multibody gravity question

[Jamie M]

On 3/18/2015 5:44 AM, Martin Brown wrote:

On 18/03/2015 11:55, Phil Hobbs wrote:

Umpteen years ago, (BC, that is Before Computers) an N-body system
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 orbit needs elliptic
integrals in general, and of
course even sines and cosines are transcendental functions that can't
be computed exactly except for special values.

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.

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

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.

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Neptune_and_Pluto.html

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)

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

http://www.ibtimes.co.uk/life-milky-way-titius-bode-law-predicts-billions-habitable-planets-among-stars-1492342

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).
....
Steffen Kjćr Jacobsen explained: "We decided to use this method to
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

 

[Jamie M]

On 3/17/2015 10:52 PM, Reinhardt Behm wrote:

Jamie M wrote:

On 3/16/2015 8:45 PM, Reinhardt Behm wrote:
Jamie M wrote:

Hi,

For a multibody stationary system of uniform mass points distributed in
2D or 3D space, is there a way to precisely find or estimate the
location in 2D or 3D space where the gravitational field strength is
lowest in a given bounded domain?

ie for 2 masses 1 meter apart, centered in a 3D space that is a 2meter
cube, the gravitational field strength will be lowest directly between
the two masses.

Are there examples of a stationary system where there are multiple
point locations with the same minimum gravitational field?

Imagine a system with an infinite number of equal masses positioned along
a straight line and equally spaced. You will have an infinity number of
point with minimum g field.


I am wondering if there is a single formula to calculate the location
of minimum field strength or if an algorithm is needed to narrow down
where the lowest field strength is and recursively narrow down the
field location which could use a lot of computation as I want to make
this calculation each time I add a new mass to the system.

cheers,
Jamie


Ya that's true but only if as you move a point down the line in one
direction there are still the same number of masses on either side of
the point, otherwise the gravitational force will be infinitesimally
larger in one direction.

cheers,
Jamie

Therefor I said "_infinite_ number of equal masses".

Hi,

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




>

 

[rickman]

On 3/16/2015 4:29 PM, jurb6006@gmail.com wrote:

Ha, I probably won't be of much help here but...

Years ago I as cavorting with a broad on a sex website. She wasn't too worried about thihngs because she is an Indiana state trooper and sharpshooter. Her 14 year old daughter had a question having to do with something like this.

The question was when out in space will you fall. Well actually after getting understood about orbits and all that we are talking about if you are just out there, and "relatively" stationary", would you fall.

I had to answer yes. Because when you are out there, even though gravitational force go by inverse square, one body's gravity will pull on you kore than another. I almost want to go so far as to say that there is no place where all the gravitational forces are equal and cancel out.

As such you will eventually fall somewhere. It might take 99 quadrillion years, but it has to happen eventually.

Even if you were to find a spot in the univers that has totally nulled out gravitational forces, that will change because everything it moving in relation to each other.

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

 

[Jamie M]

On 3/18/2015 5:44 AM, Martin Brown wrote:

On 18/03/2015 11:55, Phil Hobbs wrote:

Umpteen years ago, (BC, that is Before Computers) an N-body system
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 orbit needs elliptic
integrals in general, and of
course even sines and cosines are transcendental functions that can't
be computed exactly except for special values.

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.

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

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.

http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Neptune_and_Pluto.html

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)

Hi,

It sounds from what I just was reading that "Bode's Law" is a result
of "breaking up of a logarithmic spiral nebula into equal angular parts"

Quote from this paper:
http://adsabs.harvard.edu/full/1911ApJ....34..251S

Another article which mentions log spiral relationship to Bode's Law:
http://webcache.googleusercontent.com/search?q=cache:u_7B9SToAfYJ:www.smphillips.8m.com/pdfs/Article17.pdf

cheers,
Jamie

 

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

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.

 

[Martin Brown]

On 19/03/2015 03:39, Jamie M wrote:

On 3/18/2015 5:44 AM, Martin Brown wrote:

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)


Hi,

It sounds from what I just was reading that "Bode's Law" is a result
of "breaking up of a logarithmic spiral nebula into equal angular parts"

Quote from this paper:
http://adsabs.harvard.edu/full/1911ApJ....34..251S

Another article which mentions log spiral relationship to Bode's Law:
http://webcache.googleusercontent.com/search?q=cache:u_7B9SToAfYJ:www.smphillips.8m.com/pdfs/Article17.pdf

Not really. These papers pre-date a proper understanding of the solar
nebula and planetary formation. The current theory is actually based on
Ovenden's conjecture which is that a solar system will evolve such that
the planets minimise their mutual interactions as much as possible.

There are a lot of subtleties still being worked out about the
locations where the various planets must have formed based on their
composition and how they later moved to the positions where they are now
seen. To first order Jupiter and Saturn slugging it out determine where
the other planets in the solar system can have stable orbits.

There has been a recent BBC Horizon about the topic this year.
http://www.bbc.co.uk/programmes/b006mgxf

1) Secrets of the Solar System.
You may have to spoof a UK IP address to watch it.

--
Regards,
Martin Brown

 

[Phil Hobbs]

On 03/19/2015 03:28 AM, jurb6006@gmail.com wrote:

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

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

 

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

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.

 

[DaveC]

> Hi,

*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

 

[Phil Hobbs]

On 3/19/2015 4:57 AM, Martin Brown wrote:

On 19/03/2015 03:39, Jamie M wrote:
On 3/18/2015 5:44 AM, Martin Brown wrote:

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)


Hi,

It sounds from what I just was reading that "Bode's Law" is a result
of "breaking up of a logarithmic spiral nebula into equal angular parts"

Quote from this paper:
http://adsabs.harvard.edu/full/1911ApJ....34..251S

Another article which mentions log spiral relationship to Bode's Law:
http://webcache.googleusercontent.com/search?q=cache:u_7B9SToAfYJ:www.smphillips.8m.com/pdfs/Article17.pdf


Not really. These papers pre-date a proper understanding of the solar
nebula and planetary formation. The current theory is actually based on
Ovenden's conjecture which is that a solar system will evolve such that
the planets minimise their mutual interactions as much as possible.

There are a lot of subtleties still being worked out about the
locations where the various planets must have formed based on their
composition and how they later moved to the positions where they are now
seen. To first order Jupiter and Saturn slugging it out determine where
the other planets in the solar system can have stable orbits.

There has been a recent BBC Horizon about the topic this year.
http://www.bbc.co.uk/programmes/b006mgxf

1) Secrets of the Solar System.
You may have to spoof a UK IP address to watch it.

Wow, completely unwatchable. But thanks for the link.

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

 

[Jamie M]

On 3/19/2015 12:24 PM, DaveC wrote:

Hi,

*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

Hi,

It was actually not an astrophysics question 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

 

[Jamie M]

On 3/19/2015 12:24 PM, DaveC wrote:

Hi,

*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

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

 

[DaveC]

It was actually not an astrophysics question
...
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

 

[Phil Hobbs]

Good luck with your simulation of the Universe.

Cheers

Phil Hobbs

 

[Jamie M]

On 3/23/2015 8:59 PM, DaveC wrote:

It was actually not an astrophysics question
...
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

Probably depends what was last in the mainstream media, ie a space
based gravity story or a practical gravity related story, either
way the smart answer would have to be an EE since astrophysicist's
admittedly don't understand gravity at a fundamental level and are
prone to become sidetracked but an EE perspective is at least based in
reality due to engineers requirement of having to solve real problems.

cheers,
Jamie

 

[nuny@bid.nes]

On Saturday, March 21, 2015 at 1:35:07 AM UTC-7, Jamie M wrote:

On 3/19/2015 12:24 PM, DaveC wrote:
Hi,

*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!

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.

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)

(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.

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.

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:

http://en.wikipedia.org/wiki/Gravitational_field#Classical_mechanics

"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

 

[Martin Brown]

On 24/03/2015 09:50, Jamie M wrote:

On 3/23/2015 8:59 PM, DaveC wrote:
It was actually not an astrophysics question
...
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?


Probably depends what was last in the mainstream media, ie a space
based gravity story or a practical gravity related story, either
way the smart answer would have to be an EE since astrophysicist's

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.

admittedly don't understand gravity at a fundamental level and are
prone to become sidetracked but an EE perspective is at least based in
reality due to engineers requirement of having to solve real 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!

--
Regards,
Martin Brown

 

[Syd Rumpo]

On 24/03/2015 13:44, Martin Brown wrote:

<snip>

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
--
Syd

 

[Phil Hobbs]

On 03/24/2015 09:44 AM, Martin Brown wrote:

On 24/03/2015 09:50, Jamie M wrote:
On 3/23/2015 8:59 PM, DaveC wrote:
It was actually not an astrophysics question
...
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?


Probably depends what was last in the mainstream media, ie a space
based gravity story or a practical gravity related story, either
way the smart answer would have to be an EE since astrophysicist's

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.

admittedly don't understand gravity at a fundamental level and are
prone to become sidetracked but an EE perspective is at least based in
reality due to engineers requirement of having to solve real 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!

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

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

 

[Syd Rumpo]

On 24/03/2015 14:15, Syd Rumpo wrote:

On 24/03/2015 13:44, Martin Brown wrote:

snip

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.

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

Cheers
--
Syd