multibody gravity question

Hi,

The masses are in fixed positions so it is a static gravitational field, but new masses in fixed positions can be added.

cheers, Jamie

Does a tree out in the middle of nowhere make a sound when it falls?

Umpteen years ago, (BC, that is Before Computers) an N-body system was insoluble where n>=3. Things have improved a bit since then. To make computation a bit easier,start with the solution you do have. and posit one added item with correct position but "zero" mass, and slowly increase ts mass. I guarantee that the masses will not be in a stable configuration.

Therefor I said "_infinite_ number of equal masses".

--
Reinhardt

In that case you can always contrive to insert the next mass in such a position as to create a perfect location where all the forces sum to zero. The fields are linearly superposable so if you pick a location and work out the field there due to the current mass distribution you can place your next mass so that it produces an equal and opposite force at that location. And since you have somehow nailed them down so that they don't move at all under their mutual gravity you are done.

In practice they do move and the dynamical solutions stability depends critically on the mass ratios between participating masses. Various online simulators will let you play with multibody gravitation and some will even let you collide galaxies fairly realistically.

Equilateral triangle trying to rotate uniformly about its point of symmetry is a good one to try for starting point and highly educational.

This was all supercomputer simulation stuff way back when it was first developed but i7-3770 modern PCs are broadly comparable with 100x Cray XMP if Intels benchmarks are to be believed (seems high to me).

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Regards, 
Martin Brown

was insoluble where n>=3.

Nope, not so. Three-body _orbits_ are insoluble _in_closed_form_in_terms_of _elementary_functions. That's a far weaker statement. Even a Keplerian orbi t needs elliptic integrals in general, and of course even sines and cosines are transcendental functions that can't be computed exactly except for spe cial values.

Perturbation theory was finding new planets by the disturbance in the orbit s of other planets in the 18th Century. It doesn't need to be exact, it jus t needs to be good enough.

Cheers

Phil Hobbs

It was hard lines on the poor computors who had to do the calculations back in the days when it was all pencil paper and log tables.

Challis would have beaten Le Verrier and Galle to finding Neptune if he had trusted the calculations given to him by Adams. It is known that Galileo actually observed Neptune in the same field as Jupiter in 1612 and noted it moved but didn't see the importance at the time.

Nice history of who saw what and when online at St Andrews astronomy.

It is an interesting aside that although our solar system appears to be as regular as clockwork a proof of its long term stability is still an unsolved problem and very little progress has been made on Ovenden's conjecture which is the most plausible theory underpinning "Bode's law". (which is in fact a misnamed crude heuristic)

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Regards, 
Martin Brown

Yup, that's for sure. When Shanks finished his 707-place computation of pi (of which the last couple of hundred places were wrong), he said it had taken him "three years of Sundays". (i.e. 21 years, for the folks at home.)

Michael Ovenden was my galactic dynamics prof at UBC. A good guy, who unfortunately died pretty young.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

you get much more GFlops using the graphic card to do computation (OpenCL, Cuda,...).

Bye Jack

--
Yoda of Borg am I! Assimilated shall you be! Futile resistance is, hmm?

"Titius-Bode law predicts billions of potentially habitable planets in Milky Way"

from the page:

" Using an updated version of the 250-year-old Titius-Bode law, researchers from the Australian National University and the Niels Bohr Institute in Copenhagen worked out the probability of the number of stars in the Milky Way that have planets in the habitable zone (where there is the potential for liquid water, and therefore life). ...

calculate the potential planetary positions in 151 planetary systems, where the Kepler satellite had found between three and six planets. In

124 of the planetary systems, the Titius-Bode law fit with the position of the planets. "

Interesting they are predicting where to look for more planets!

cheers, Jamie

Hi,

Just a difference in view between infinity-1 and infinity+1 :)

>

As long as you limit the thought experiment to the solar system or some other relatively small region then yes, your point holds. But once you reach the intergalactic spaces the universe is expanding and you could actually "fall" forever and not reach any other body. A very lonely thought...

The problem is that while gravity seems to explain things in any finite region of space, it can't explain how the universe can be expanding. So we add other forces and mysterious dark matter and dark energy to try to make it all match the observations. In reality I think we are in a similar period between the Michelson-Morley experiment and Einstein's theories. We are trying to fill the gap with something like the aether but it isn't working.

--

Rick

if there is one being on the planet that can hear it yes. Period. If the sound happens to be 10,000 miles away and their hearing is not good enough to pick it up, it is not the tree's problem. Nor mine. Fukum.

The osund is there, unless the planet (and this the soundsphere) is ocmpetely devoid of anmy creature the could describe the vibrations in the air as sound.

Maybe.

Back in the days when English Idealism was the prevailing philosophical view at Oxbridge, there was an amusing exchange on this point. Ronald Knox posted a limerick on a tree in the college quad, as follows:

There once was a man who said, "God must find it exceedingly odd if He finds that this tree continues to be when there's no one about in the Quad."

Next morning, this appeared under it (by an unknown hand):

"Dear Sir: Your astonishment's odd. _I_ am always about in the Quad. And that's why this tree continues to be since observed by, yours faithfully, God."

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

*this is not a complaint* (I'm fascinated by this subject about which I know 0/0)

What made you decide to approach members of an electronics NG with an astrophysics question?

I never knew so many SED'ers knew so much about gravity and such!

Keep it going!

Cheers, Dave

That is about standard operating procedure. Got everything, economics, social issues, politics and religion.

And then when everyone is pissed off at each other over those arguments, a real electronics issue pops up and the process starts over as if it never happened.

Hi,

It was actually not an astrophysics question :D I just needed to know the position of minimum "potential" (ie gravitational field) of a static distribution with elements added to the distribution one at a time (in random locations) and with each one having a property somewhat similar to gravity ie 1/r^2 force attenuation! It is for an algorithm that needs to find that location given all the previous "masses". I think there are simpler algorithms though to do an equivalent thing maybe.

cheers, Jamie

Hi,

This is a more formal question if anyone is interested or crazy enough to try!

question: give an example of calculating the gravitational field minimum given these scenarios: (1dimensional, 2dimensional and

3dimensional)

mass Xposition

1kg 3 1kg 5 1kg 8 X coordinate of minimum gravitational field =

mass Xposition Yposition

1kg 3 4 1kg 5 7 1kg 8 2 XY coordinate of minimum gravitational field =

mass Xposition Yposition Zposition

1kg 3 4 10 1kg 5 7 3 1kg 8 2 7 XYZ coordinate of minimum gravitational field =

I need to be able to add new stationary masses in random positions as well, so if it is hard to recalculate the formula this wont work.

None of the masses ever move, and I'm not trying to find the points of balanced gravitational force, but the point(s) of minimum gravitational field intensity.

cheers, Jamie

OK, I'll simplify: If you asked Jack or Jane on the street:

"Who would you pose a gravity question to: a EE or an astrophysicist?"

what do you think the likely answers would be?

Dave