[coldcreation]

Originally Posted by snoopy

Hi everyone,

I would just like to say that I believe a final theory of gravity would explain its fractal nature... why galaxies look like they do , terrain of planets and trees for example.

How do you figure gravity is fractal (or has a fractal nature)?
...

Originally Posted by snoopy

... or a theory that looks like +...+...+ etc ad infinitum, ie, you end up with infinties unless you just keep it simple and avoid complex gravitiational situations.

Or a theory that looks like -...-...- etc until gravity attains zero.


CC

[coldcreation]

Originally Posted by modest

I believe my two main critiques have been worked out.

• Lagrange points do not have zero potential

Let's be clear. We are referring to local potential not absolute potential. L1 is a saddle point so it's potential is not zero. Correct. The Lagrange point L1 marks the position where the combined gravitational field of the two massive bodies provides precisely the 'centripetal force' required to rotate with them. The centripetal component of the potential has for effect (however fictitious) of displacing the location where the gravitational fields (alone) cancel to zero.

H (see above and link below) is the location (very close to L1) where the fields (of M1 and M2) cancel precisely, regardless of centripetal force. Recall; when we examining this point where the effective potential drops to zero, we find a smooth surface, not a sharp peak. This means that from H to the surface of M1 or M2 there is a gradual transition in the gradient that tends from a local minimum value of zero to whatever it might be on the surface of a celestial object. The fact emerges: the gravitational field curvature gradient is different along the M1-L1-M2 line than the potential at, say, an angle 90 degrees. It follows that the field surrounding M1 (and M2) is not spherically symmetrical.

Originally Posted by modest

• Spacetime is not flat at L1

Unless the primary and secondary bodies (M1 and M2) have similar masses.

There is a point H between L1 and the less massive body at which there is no net gravitational force from the fields of M1 and/or M2, i.e., the spacetime curvature gradient is flat (yet it may or may not be the minimum value of potential of the system). See this general explanation, as well as the larger of the two illustration pictured here.

All Lagrangian points, with the exception of L1, exist only in rotating systems. An outward fictitious centrifugal force is balanced, at these points, by the 'attractive' gravitational forces of M1 and M2.

In a non-rotating static or inertial system Lagrange point L1 (and/or H) would still exist. Rotation slightly pushes L1 away from the more massive body towards the less massive object.

Moving away from the L1 (or H) saddle point the potential is curving 'up' in two directions and 'down' in two directions (along the M1-L1-M2 line).

The Lagrange points, generally, are critical points of the potential where the force is zero, i.e., the potential gradient of the gravitational field plus the fictitious centrifugal force are in balance. H (or L1) is different, since the centrifugal force becomes irrelevant.

Spacetime is flat at H.

Originally Posted by modest

Which leaves only the question of stability. From quotes like this:

It looks like you are saying L-points are stable in your way of thinking. I insist only L4 and L5 are stable. And, that is not a permanent stability as it relies on the stability of M1 and M2 where GR’s equations of motion do not allow permanent stability. So, I think it would be good to expand on that just a bit. I hope I’m not sidetracking you too badly here, but the quote above looks wrong to me. It would be a fine tuning problem to settle something at L1 or L2 by my way of thinking.

-modest

A couple of points, first. Permanent stability may or may not exist. The fact is that systems can (and do) remain in stable configurations (perhaps several Gyr) in accord with GR. So we should be speaking of quasi-stable systems. I am not so much concerned with the stability of test particles placed at L-points, but more so with the stability of gravitating systems and their components, in general.

In the quote above I was referring to the way the earth (for example) remains in orbit around the sun at precisely the right distance according to its mass and velocity, where if velocity were greater the centrifugal force would over power gravity resulting in the dispersal of the system, or the contrary (slower orbital motion and weaker centrifugal force leading to collapse or collision with the sun).

The fact that there is an exact cancelation of the two forces leads me to believe that a fine-tuning problem inherent in celestial mechanics. I don't buy (or I won't pay full price for) the natural selection hypothesis during some initial condition process. The solar system appears to well organized for that, not to mention other gravitating systems.

At the same time, I realize that the general relativistic approach to the relationship between inertia and gravitational force reduces the physical phenomenon to the same constant, i.e. equality of inertial and gravitational force. Centrifugal forces act (in a way) exactly like the force of gravity, proportional to the masses of the bodies. But there seems to be a need for something more (or something less, I should say).

I argue that there is a mechanism in space responsible for generating equilibrium, independent of centrifugal force; that there is no need for a finely tuned counter-force (especially not a fictitious centrifugal force) to justify gravitational stability of the kind where attraction and repulsion are in perpetual competition, and where one wins sporadic exchanges. For sure, the centrifugal force interpretation, generally accepted today, does away with any supernatural intervention (of the Newtonian kind), but it is left with a severe fine tuning problem.

The fine-tuning of both large and small-scale gravitating systems results from a harmonious interaction between the intrinsic gravitational fields surrounding massive bodies in relation to neutral points present in the physical environment where objects are situated: these positions possess properties consistent with the spacetime substratum itself, the spatiotemporal ground-state, the field-free vacuum, empty space, zero local potential, and yes, even the cosmological constant (lambda), and serve to mediate stability.


So instead of a competition between an attractive gravitational force and a countering outward centrifugal force, we have curved spacetime in competition with spacetime that is not curved.

To be continued...


CC

[modest]

Originally Posted by coldcreation

In the quote above I was referring to the way the earth (for example) remains in orbit around the sun at precisely the right distance according to its mass and velocity, where if velocity were greater the centrifugal force would over power gravity resulting in the dispersal of the system, or the contrary (slower orbital motion and weaker centrifugal force leading to collapse or collision with the sun).

The fact that there is an exact cancelation of the two forces leads me to believe that a fine-tuning problem inherent in celestial mechanics. I don't buy (or I won't pay full price for) the natural selection hypothesis during some initial condition process. The solar system appears to well organized for that, not to mention other gravitating systems.

No, I wouldn't buy that either. But, I see some big problems here that should be easily rectified. It is not as you say that if the earth lost a bit of velocity it would hit the sun. In fact, Earth would have to shed a whole lot of orbital angular momentum to hit the sun. If it shed a little bit, it would just find a closer stable orbit. If it gained a little angular momentum it would find a stable orbit a bit further out.

I'm sure there are NASA and soviet missions that can be referenced here. I know the "solar probe" is going to Jupiter to shed momentum - that being the easiest way to use a gravity assist to accomplish a close orbit to the sun. To use rocket fuel alone to shed that much angular momentum in order to achieve a close orbit to the sun would require way to much fuel... I'll look for some references.

My only other question is: if the equations we use now describe orbital dynamics so well, why are we looking for a solution that guarantees stability? Doesn't the current method predict the correct amount of stability? I believe it does.

~modest

[coldcreation]

Originally Posted by modest

No, I wouldn't buy that either. But, I see some big problems here that should be easily rectified. It is not as you say that if the earth lost a bit of velocity it would hit the sun. In fact, Earth would have to shed a whole lot of orbital angular momentum to hit the sun. If it shed a little bit, it would just find a closer stable orbit. If it gained a little angular momentum it would find a stable orbit a bit further out.

Yes, there is a little margin for stability. Granted. But it is a delicate one (a 'little' one).

Originally Posted by modest

My only other question is: if the equations we use now describe orbital dynamics so well, why are we looking for a solution that guarantees stability? Doesn't the current method predict the correct amount of stability? I believe it does.

There is an obvious problems with orbital mechanics. The problem manifests itself to a greater extent in systems such as galaxies. Orbital mechanics cannot explain why there are stars that orbit galaxies too quickly to be accommodated for using standard orbital mechanics.

See this Wiki article: Galaxy rotation curve. Stars revolve around the center of galaxies at a constant speed over a large range of distances from the center of the galaxy. Thus they revolve much faster than would be expected if they were in a free Newtonian potential...

...matter (such as stars and gas) in the disk portion of a spiral should orbit the center of the galaxy similar to the way in which planets in the solar system orbit the sun, that is, according to Newtonian mechanics. Based on this, it would be expected that the average orbital speed of an object at a specified distance away from the majority of the mass distribution would decrease inversely with the square root of the radius of the orbit (the dashed line in Fig. 1). At the time of the discovery of the discrepancy, it was thought that most of the mass of the galaxy had to be in the galactic bulge, near the center.

Observations of the rotation curve of spirals, however, do not bear this out. Rather, the curves do not decrease in the expected inverse square root relationship but are "flat" -- outside of the central bulge the speed is nearly a constant function of radius (the solid line Fig. 1). The explanation that requires the least adjustment to the physical laws of the universe is that there is a substantial amount of matter far from the center of the galaxy that is not emitting light in the mass-to-light ratio of the central bulge.

And so something else that is entirely speculative in nature need to be introduced that is not made of matter as we know it, i.e., not made of electron, protons and neutrons. It is believed to be nonbaryonic.

At the other end of the scale, as it were, there is a need to introduce supermassive black holes.

See this Wiki article: Supermassive black hole Direct Doppler measures of water masers surrounding the nucleus of nearby galaxies have revealed a very fast keplerian motion, only possible with a high concentration of matter in the center. Currently, the only known objects that can pack enough matter in such a small space are black holes, or things that will evolve into black holes within astrophysically short timescales.

It is this discrepancy between theory and observation that I feel should be reconciled but without SMBH's and without some form of CDM. I am certain that this issue can find resolution without ad hoc inclusions once the mechanism of gravity comes to light; and this without a whole-scale revision of GR. The curved spacetime approach is the correct one, but rather than tweaking results with CDM, or on the deep end of the scale (where curvature is though to reach infinity, or nearly so), the focus should be on the low energy regime, where gravitational potential is at its lowest value, locally zero, at local minima, as well as saddle points.

Instead of 'that which fills space' being the culprit, the properties of 'that which is space' should be identified.


CC

[modest]

Originally Posted by coldcreation

There is an obvious problems with orbital mechanics. The problem manifests itself to a greater extent in systems such as galaxies. Orbital mechanics cannot explain why there are stars that orbit galaxies too quickly to be accommodated for using standard orbital mechanics.

And so something else that is entirely speculative in nature need to be introduced that is not made of matter as we know it, i.e., not made of electron, protons and neutrons. It is believed to be nonbaryonic.

Aye, you've got a good point there. The larger the distance involved - the greater the deviation for expected GR results. I would also like to add that I think it is a worthwhile goal to find alternative solutions to dark matter. I do not take your stance that dark matter is improbable. But, it's by no means a settled case. Indirect evidence is not at all conclusive. So, I think you're right.

But, I think you may have missed my point here:

Originally Posted by coldcreation

Yes, there is a little margin for stability. Granted. But it is a delicate one (a 'little' one).

As long as the orbit remains circular - it would actually require massive amounts of energy to change the orbit of a planet. To hit the sun or escape the solar system may be unimaginable. Consider visiting mercury:

Reaching Mercury from Earth poses significant technical challenges, since the planet orbits so much closer to the Sun than does the Earth. A Mercury-bound spacecraft launched from Earth must travel over 91 million kilometers into the Sun’s gravitational potential well. Starting from the Earth’s orbital speed of 30 km/s, the change in velocity (delta-v) the spacecraft must make to enter into a Hohmann transfer orbit that passes near Mercury is large compared to other planetary missions.[93]

The potential energy liberated by moving down the Sun’s potential well becomes kinetic energy; requiring another large delta-v change to do anything other than rapidly pass by Mercury. In order to land safely or enter a stable orbit the spacecraft must rely entirely on rocket motors since aerobraking is ruled out because the planet has very little atmosphere. A trip to Mercury actually requires more rocket fuel than that required to escape the solar system completely. As a result, only two space probes have visited the planet so far.[94] A proposed alternative approach would use a solar sail to attain a Mercury-synchronous orbit around the Sun.

Mercury (planet) - Wikipedia, the free encyclopedia

Not an easy thing to accomplish. The laws of orbital dynamics already allow for stability in this regard. Earth travels at 29800 m/s and mercury travels at 47880 m/s. So, the difference in orbital angular momentum would be a lot. Actually, angular momentum is:
L = mvr
where m is mass, v is speed, and r is radius.

By this we can calculate earth's current angular momentum to be:
2.663 x 10^40 kg m^2 s^-1. To reach Mercury's orbit, earth would need:
1.656 x 10^40 kg m^2 s^-1

So, we would have to shed 38 percent of our momentum to reach Mercury's orbit. That's not easy - that's not a balancing act. I'm trying to say, loosing energy would get us closer to the sun and gaining energy would take our orbit further out - but not in a "fall into the sun" and "fling out of the solar system" kind of way.

The orbit would adjust is all. It's the same way with the sun loosing mass which it has done since the solar system began. Earth's orbit surely grew a bit as a result - but we didn't go flying out of the system. Newton's laws don't necessitate that as you may be thinking they do.

~modest

EDIT:
I admit, this is a different than I was thinking back in the "dynamic equilibrium" thread. I was not thinking it would be this hard to deestablish an orbit. But, it appears from the calculations and everything I'm reading - Maybe it is. Then again, I'm not real good with orbits - we may need to find some sources to establish this. Or, perhaps a third opinion...

[coldcreation]

Off topic:

For my 1000th post here at Hypography I would have liked to write something special, but I'm not into numerology (1000 is no more special than 999 or 1001), so I won't.

I would just like to take this opportunity, anyway, to thank Tormod and the whole crew (not to forget all the others who contribute) for having made such a virtual space of rich, creative and open discussion possible.

Chapeau.





CC

[DougF]

coldcreation
Off topic:

For my 1000th post here at Hypography I would have liked to write something special, but I'm not into numerology (1000 is no more special than 999 or 1001), so I won't.

I would just like to take this opportunity, anyway, to thank Tormod and the whole crew (not to forget all the others who contribute) for having made such a virtual space of rich, creative and open discussion possible.

Chapeau.

As I reach this magic number of 1000 (Currently 946) I plan on no special post but would like to thank all of you here at Hypo,


now back to the point:

on with the thread!

[coldcreation]

Originally Posted by modest

Aye, you've got a good point there. The larger the distance involved - the greater the deviation for expected GR results. I would also like to add that I think it is a worthwhile goal to find alternative solutions to dark matter. I do not take your stance that dark matter is improbable. But, it's by no means a settled case. Indirect evidence is not at all conclusive. So, I think you're right.

This is just one reason why the mechanism of gravity needs to be illuminated.

Originally Posted by modest

As long as the orbit remains circular - it would actually require massive amounts of energy to change the orbit of a planet. To hit the sun or escape the solar system may be unimaginable.

Okay, it's a nice thought experiment, but the point is that objects, such as the Earth, reach equilibrium at a distance from the primary body (the Sun) that is in direct (or nearly direct) relation to the objects mass and velocity (relative to the sun). Or, objects reach equilibrium at a velocity that is in direct relation to the objects mass and distance from the primary body. Or, depending on mass in relation to its velocity and distance from the primary body. Either way, equilibrium is attained and maintained, yet time and again it is observed that the laws of orbital mechanics are violated as scale and complexity increase. For this reason, a continued search for a natural solution to the problem should be sought. Obviously, I imply that cold dark matter (or nonbaryonic matter) is not a natural solution.

Originally Posted by modest

Newton's laws don't necessitate that as you may be thinking they do.

At the same time I don't believe that Newton's laws or even GR need to be complemented with CDM, as you may be thinking they do.

The goal here is not to discredit standard orbital mechanics, simply, to point out where revision could and should be made (notably with respect to rotational curves), and to shed light on the mechanism of gravity. If both goals are related, and I will attempt to point out that they are, then something more, or something less, will have to be added or subtracted from orbital mechanics (respectively).

That will be the subject of the following posts.



CC

[coldcreation]

Gentlemen,

I just sent in my absentee ballot, so it is time to return to serious business: the problem of gravity.

We were discussing the rotational curves of galaxies and how these deviations (or anomalies, which have become the norm) might be explain without the injunction of nonbaryonic dark matter or MOND.

First, let's take a look at the problem, in brief.

The stars in most galaxies appear to be orbiting the galactic core faster than they should be according to both Newtonian mechanics and GR.

Plot showing the relationship between orbital speed and distance from the galactic core for stars and gas of a spiral galaxy.*Source




Spiral galaxy NGC 4736 (enhanced beyond its original splendor with artificial colors by Coldcreation) does not need dark matter to explain the rotational curves of stars and gas, since the rotational curve appears not to be flat (as the diagram above): This is a problem for galaxy formation models, where dark matter is thought to be important. Source

In the spiral galaxy NGC 4736, however, the rotation slows down as you move farther out from the crowded inner reaches of the galaxy. At first glance, that declining rotation curve is just what you would expect if there is no extended halo of dark matter, and no modification to gravity. As you move far away from the swarming stars of the inner galaxy, gravity becomes weaker, and so motions become more sedate.

Hubble image of Galaxy Cluster CL 0024+17 (enhanced by Coldcreation) Source

Astronomers using NASA's Hubble Space Telescope have discovered a ghostly ring of dark matter that formed long ago during a titanic collision between two massive galaxy clusters. The ring's discovery is among the strongest evidence yet that dark matter exists. Astronomers have long suspected the existence of the invisible substance as the source of additional gravity that holds together galaxy clusters. Such clusters would fly apart if they relied only on the gravity from their visible stars. Although astronomers don't know what dark matter is made of, they hypothesize that it is a type of elementary particle that pervades the universe.

This Hubble composite image shows the ring of dark matter in the galaxy cluster Cl 0024+17. The ring-like structure is evident in the blue map of the cluster's dark matter distribution. The map was derived from Hubble observations of how the gravity of the cluster Cl 0024+17 distorts the light of more distant galaxies, an optical illusion called gravitational lensing. Although astronomers cannot see dark matter, they can infer its existence by mapping the distorted shapes of the background galaxies. The map is superimposed on a Hubble Advanced Camera for Surveys image of the cluster taken in November 2004.

Source

Discussion to follow...


CC

[Pluto]

G'day from the land of ozzzzzzzzz

Coldcreation said

The stars in most galaxies appear to be orbiting the galactic core faster than they should be according to both Newtonian mechanics and GR.

What is fast?