lead to rapid local spacetime expansion which will then quickly reduce the gravitational field intensity, and can lead to oscillation in this manner.

This type of idea applies at all scales, ie a supernova has a high mass density, and when the size of it approaches a small enough dimension, and it eventually explodes, the increased matter concentration around the supernova leads to a local spacetime expansion in the universe which acts to accelerate the exploding matter away from eachother.

The two competing forces are gravity acting on matter, and integrated gravitational fields acting on spacetime.

Gravity pulls matter together, and integrated gravitational fields push spacetime apart.

This is a good idea as it explains the acceleration of the universe, dark energy, and explains "singularities" ie shows they can't exist!

cheers, Jamie

especially when you can port math from one to another.

less than four masses.

Hi,

The field intensity is different at two points where the forces balance:

cheers, Jamie

Heard a great quote yesterday about astrophysicists and their latest theorems:

"They are frequently wrong but never in doubt."

That applies more to certain individuals here...

I know several of them, and that's not how they operate at all. Popularizers and shills, do, yes.

Cheers

Phil Hobbs

He does. See the Book of Job.

Cheers

Phil Hobbs

Quantum mechanics should prevent this. Squeezing an object into zero space would make its energy infinite. But since we still do have a unification of QM and general relativity, we don't what will happen in this case.