multibody gravity question

[Martin Brown]

On 24/03/2015 14:34, Phil Hobbs wrote:

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

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.

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

--
Regards,
Martin Brown

 

[Phil Hobbs]

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

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

 

[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 (2005 Nobel Prize on physics) who has always designed his own stuff.

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

Cheers

Phil

 

[Martin Brown]

On 21/03/2015 08:35, 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!

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.

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 =

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.

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 =

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

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.

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.

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

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.

--
Regards,
Martin Brown

 

On Tue, 24 Mar 2015 04:58:46 -0700 (PDT), Phil Hobbs
<pcdhobbs@gmail.com> wrote:

>Good luck with your simulation of the Universe.

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

 

[Jamie M]

On 3/24/2015 4:58 AM, Phil Hobbs wrote:

Good luck with your simulation of the Universe.

Cheers

Phil Hobbs

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

 

[Jamie M]

On 3/24/2015 11:45 AM, Martin Brown wrote:

On 21/03/2015 08:35, 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!

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.

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 =

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.


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 =

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

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.

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.

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

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.

Hi,

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

https://www.dropbox.com/s/6s4smimj7t15an0/gravity%20examples1.xls

screenshot of the spreadsheet:
https://www.dropbox.com/s/f8ik31aul1snwul/excel1.png

screenshot of output graphs of gravitational field intensity and
gravitational induced spacetime curvature from the three masses:
https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

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

 

[Jamie M]

On 3/24/2015 10:26 AM, nuny@bid.nes wrote:

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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png


cheers,
Jamie

 

[DaveC]

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

Cheers

Phil Hobbs

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

"They are frequently wrong but never in doubt."

 

[John Devereux]

DaveC <invalid@invalid.net> writes:

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

Cheers

Phil Hobbs

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...

--

John Devereux

 

[Phil Hobbs]

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

Cheers

Phil Hobbs

 

[Phil Hobbs]

He does. See the Book of Job.

Cheers

Phil Hobbs

 

[Reinhardt Behm]

On 25.03.2015 08:52, Jamie M wrote:

On 3/24/2015 11:45 AM, Martin Brown wrote:
On 21/03/2015 08:35, 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!

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.

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 =

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.


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 =

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

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.

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.

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

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.



Hi,

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

https://www.dropbox.com/s/6s4smimj7t15an0/gravity%20examples1.xls

screenshot of the spreadsheet:
https://www.dropbox.com/s/f8ik31aul1snwul/excel1.png

screenshot of output graphs of gravitational field intensity and
gravitational induced spacetime curvature from the three masses:
https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

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.

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.

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

--
Reinhardt

 

[Martin Brown]

On 25/03/2015 03:21, DaveC wrote:

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

Cheers

Phil Hobbs

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

"They are frequently wrong but never in doubt."

It isn't true either at least not of scientists in general.

Politicians and economists are far more worthy of that saying.

BTW A theorem can be proved from some given set of starting axioms.

Those axioms may or may not be correct in reality but if the chain of
reasoning is correctly followed then a theorem can be proved from your
chosen starting axioms using formal mathematical logic. Comparison of a
models predictions with the real world is the ultimate arbiter.

Requiring the internal angles of a triangle to always add up to 180
degrees give you flat Euclidean geometry. Relaxing that restriction
allows what turns out to be a useful generalisation of spacetimes.

I am yet to be convinced that string theory will ever be a useful
replacement formalism but only time will tell. Some very bright guys are
convinced that it is *the* way forward.

Astrophysicists are painfully aware of the limitations of trying to work
out how a forest works by studying only the largest and nearest trees.

It is a sobering thought that 10% of everything in the peer reviewed
literature will subsequently be shown to be incorrect or misleading.
Even papers that are mostly correct occasionaly suffer proof editors
"improvements" that can in the worst case invert the intended meaning of
the authors. Letters to the editor can be quite feisty if it happens.

--
Regards,
Martin Brown

 

[nuny@bid.nes]

On Tuesday, March 24, 2015 at 6:18:51 PM UTC-7, Jamie M wrote:

On 3/24/2015 10:26 AM, nuny@bid.nes wrote:
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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

I was picking terminological nits:

http://www.syvum.com/physics/gravitation/gravitation3.html

"The gravitational intensity I is defined as the force experienced by a unit mass when placed in the gravitational field of another mass M."

You represent that as local horizontal slope at a point on your curves.

"The gravitational potential V at a point in the gravitational field is defined as the work done in taking a unit mass from that point to infinity against the force of gravitational attraction."

That you represent as the height of a given point on a curve above y = 0.

(The work done taking a unit mass from one point to another is the difference in height of two points on a curve.)

The potential can be different but the intensity the same (zero), just as in electrical circuits as I mentioned elsewhere.

Your diagrams seem to feature singularities, which I find distracting.

Have you seen this?

https://xkcd.com/681/

Notice that the top of each "peak" between wells is locally flat, IOW field intensity = force on a particle placed there = zero, same as at the bottom of each well despite them all being at different depths.

This diagram includes the exaggerated curvature of the universe:

http://wps.prenhall.com/wps/media/objects/1352/1385128/image/ncsu_binary_potential.gif

Visualizing that to be a patch of the surface of an inflating balloon (2D analog of 3D spacetime) explains dark energy. I think.


Mark L. Fergerson

 

[Phil Hobbs]

https://xkcd.com/681/

  Notice that the top of each "peak" between wells is locally flat, IOW field intensity = force on a particle placed there = zero, same as at the bottom of each well despite them all being at different depths.

Well, of course the planets aren't arranged in a straight line like that, even if they were stationary, and the plot ignores angular momentum, which is what keeps everything from falling into the Sun.

BTW I just finished reading that book Martin suggested, "Celestial Encounters". It's an interesting read for the mathematically inclined. It has no actual math at all, but it helps to know a bit about Cantor sets and measure theory in order to get the gist of how interacting orbits become chaotic. Five bucks including shipping from ABEbooks.

Cheers

Phil Hobbs

Phil Hobbs

 

[Jamie M]

On 3/25/2015 2:59 PM, nuny@bid.nes wrote:

On Tuesday, March 24, 2015 at 6:18:51 PM UTC-7, Jamie M wrote:
On 3/24/2015 10:26 AM, nuny@bid.nes wrote:
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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

I was picking terminological nits:

http://www.syvum.com/physics/gravitation/gravitation3.html

"The gravitational intensity I is defined as the force experienced by a unit mass when placed in the gravitational field of

another mass M."

You represent that as local horizontal slope at a point on your curves.

"The gravitational potential V at a point in the gravitational field is defined as the work done in taking a unit mass from that

point to infinity against the force of gravitational attraction."

That you represent as the height of a given point on a curve above y = 0.

(The work done taking a unit mass from one point to another is the difference in height of two points on a curve.)

The potential can be different but the intensity the same (zero), just as in electrical circuits as I mentioned elsewhere.

Your diagrams seem to feature singularities, which I find distracting.

Have you seen this?

https://xkcd.com/681/

Notice that the top of each "peak" between wells is locally flat, IOW field intensity = force on a particle placed there = zero,

same as at the bottom of each well despite them all being at different
depths.

This diagram includes the exaggerated curvature of the universe:

http://wps.prenhall.com/wps/media/objects/1352/1385128/image/ncsu_binary_potential.gif

Visualizing that to be a patch of the surface of an inflating balloon (2D analog of 3D spacetime) explains dark energy. I think.


Mark L. Fergerson

Hi,

I think this type of situation could be described by expanding
space-time possibly, where a galaxy core has faster space-time
expansion than its perimeter.

"huge molecular outflows from deep inside the galaxy's core"

http://phys.org/news/2015-03-supermassive-black-hole-star-making-gas.html

Other explanations being blackhole's and/or stars pushing matter away
from the center of the galaxy.

cheers,
Jamie

 

[Jamie M]

On 3/25/2015 2:59 PM, nuny@bid.nes wrote:

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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

I was picking terminological nits:

http://www.syvum.com/physics/gravitation/gravitation3.html

"The gravitational intensity I is defined as the force experienced by a unit mass when placed in the gravitational field of another mass M."

You represent that as local horizontal slope at a point on your curves.

"The gravitational potential V at a point in the gravitational field is defined as the work done in taking a unit mass from that point

to infinity against the force of gravitational attraction."

That you represent as the height of a given point on a curve above y = 0.

(The work done taking a unit mass from one point to another is the difference in height of two points on a curve.)

The potential can be different but the intensity the same (zero), just as in electrical circuits as I mentioned elsewhere.

Your diagrams seem to feature singularities, which I find distracting.

Have you seen this?

https://xkcd.com/681/

Notice that the top of each "peak" between wells is locally flat, IOW field intensity = force on a particle placed there = zero,

same as at the bottom of each well despite them all being at different
depths.

This diagram includes the exaggerated curvature of the universe:

http://wps.prenhall.com/wps/media/objects/1352/1385128/image/ncsu_binary_potential.gif

Visualizing that to be a patch of the surface of an inflating balloon (2D analog of 3D spacetime) explains dark energy. I think.


Mark L. Fergerson

Hi,

Thanks nice comic. I was using gravitational field instead of
potential since gravitational potential makes it sound more
that it is a effect of mass achieving escape velocity, but as
you say considering gravitational fields acting on space time
instead of just on matter could explain dark energy. It makes
sense that gravitational field induced shapes in spacetime
would tend to want to find their lowest energy state, which would
be to stretch out the ripples, and the curvature from matter in
spacetime is one of those ripples (on local scales small ripples,
and on universe size scale much higher amplitude ripple that
should have a correspondingly larger force towards equilibrium
reducing the ripples (dark energy).

cheers,
Jamie

 

[Martin Brown]

On 27/03/2015 04:19, Jamie M wrote:

On 3/25/2015 2:59 PM, nuny@bid.nes wrote:

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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

I was picking terminological nits:

http://www.syvum.com/physics/gravitation/gravitation3.html

"The gravitational intensity I is defined as the force experienced
by a unit mass when placed in the gravitational field of another mass M."

You represent that as local horizontal slope at a point on your
curves.

"The gravitational potential V at a point in the gravitational
field is defined as the work done in taking a unit mass from that point

to infinity against the force of gravitational attraction."

That you represent as the height of a given point on a curve above
y = 0.

(The work done taking a unit mass from one point to another is the
difference in height of two points on a curve.)

The potential can be different but the intensity the same (zero),
just as in electrical circuits as I mentioned elsewhere.

Your diagrams seem to feature singularities, which I find distracting.

Have you seen this?

https://xkcd.com/681/

Notice that the top of each "peak" between wells is locally flat,
IOW field intensity = force on a particle placed there = zero,

same as at the bottom of each well despite them all being at different
depths.

This diagram includes the exaggerated curvature of the universe:

http://wps.prenhall.com/wps/media/objects/1352/1385128/image/ncsu_binary_potential.gif


Visualizing that to be a patch of the surface of an inflating
balloon (2D analog of 3D spacetime) explains dark energy. I think.


Mark L. Fergerson


Hi,

Thanks nice comic. I was using gravitational field instead of
potential since gravitational potential makes it sound more
that it is a effect of mass achieving escape velocity, but as
you say considering gravitational fields acting on space time
instead of just on matter could explain dark energy. It makes
sense that gravitational field induced shapes in spacetime
would tend to want to find their lowest energy state, which would
be to stretch out the ripples, and the curvature from matter in
spacetime is one of those ripples (on local scales small ripples,
and on universe size scale much higher amplitude ripple that
should have a correspondingly larger force towards equilibrium
reducing the ripples (dark energy).

cheers,
Jamie

Jamie,

You can't just type in this random word salad with no mathematical
foundations. Before you can say anything that makes the remotest sense
in this field you have to at least have read and understood Misner,
Thorne & Wheelers classic book "Gravitation" which details current
knowledge about general relativity upto the 1980's and is heavy enough
to disturb the local gravitational field. There is new stuff since then
but without good foundations anything you build falls down instantly.

Frantic handwaving with no mathematical or even rational foundations
based on random use of buzzwords simply doesn't hack it.

--
Regards,
Martin Brown

 

[Jamie M]

On 3/27/2015 2:08 AM, Martin Brown wrote:

On 27/03/2015 04:19, Jamie M wrote:
On 3/25/2015 2:59 PM, nuny@bid.nes wrote:

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.

Hi,

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

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

https://www.dropbox.com/s/3yh8pw1is80hoj5/excel2.png

I was picking terminological nits:

http://www.syvum.com/physics/gravitation/gravitation3.html

"The gravitational intensity I is defined as the force experienced
by a unit mass when placed in the gravitational field of another mass
M."

You represent that as local horizontal slope at a point on your
curves.

"The gravitational potential V at a point in the gravitational
field is defined as the work done in taking a unit mass from that point

to infinity against the force of gravitational attraction."

That you represent as the height of a given point on a curve above
y = 0.

(The work done taking a unit mass from one point to another is the
difference in height of two points on a curve.)

The potential can be different but the intensity the same (zero),
just as in electrical circuits as I mentioned elsewhere.

Your diagrams seem to feature singularities, which I find
distracting.

Have you seen this?

https://xkcd.com/681/

Notice that the top of each "peak" between wells is locally flat,
IOW field intensity = force on a particle placed there = zero,

same as at the bottom of each well despite them all being at different
depths.

This diagram includes the exaggerated curvature of the universe:

http://wps.prenhall.com/wps/media/objects/1352/1385128/image/ncsu_binary_potential.gif



Visualizing that to be a patch of the surface of an inflating
balloon (2D analog of 3D spacetime) explains dark energy. I think.


Mark L. Fergerson


Hi,

Thanks nice comic. I was using gravitational field instead of
potential since gravitational potential makes it sound more
that it is a effect of mass achieving escape velocity, but as
you say considering gravitational fields acting on space time
instead of just on matter could explain dark energy. It makes
sense that gravitational field induced shapes in spacetime
would tend to want to find their lowest energy state, which would
be to stretch out the ripples, and the curvature from matter in
spacetime is one of those ripples (on local scales small ripples,
and on universe size scale much higher amplitude ripple that
should have a correspondingly larger force towards equilibrium
reducing the ripples (dark energy).

cheers,
Jamie

Jamie,

You can't just type in this random word salad with no mathematical
foundations. Before you can say anything that makes the remotest sense
in this field you have to at least have read and understood Misner,
Thorne & Wheelers classic book "Gravitation" which details current
knowledge about general relativity upto the 1980's and is heavy enough
to disturb the local gravitational field. There is new stuff since then
but without good foundations anything you build falls down instantly.

Frantic handwaving with no mathematical or even rational foundations
based on random use of buzzwords simply doesn't hack it.

Hi,

Well before math can be used the initial properties of a system need
to be known, math has been used already extensively and has not solved
dark energy, which indicates a fundamental missing premise!

The two premises I am putting forward is that gravitational curvature
is not just a mathematical property but is a real property of space
time that exists, and the other premise is that a standing wave of
space time curvature will have a equilibrium force which causes it
to expand into surrounding space time as a standing wave is higher
energy than surrounding space time.. It is the same idea as the
surface of water being flat, the only standing wave that is stable
on the surface of water is if there are waves travelling in multiple
directions, but if a single standing wave, ie a parabolic shape
is put into water, ie by lifting a water filled cup upside down
out of the water until the cup lets the water splash back down,
the water will return to a flat state soon after.

If a slightly gelatinous or higher viscosity mix of water with
some other ingredient is dropped into the water the same way, if
it floats, it will maintain its parabolic shape and disperse slower.

Matter is like a glue for spacetime in that sense, it is holding
space time in a standing wave parabolic shape, but if space
time rate of expansion increases that indicates that the glue force
provided by matter is less than the dispersion force towards equilibrium
(flat) spacetime.

It is the same idea whether physics terms or analogous terms are
used when describing it!

cheers,
Jamie