Is there a 'gentler' MOND effect in our solar system..?

nutant gene 71 · #1 (**permalink**) 27-March-2007, 06:02 PM

Is there a 'gentler' MOND effect in our solar system to account for Pioneer Anomaly?

It seems this Pioneer Anomaly is getting press again.
Newfound Data Could Solve NASA's Great Gravity Mystery
From the article:

Quote:

Edward Belbruno, a former JPL researcher and gravitational trajectory expert at Princeton University who also served the panel but is unconnected with the anomaly research, said that another possible explanation for the Pioneer Anomaly rests in the mass of the Milky Way galaxy, which – when taken to account – yielded the exact acceleration change for Pioneer 10 as that observed. While he found that the technique did not yield a specific direction for the acceleration, it may shed some insight into the anomaly and warrants further study, Belbruno added.

Have they found something new in the data? The above quote sounds hollow, since Pioneer 10 and 11 are traveling out of the solar system in opposite directions, so the Milky Way galactic mass may be only coincidental to their anomalous acceleration towards the Sun. Could there be a MOND type effect in our solar system to account for this acceleration, for example, that would better explain this mysterious slowing of the two Pioneer spacecrafts? Is there an ATM idea of MOND (M. Milgrom's "modified Newtonian dynamics") that is solar system specific? I worked this following value for MOND's a_0 elsewhere, which looks like this, though it is a modification of MOND into a 'gentler slope' for our solar system:

Quote:

Newton postulated that his gravity ratio between masses is a ‘universal constant’ G, and it had been used as such ever since. However, though we get good orbital results for our solar system, this ran into difficulty when orbital behavior for outer galaxy arms were observed, where they acted as if there was more massive matter there, invisible to us, so dubbed ‘dark matter’. Mordehai Milgrom’s MOND solution was to factor in an acceleration force, F = ma^2/ a_o, which translates using F = GMm/ r^2, into a = (GM a_o/ r^2)^1/2, where Milgrom calculated the value for a_0=1.2×10^−10 ms^−2 empirically. This does not invalidate Newton’s constant G, but it does indicate that over great astronomical distances, force from gravity may have a modifier in it.

Since the discovery of the Pioneer Anomally by Anderson, Nieto, Turyshev et al, there had been independent speculations that perhaps a similar modifier may be at work within our solar system to account for the anomalous acceleration towards the Sun by Pioneers, Galileo, and Ulysses space crafts, though non- gravitational systemic reasons were not fully disqualified. However, if the Pioneer Anomaly is telling us something about our solar system that is gravitational, ‘dark matter’ like, for our solar system (where the computed –a = ~8E^-10 ms^−2 approximates Milgrom’s a_0), then there may be cause to look for a gravitational anomaly within our solar system as well. Such an anomaly, for example, may account for the very large atmospheres of the outer gas giants, or some moons like Titan’s atmosphere, or Pluto’s atmosphere, where the masses of distant bodies calculated using a constant Newton’s G works for orbital dynamics, but may be giving us erroneous readings for planetary mass densities.

One possible indication of this is by using Milgrom’s MOND’s a = (GM a_o/ r^2)^1/2 and modifying it for our solar system, but to drop Newton’s assumption of a constant universal G, and give it a variable value instead. For example, if we ‘assume’ a variable G at the rate of 1G per 1AU with distance from the Sun (at present unsubstantiated empirically), we get an approximation of the Pioneer Anomaly, as follows:

-a = (GM a_o/ r^2)^1/2, which becomes modified with 1G per 1AU as:

-a = [G(AUn)M a_o/ r(AUr)]^1/2, where AUn is the number of AU distance, and AUr is the distance r for one AU, so with numbers, for Earth’s orbital:

-a = [(6.67E-11)(1)(1.98E+30)(1.2E-10) / (1.5E+11)(1.5E+11)]^1/2, gives us a value of:

-a = (15.8479E+9 / 2.25E+22)^1/2 = (70.435E-14)^1/2

-a = 8.3934E-7 m/s^2, which is three orders of magnitude greater than Pioneer’s –a = ~8E-10 m/s^2, too far out of ball park.

The same calculation for any distance in AU will yield the same result, i.e., at Saturn’s 9.5AU, where r = 1.429E+12 m, gets nearly same result, viz. –a = 8.38E-7 m/s^2

However, what Milgrom calculated for the outer galaxy flat rotation curves may not be the same as what is operable within the limits of our solar system, so that a ‘gentler’ MOND effect may be the case here, which can be calculated as follows, solving for a_os within our solar system:

-a = = [G(AUn)M a_o/ r(AUr)]^1/2, and plugging in known values for Pioneer Anomaly:

-8E-10 m/s^2 = [(6.67E-11)(1)(1.98E+30)(a_o) / 2.25E+22]^1/2, and solving for our solar system’s a_os we get:

-8E-10 m/s^2 = [13.2066E+19)(a_os) / 2.25E+22 ]^1/2

a_os = 1.0908E-16 m/s^2, for our solar system, which is a far lower, gentler value for our solar system then what was computed for the outer galaxy curves, viz. a_o = 1.2 E-10 m/s^2.

This is a follow up on an earlier post, where I teased this idea but never really took it further: Jerry Jensen's ATM idea

Okay, we got 30 days to shoot this down, or make some hay here, under new ATM rules.

Jerry · #2 (**permalink**) 27-March-2007, 08:07 PM

There is another 'new' explanations floating around - thermal energy from the RTG's; but both of these explanations have been addressed as 'improbable' in two decades of searching. You are correct that the acceleration of the two Pioneers in opposite directions rules out most galactic biasing vectors (and it would be an unlikely coincidence that both probes would experience the same net effect). Likewise, if thermal energy were the culprit, there should be a decay in the acceleration and there is not.

We need a new experiment.

Utad3 · #3 (**permalink**) 27-March-2007, 09:55 PM

Quote:

Originally Posted by nutant gene 71

Is there a 'gentler' MOND effect in our solar system to account for Pioneer Anomaly? (...)

(...) Could there be a MOND type effect in our solar system to account for this acceleration, for example, that would better explain this mysterious slowing of the two Pioneer spacecrafts? Is there an ATM idea of MOND (M. Milgrom's "modified Newtonian dynamics") that is solar system specific? I worked this following value for MOND's a_0 elsewhere, which looks like this, though it is a modification of MOND into a 'gentler slope' for our solar system:

Hi! Please forgive my insistence, but - taking the risk of being banned from this forum and also being aware that current fashion seems to be to convey the idea that the Pioneer anomaly should be regarded as ''an unknown systematic" (is this a sort of a scientific term for taboo?!) and not as any 'new physics' issue - doesn't the following unpublished paper ("I'm afraid I cannot accept your manuscript for publication in Physics Letters B.") gives a sound approach to the anomaly like a kind of a 'modified Newtonian' effect?:

Quote:

(...)
The explanation may be found by heeding an assertion by Heaviside which dates from 1893: "To form any notion at all of the flux of gravitational energy, we must first localise the energy. Whether the notion will turn out to be a useful one is a matter for subsequent discovery". This opinion was further endorsed by Brillouin [3] in his book 'Relativity Reexamined', which included this quotation as an intial preface to the work. The point is that, if it takes time for gravitational field energy to adjust to change of relative position of two interacting bodies, then, as a function of their motion, one might find that G, in effect, has a slightly different value in governing that motion. Note here that there is, indeed, a difference between the motion of our Earth in near circular orbit around the Sun and the motion of a spacecraft moving radially away from the Sun.

The mention in the above abstract that the background to this is 'well documented' is a reference, for example, to a paper entitled 'The inverse-square law of force and its spatial energy distribution' [4], where it is shown that G as it applies between two masses M and m has a higher value given by GMm/R^2 times the increment of R if there were no gravity force for the retardation period involved.

For a planet in orbit around the Sun this is found to modify Newton's law of gravitation and bring it into conformity with Einstein's law of gravitation by which the anomalous perihelion motion of planet Mercury is explained, provided the effective speed at which energy traverses the distance R is 0.707 times the speed of light. The retardation time T is such that:

T^2 = 2(R/c)^2 .......... (1)

It was the subject of that paper to show how, in acting on Heaviside's suggestion, this equation (1) is derived, it being self-evident that any energy transfer at the speed of light can hardly be confined to a narrow pathway drawn between the Sun and the planet. The analysis had regard to the deployment of gravitational potential energy in the whole of the field affected by the interaction and indicated that the mean route for energy travel between Sun and planet via the field had to be longer by the factor (2)^1/2 than their separation distance. The implicit assumption was that adjustment of gravitational energy occurs by energy quanta moving at the same speed as the photon, the speed c of light.

Thus one finds that the relevant increment of R is fT^2/2, f being the acceleration v^2/R, and this gives a change of gravitational energy potential by the factor (v/c)^2 in the case of Sun and planet interaction, v being the speed of the planet in its orbit.

For the case under consideration, a spacecraft moving away from the Sun at a relative speed v, this energy retardation factor has the effect of increasing the gravitational potential by the factor vT/R or (2)^1/2 (v/c). Being a linear term instead of one of second order, this is far more significant than the term in (v/c)^2 that applies to the planetary case.

Note that a speed of Pioneer 11 of 15 km/s would then be needed to imply an enhanced pull of gravity amounting to 7.07x10^-5 times 1.225x10^-3 at 22 AU, which is 8.7x10^-8 gm/s^2, the median value measured. Although the relevant speed may have then been a little lower than 15 km/s, the loss of energy in escaping from the Sun's gravitational field is in reasonable accord with that reduction to onward travel through space at 11.6 km/s and the argument here does point to the fact that observed anomaly is in some substantial measure explained by the energy retardation effect under discussion.

It is submitted that in considering anomalies such as that posed by the Pioneer 10/11 observations, cosmologists, in applying the theory of gravity, should put more emphasis on the analysis of energy deployment and not just concentrate attention on the gravitation as a law of force defined by the standard formulation. The Appendix below, which summarizes in a reversed order the analysis of record in reference [4], warrants attention in this regard.
(...)
in A New Insight into the Pioneer 10/11 Gravitation Anomaly (August 2002)

Thank you for your attention.
P.S: I am not the author; just a guy with a keen devotion

tusenfem · #4 (**permalink**) 28-March-2007, 02:06 PM

I am not sure, but has it not been shown that there cannot be a retardation in gravitiation? IIRC in that case the whole solar system would be unstable, and we would not be here.

nutant gene 71 · #5 (**permalink**) 28-March-2007, 06:19 PM

Quote:

Originally Posted by tusenfem

I am not sure, but has it not been shown that there cannot be a retardation in gravitiation? IIRC in that case the whole solar system would be unstable, and we would not be here.

Thanks tusenfem, I think this is correct, that gravity potential cannot have a retardation, or else orbital mechanics would be jeapordized. I believe it was Van Flandern who estimated that gravity U is much faster than light c, per this speed of gravity paper: "Conclusion: The Speed of Gravity is > 2x10^10c," per Van Flandern.

If so, Aspden's paper on Pioneers 10/11 (referenced by Utad3 above) may explain the 'loss of energy' but perhaps not for the reason of gravitational retardation; rather it might be 'for reasons that mimic it only. Aspden says in his paper:

Quote:

Keep in mind that inertial, as opposed to frictional, retardation involves actions that tend to be governed by the square of the time involved. This means that, in working out a mean retardation time for the action by which energy change occurs in that range up to the separation distance z, we must evaluate the root mean square of the elemental time components. So, given that all the action occurs over that limited range z, if the energy distribution within that range is linear, being proportional to x at radius x, with x as the distance to travel from charge to field, the root mean square of the integral of x3dx divided by the square root of the integral of xdx over the range 0 to x gives the effective distance of travel. Upon evaluation, this is r/(2)1/2. The retardation time then could be the time taken to travel this distance from one charge to the field at speed c plus the time to make a similar return journey between the field and the other charge. This gives a retardation time T for which:

T2 = 2 (r/c)2

exactly, as we found empirically for the gravitational action in derving equation (6).

I worked it out instead using the 'retardation' not of time but by factoring in a 'hypothetical' retardation due to interital mass increase per r. This is something on which I must play my own 'devil's advocate' because how can I justify modifying the inverse square law, in the manner of MOND, to insert r into the upper portion of F=GMm/r^2 without doing the same for the lower? Viz. F = G(r)Mm/r^3? So this is a conundrum, since if G is growing at the flat rate of G per r, or 1G per 1AU as hypothesized (not crickey until empirically proven!), then what happens to the lower r^3? By using Milgrom's F = ma^2/a_o, combining them, I came up with G(r)Mm/r^3 = ma^2/a_o, canceling out the m, and re-defining G(r) as G(AUn) in the upper (merely a multiplier), canceling the r above and below, so that now the lower r^2 became r(AUr), to remain consistent with 1G=1AU. The net effect was thus G(AUn)M/r(AUr) = a^2/a_o, which reworked for finding a became: a^2 = G(AUn)a_o/r(AUr), and taking square root: a = [G(AUn)a_o/r(AUr)]^1/2. (I list this here for clarification of why r drops out in the lower, though not certain all crickey in doing so.) Then when I worked out the numbers for Pioneer Anomaly, the acceleration -a towards the Sun worked out as 6 orders of magnitude weaker than Milgrom's.

I also think, as mentioned by Jerry, that the vector alignments cannot both be pointing towards the Milky Way's galactic mass if they're traveling in opposite directions. The coincidence of this is intriguing, however. The only thing I can think of to possibly account for this 'coincidence' is that our 'measurements' of Milky Way mass is somehow related to the 'effect' felt by the Pioneers, but really don't have a good idea on this.

Utad3 · #6 (**permalink**) 29-March-2007, 12:30 AM

Quote:

Originally Posted by tusenfem

I am not sure, but has it not been shown that there cannot be a retardation in gravitiation? IIRC in that case the whole solar system would be unstable, and we would not be here.

Quote:

Originally Posted by nutant gene 71

Thanks tusenfem, I think this is correct, that gravity potential cannot have a retardation, or else orbital mechanics would be jeapordized. I believe it was Van Flandern who estimated that gravity U is much faster than light c, per this speed of gravity paper: "Conclusion: The Speed of Gravity is > 2x10^10c," per Van Flandern.

If so, Aspden's paper on Pioneers 10/11 (referenced by Utad3 above) may explain the 'loss of energy' but perhaps not for the reason of gravitational retardation; rather it might be 'for reasons that mimic it only. Aspden says in his paper:
(...)

Thank you tusenfem for having raised the issue on the retardation effect, and for your continued interest in spite of an earlier not so polite comment of mine, and nutant gene 71 for your detailed approach and explanation.

I am no expert in physics and maths, however from my perspective those two fields, as central as they may be to our quest for knowledge, they are not the only available tools to acquire understanding of the same surrounding world in which we live.

As such, comparing to what I have been able to learn [not in physics and maths] the central aspects of Dr. Aspden's theories are correct, that is, in accordance with reality [as I am able to grasp it, and other seekers for sure far better than me]. Taking into consideration the immense aspects of Nature that are needed to take into account when creating a theory intended to describe how Nature works, and also the amount of knowledge in various fields that the individual must previously gather in order to start such an enterprise, it is reasonable to assume that one individual in an always short physical lifetime will not be able to include and develop on every aspect of Nature, or that such individual may even interpret minor aspects in a not entirely correct manner [however, as a carefull study of history can show, the enhancement of the knowledge of particular aspects is usually left onto other individuals continuing the path initiated by such pioneer individual].

All in all, not being myself expert in these fields and therefore not being able to discuss them in a technical manner, please allow to quote, like if here in an humble "Advocatus Dei" position, a passage that I found about what the author, Dr. Aspden, has to say about how gravitational action asserts a retarded effect, being a central tenet of his exposition about the Pioneer 10/11 gravitational anomaly; I leave it open to discussion if possible or if any expert might be willing to explain it or to counter argumenting, I'll do my best to understand the perspectives hereafter presented:

Quote:

(...)
The Debate

The reference to the ‘speed of gravity’ is itself something that needs definition. If one considers the speed of light, at least one can interrupt the light beam at a distance from the point of measurement and so relate time and distance as needed to make the measurement. Gravity as a force exists given the existence of a source body and we really have no way of turning that force on and off. All we can do is to move the body itself and then the question arises as to whether the gravitational field shares that motion as if rigid (instantaneous action) or adjusts to the motion with a time delay.

Keep in mind that there is a world of difference in physics as between the notional retardation of the action of a force such as gravity and the delay involved in gravitational potential energy redeploying in the field system which envelops the mass involved. The reader, in yielding to theoretical notions, has to decide whether to think in terms of force or in terms of energy, whereas Mother Nature does not ‘think’ but simply ‘acts’ by a process of adjusting the distribution of the energy in the system to optimise action leading to a minimum energy potential state.

If the motion of a planet around the sun were truly a circular motion with the planet’s orbit having a constant radius, then the mutual gravitational energy potential between sun and planet would surely be constant as no energy is being transferred to cater for changes of kinetic energy by the two interacting bodies. If, however, there were to be a cyclical change of that radius, as applies for elliptical orbital motion of the planet, then there would be energy transfer to and from the planet drawing on, or replenishing, that gravitational potential resource. Now, in the context of this situation, what is meant by ‘speed of gravity’? Gravity does not move, so are we referring to the speed of energy that is traversing between planet and the gravitational field system? Then one must ask where that potential energy is seated as it can hardly be that it sits at the Sun’s centre and to apply the proposition that the energy we associate with gravity travels at the speed of light we need to know where it sets out from in its journey in order to reach the planet and resettle as it adds to the kinetic energy of that planet.

As to the basic orbital component of circular motion, the radius is determined by a balance of centrifugal force and the force of gravity. The balance is an unchanging quantity and if ‘gravity has a speed’ is this something that was only a factor when the solar system was first created or is it somehow something that affects the planet’s motion on an ongoing basis?

The history of this subject tells us that, if we assume the circular component of orbital motion is not affected by the ‘speed of gravity’ but the radial component of motion is so affected, then the radial period of the oscillations will be slightly retarded in relation to the orbital period. This explains why the orbit is subject to a slow progressive advance of its perihelion, something observed and particularly noticeable in the case of planet Mercury.

Indeed, to get the theory to fit what is observed, namely the 43 seconds of arc anomalous advance of perihelion per century, the speed of that radial gravitational retardation effect has to be deemed to involve the speed of light. Gerber in 1898 (Zeitschrift f. Math. u, Phys., 43, 93), in explaining this 43 second of arc advance per century, assumed the gravitational action to have that speed of light limitation.

Readers who regard Einstein as the genius who discovered why the planet Mercury has such an anomalous motion should take note that Gerber’s paper was published 18 years before that of Einstein. Gerber’s formula for the anomaly was exactly that which later appeared in Einstein’s paper. Gerber’s paper was entitled: ‘The Space and Time Propagation of Gravitation’ and, though not published until after Gerber’s decease, a second paper repeating and expanding on Gerber’s analysis appeared in January 1917 in Gerber’s name in the same German scientific periodical: Ann. d. Phys. in which Einstein’s 1916 paper had appeared. It was obvious that there was concern that Gerber’s contribution had been ignored and there was then onward debate as Seelinger drew attention to a mathematical flaw in Gerber’s analysis. Oppenheim responded, stressing that the issue of finite speed was still open, but Seelinger reasserted his position to ensure that his arguments were not eroded by Oppenheim’s views. (See: Ann. d. Phys., 52, 415; 1917: 53, 31 & 163; 1917 and 54, 38; 1917).

That debate revealed the difficulties of picturing how gravitational action asserts a retarded effect, given that one can hardly expect the flow of energy to be along a pencil thin line drawn between Sun and planet and given that point above that one is not even sure where the energy that is fed to the planet is seated before it sets off on that journey. However, one can be certain that somehow the speed of light is a governing factor and that what was needed was the proper interpretation of that observed 43 arc-second value to gain insight into the physical action.

(...)

The Way Forward

To reach a position on common ground with that of physicists familiar with Einstein’s theory I will proceed by making an assumption and I will show how this leads directly to the formulation of Einstein’s law of gravitation. This should be seen as verification of that assumption. Then I will show by separate aether-based theory that the formulation governing light ray deflection arises from the effect of gravity upon the refractive index of the aether. The inference is that, whereas Einstein’s theory explains the perihelion anomaly and light ray deflection by the same modification of the Newton’s law of gravitation, the physics of gravitation requires two separate theoretical foundations for these two phenomena, because there is no analogy between planetary mass and the electromagnetic wave.
I note, however, that before leaving this chapter I will discuss the fascinating topic of whether gravity is an electrodynamic phenomenon, as assumed so far by those who seek a unified field theory, or an electrostatic phenomenon as implied earlier in this work.

(...)

[End of Chapter Footnote]

(...)
All I say is that the speed of gravity, meaning energy in transit owing to change of relative position of Sun and planet does travel at speed c, but, as to the effect Jupiter has on the deflection of the signals we receive from
a quasar, this concerns energy deployment as between Jupiter and the aether through which those signals travel and, whatever the answer, I cannot see how Einstein’s theory could thereby be proved.

in The Law of Gravity (Chapter 5), The Physics of Creation, 2003

Cheers.
P.S.: I'm aware my written English is still far from perfect

publius · #7 (**permalink**) 29-March-2007, 06:17 AM

Quote:

Originally Posted by tusenfem

I am not sure, but has it not been shown that there cannot be a retardation in gravitiation? IIRC in that case the whole solar system would be unstable, and we would not be here.

Glad I stumbled across this thread. We've had several discussion here about the "speed of gravity". Search for threads with "Carlip" in them, and you should find them.

Gravitational field changes do propagate at 'c'. However, GR gravity does a much better job than EM of "hiding" that propagation delay. Like with EM, radiation can be seen as the result of propagation delay, and the quadropole nature of gravitational radiation indicates it "extrapolates" acceleration as well as velocity. In GR gravity, that goes as (v/c)^5 (among other ways to put it), while in EM it is (v/c)^3. Two orders of magnitude difference.

IOW, gravity will only "miss" due to changes in acceleration, not due to changes in velocity as EM does. The gravitational radiation of the earth in orbit about the sun is a mere 300W total power.

-Richard

Tassel · #8 (**permalink**) 29-March-2007, 02:15 PM

I have a question, nutant. The much discussed Pioneer acceleration (-8E-10 m/s^2) is actually the differential between what we expect the acceleration to be and what is observed. Using your variable G idea, how do I calculate the acceleration due to the sun's gravity on objects at various locations in the solar system?

nutant gene 71 · #9 (**permalink**) 29-March-2007, 04:37 PM

Quote:

Originally Posted by Tassel

I have a question, nutant. The much discussed Pioneer acceleration (-8E-10 m/s^2) is actually the differential between what we expect the acceleration to be and what is observed. Using your variable G idea, how do I calculate the acceleration due to the sun's gravity on objects at various locations in the solar system?

Good question Tassel, but it might be better asked on the Q&A forums, where someone with better math and astronomy skills might answer that. It seems Turyshev et al calculated this small difference in acceleration towards the Sun, based upon what expected acceleration should be at any given point in the Pioneer's exit path. Q&A might better offer the answer to that.

What the MOND version for our solar system seems to indicate, using Milgrom's modification, is that there is a similar smaller effect at work here, within the solar system, that mimics the effect computed for how the outer galaxy spins. The equations above are only meant to show how this might work. My concern is with the math, that perhaps the equations are not right, so I play my own 'devil's advocate' in what this solar version of MOND seems to show. Any thoughts on how it could be falsifiably proven or disproven, or where the math is wrong? Thanks.

Nereid · #10 (**permalink**) 29-March-2007, 04:49 PM

Aren't the ATM ideas presented by nutant gene 71 and Utad3 quite different? Sure they refer to the Pioneer anomaly, but propose quite incompatible explanations, don't they?

If so, then there should be two ATM threads.

If not, can someone please demonstrate how the two are compatible?

Tassel · #11 (**permalink**) 29-March-2007, 05:11 PM

Quote:

Originally Posted by nutant gene 71

Good question Tassel, but it might be better asked on the Q&A forums, where someone with better math and astronomy skills might answer that.

I know how to calculate it using standard Newtonian physics. My question doesn't necessarily have anything to do with Pioneer. I'm just asking how to calculate acceleration due to gravity using your variable G idea.

nutant gene 71 · #12 (**permalink**) 29-March-2007, 05:13 PM

Utad3, in Aspden’s paper in the ‘Debate’ he says:

Quote:

As to the basic orbital component of circular motion, the radius is determined by a balance of centrifugal force and the force of gravity. The balance is an unchanging quantity and if ‘gravity has a speed’ is this something that was only a factor when the solar system was first created or is it somehow something that affects the planet’s motion on an ongoing basis?

This may also refer to Tassel’s question on orbital “acceleration due to the sun's gravity on objects at various locations in the solar system”, where the planets found their ‘balanced’ locations based upon the gravitational potential from the Sun and their relative velocities in orbit. Then, whether this gravity potential is a ‘fixed’ constant force, or is it traversing space at some ‘velocity’, is a question to which some have answered satisfactorily with Mercury’s perihelion advance, that there seems to be a ‘retardation’ effect. Does this explain the Pioneer Anomaly? Does this hypothesized retardation of gravity velocity account for what appears to be a MOND effect within our solar system? I don’t know the answer to that. OTOH, does a variation in inertial mass, as suggested by what MOND seems to infer, explain anything about the planetary orbits? Probably not, if the planets are ‘balanced’ to remain within their orbits. We do not see any evidence from our calculations of planetary orbital mass, having assumed a universal constant G, so whatever anomalous behavior their orbits would exhibit is ‘hidden’ within the balanced locations they found. Perhaps when the solar system was still in its infancy and orbits not yet fixed, there would have been evidence of whether or not there is a gravity retardation effect, but we can’t turn off gravity to check, so we can’t prove what we hypothesized. The only clue that something might be amiss, if it is amiss, is that the planetary mass and atmospheric densities may not match up with what a non-MOND effect would predict. This might account for the gas giants atmospheres, or some of their moons’s atmospheres, being as thick as they are. Also, comets with highly elliptical orbits might offer some clues, though I don’t think anyone had ever found any. So whether gravity force potential is nearly instantaneous or at some velocity, whether or not greater than c, is still an unresolved issue, IMO.

nutant gene 71 · #13 (**permalink**) 29-March-2007, 05:17 PM

Quote:

Originally Posted by Nereid

Aren't the ATM ideas presented by nutant gene 71 and Utad3 quite different? Sure they refer to the Pioneer anomaly, but propose quite incompatible explanations, don't they?

If so, then there should be two ATM threads.

If not, can someone please demonstrate how the two are compatible?

Right, I think the two topics are only indirectly related to the Pioneer Anomaly, rather than to the possible MOND effect within our solar system. The point of compatibility seems to be that some effect is responsible, possibly, for both effects. As to whether or not this effect is from gravational 'retardation' or from some other source, we at this point don't know, except that perhaps Pioneers offer a clue. Glad to leave it on the table, if anyone else has an idea they want to put forward. Thanks.

nutant gene 71 · #14 (**permalink**) 29-March-2007, 05:19 PM

Quote:

Originally Posted by Tassel

I know how to calculate it using standard Newtonian physics. My question doesn't necessarily have anything to do with Pioneer. I'm just asking how to calculate acceleration due to gravity using your variable G idea.

The 'variable G' idea does not affect planetary orbital behavior, from my perspective, though it does affect 'exit path' behavior of any body traveling out of the solar system, from my understanding. The two are not related. Thanks.

Tassel · #15 (**permalink**) 29-March-2007, 05:52 PM

Quote:

Originally Posted by nutant gene 71

The 'variable G' idea does not affect planetary orbital behavior, from my perspective, though it does affect 'exit path' behavior of any body traveling out of the solar system, from my understanding. The two are not related.

That's quite a claim. But it doesn't answer my question. Actually, it prompts me to add another question.

Now I want to know how to calculate acceleration due to gravity using your idea, and I want to know why there would be a difference between the acceleration felt by an object in orbit versus an object on an escape trajectory. I would imagine both of these could be answered with some math demonstrating your idea.

nutant gene 71 · #16 (**permalink**) 29-March-2007, 06:01 PM

Quote:

Originally Posted by Tassel

That's quite a claim. But it doesn't answer my question. Actually, it prompts me to add another question.

Now I want to know how to calculate acceleration due to gravity using your idea, and I want to know why there would be a difference between the acceleration felt by an object in orbit versus an object on an escape trajectory. I would imagine both of these could be answered with some math demonstrating your idea.

Sorry, but I can't answer that. To pursue this further is to throw this thread off topic, so not in interest to do that. I do not see how a 'balanced' planetary orbit is related to a 'retardation' effect for escape trajectory. Unless you can demonstrate how the two are related, I think your question should defer to Q&A forum. Or else if someone else can answer it here on ATM, with Mods' appproval, I think it's OT.

You might ask this question on the Q&A discussion at: Testing MOND in our solar system , where I think it would be more appropriate.

Tassel · #17 (**permalink**) 29-March-2007, 07:46 PM

Quote:

Originally Posted by nutant gene 71

Sorry, but I can't answer that. To pursue this further is to throw this thread off topic, so not in interest to do that. I do not see how a 'balanced' planetary orbit is related to a 'retardation' effect for escape trajectory.

How is my question off topic? You presented a potential mathematical model of the Pioneer anomaly that appears to be a combination of your variable G idea, and a...modified version of MOND (Double Modified Newtonian Dynamics perhaps?

).

In any case, your variable G idea is presented in the original post, and you are using it as part of the foundation for your proposed mathematical modeling of the Pioneer anomaly. It's perfectly fair for me to ask a question about it.

nutant gene 71 · #18 (**permalink**) 29-March-2007, 08:13 PM

Quote:

Originally Posted by Tassel

How is my question off topic? You presented a potential mathematical model of the Pioneer anomaly that appears to be a combination of your variable G idea, and a...modified version of MOND (Double Modified Newtonian Dynamics perhaps?

).

In any case, your variable G idea is presented in the original post, and you are using it as part of the foundation for your proposed mathematical modeling of the Pioneer anomaly. It's perfectly fair for me to ask a question about it.

Well, you can ask any question you think fair, but there may not be a meaningful answer here, so why I suggested you ask it at Q&A instead.

Here is an article that forcusses more on the MOND conundrum, both as a 'gravitational' and 'inertial' modification of Newton's laws. The test proposed to measure for this anomaly is interesting, since it can be performed on Earth at the time of Equinox. The proposal to run the same test at the La Grange points between Earth and Moon is also interesting, but perhaps too expensive to do anytime soon. Nevertheless, the results of such tests would be of note, since they would lend empirical credibility to MOND within our solar system, if the results proved positive. See this current NewScientist: Equinox challenge to Newton's law. I think this brings it back on topic. Thanks.

Tassel · #19 (**permalink**) 29-March-2007, 08:30 PM

But...I'm not asking a question about MOND. There are plenty of resources available to answer just about any question I may have about MOND. I'm asking a question about your variable G idea.

nutant gene 71 · #20 (**permalink**) 29-March-2007, 08:37 PM

Tassel, I answered your initial question here, where I said:

Quote:

The 'variable G' idea does not affect planetary orbital behavior, from my perspective, though it does affect 'exit path' behavior of any body traveling out of the solar system, from my understanding. The two are not related.

Sorry if this is not acceptable to you, but I have no further answer to this.

Tassel · #21 (**permalink**) 29-March-2007, 09:25 PM

Quote:

Originally Posted by nutant gene 71

Tassel, I answered your initial question here, where I said: Sorry if this is not acceptable to you, but I have no further answer to this.

In Newtonian physics, acceleration due to gravity is calculated like so:

a = GM/r^2

My initial question asked for an example of how this is done under your variable G idea. Are you saying that you cannot produce "a" with your idea?

nutant gene 71 · #22 (**permalink**) 29-March-2007, 10:10 PM

Quote:

Originally Posted by Tassel

In Newtonian physics, acceleration due to gravity is calculated like so:

a = GM/r^2

My initial question asked for an example of how this is done under your variable G idea. Are you saying that you cannot produce "a" with your idea?

Remember I addressed it above with this:

Quote:

Mordehai Milgrom’s MOND solution was to factor in an acceleration force, F = ma^2/ a_o, which translates using F = GMm/ r^2, into a = (GM a_o/ r^2)^1/2, where Milgrom calculated the value for a_0=1.2×10^−10 ms^−2 empirically. This does not invalidate Newton’s constant G, but it does indicate that over great astronomical distances, force from gravity may have a modifier in it.

The 'modifier' I'm refering to here is 'netted out' in stable orbits, so not visible in normally balanced planetary orbits, regardless of what happens to G. For this reason, I cannot answer your question, since there is no effect on 'balanced' orbits for planets or other bodies. The exception could be very elliptical comets, but no such variance from expected orbital behaviors had been observed to date. So to pursue yours further, and this is becoming something of a repeat again, does not address the original question on this thread, as to whether or not the math presented is correct. Do you see a problem with the above math? If there is, I'd like to know, the reason for this ATM.

As an aside, I used a variable G idea in the equation to demonstrate how it 'might' hypothetically affect MOND in our solar system. However, the variable G idea is a 'strawman' here, not the main issue. The real issue is whether or not Milgrom's MOND can apply not only to outer galaxy rotations, but also to our solar system. However, if you have some examples of how you think this might apply to stable planetary orbits, I'd like to see it. Does our calculation for any planet's orbital mass get affected by a 'hypothetical' variable G, for example? If so, how would it impact the orbital behavior, to show something different from what we see now? Remember, we calculated everything at a distance using Newtonian laws. So how would Newton's laws change planetary behaviors if G were not the universal constant now assumed? How would it impact Milgrom's MOND acceleration a_0? I think this would be more on topic.

Cheers.

Tassel · #23 (**permalink**) 29-March-2007, 11:11 PM

Quote:

Originally Posted by nutant gene 71

Remember I addressed it above with this: [a = (GM a_o/ r^2)^1/2]

Excellent. I assume the above equation is the one you were referring to as having addressed my question. Now, according to your idea, what value should I plug in for "G" in the above equation at various points in the solar system in order to determine "a"?

dgavin · #24 (**permalink**) 30-March-2007, 02:13 AM

http://www.bautforum.com/showpost.php?p=959143&postcount=2

nutant gene 71 · #25 (**permalink**) 30-March-2007, 02:47 AM

Quote:

Originally Posted by Tassel

Excellent. I assume the above equation is the one you were referring to as having addressed my question. Now, according to your idea, what value should I plug in for "G" in the above equation at various points in the solar system in order to determine "a"?

Yes, that's the one. G is the same as Newton's G, viz. ~6.67E-11 m^3 kg^-1 s^-2. What I changed was the AUn function, which is a multiplier for distance r, so that at 9.5AU, the AUn=9.5, for example. I did not change the G constant here. On Earth, for example, AUn=1. Remember that I balanced this equation above and below by factoring in G times AUn for each distance of r. What remains is a constant value for a_0, viz. ~1.09E-16 m/s^2.

nutant gene 71 · #26 (**permalink**) 30-March-2007, 02:53 AM

Quote:

Originally Posted by dgavin

This could quite eaisly explain the pioneer anomoly, as the further away from the the solar system they get, the more the gravitational waves from increased number of solar system bodies are intersecting in the mergering fasion then the destructive fasion.

This effect might also explain some percentage of the missing mass gravity(dark matter) that galaxy's, and the universe itself have.

Neat idea, though I suspect the gravitational forces here are not wavelike, but rather aggregated into a whole force. However, has it been calculated that the total gravitational mass of the Sun and planets together actually translates into the Pioneer Anomaly? I suspect not, since the anomalous acceleration towards the Sun was already noticed at about Saturn, where there were still another couple of massive planets beyond, not counting the now non-planet Pluto. Also, the anomaly seems to be constant, whereas what you suggest might have shown up as a variable, I suspect. However, the MOND modified acceleration works out as a constant, as I showed above. Still, worth considering... Thanks.

dgavin · #27 (**permalink**) 30-March-2007, 05:03 AM

http://www.bautforum.com/showthread....141#post959141

dgavin · #28 (**permalink**) 30-March-2007, 05:28 AM

To save the moderators some trouble, i'm going to split my idea off to a new thread as it's really not related to MOND.

czeslaw · #29 (**permalink**) 30-March-2007, 09:11 AM

Quote:

Originally Posted by nutant gene 71

Neat idea, though I suspect the gravitational forces here are not wavelike, but rather aggregated into a whole force. However, has it been calculated that the total gravitational mass of the Sun and planets together actually translates into the Pioneer Anomaly? I suspect not, since the anomalous acceleration towards the Sun was already noticed at about Saturn, where there were still another couple of massive planets beyond, not counting the now non-planet Pluto. Also, the anomaly seems to be constant, whereas what you suggest might have shown up as a variable, I suspect. However, the MOND modified acceleration works out as a constant, as I showed above. Still, worth considering... Thanks.

The anomaly seems to be constant like in MOND picture. The MOND does not explains the anomaly but we observe this constant anomaly on cosmic scale.
If the gravitational field is a substance (vacuum energy of the virtual particles) it may behave like a wave

In my idea are there tiny inwards oscillation of the field according to the mass and it causes the Gravitation. The field has its relativistic mass and it causes additional curvature of the space.

It is a constant anomaly like in MOND but not always. If there is a fast moving heavy object its gravitational field might be distorted on cosmic scale.
The gravitational field of the distant galaxy clusters is distorted in cosmic filament. The virtual particles of the gravitational field are not uniform in the space. They are pulled by galaxy cluster and cosmic void is realy almost empty. In cosmic void is the gravitational field very weak. This distorts an image of the Universe structure.

In the galaxy cluster is more gravitational field and more relativistoc energy than it would be in an uniform Universe.

nutant gene 71 · #30 (**permalink**) 30-March-2007, 07:37 PM

Quote:

Originally Posted by czeslaw

The anomaly seems to be constant like in MOND picture. The MOND does not explains the anomaly but we observe this constant anomaly on cosmic scale.

Once upon a time there was a discussion on ATM here where the cosmic scale was redefined as a variable mass, in particular the 'inertial mass' as responsible for what MOND may account for. However, that discussion was dropped, since there was no way to prove any of it without actually measuring for such change deep in space or the outer solar system. This new MOND for our solar system is not in the same vein, but rather looks at the solar system scale, closer to home.

Quote:

If the gravitational field is a substance (vacuum energy of the virtual particles) it may behave like a wave

I believe this is more in line with a Quantum Gravity idea, though such waves are yet to be detected. The Quantum vacuum appears to have energy locked in it, such as Wiki describes here: Vacuum Energy , and others like Rueda & Haisch worked on Zero-point energy, but this is still work in its infancy, IMO. However, this may point to what you say in yours:

Quote:

In my idea are there tiny inwards oscillation of the field according to the mass and it causes the Gravitation. The field has its relativistic mass and it causes additional curvature of the space.

On your last:

Quote:

It is a constant anomaly like in MOND but not always. If there is a fast moving heavy object its gravitational field might be distorted on cosmic scale.
The gravitational field of the distant galaxy clusters is distorted in cosmic filament. The virtual particles of the gravitational field are not uniform in the space. They are pulled by galaxy cluster and cosmic void is realy almost empty. In cosmic void is the gravitational field very weak. This distorts an image of the Universe structure.

In the galaxy cluster is more gravitational field and more relativistoc energy than it would be in an uniform Universe.

I suspect in your "in an uniform Universe" there is an implied unity of energy budget that is universal in scale. For example, just a thought to not go too far off topic, if we imagine that both vacuum energy and gravity energy are part and parcel fo the same energy budget, then together they represent a factor of one, so that if one is displaced the other is enhanced. Let's say a fast moving mass travels through this vacuum energy, then it may tap into the gravity side of the energy budget, which may be what happens to Pioneers as they travel farther and farther from our solar system into the deep space vacuum 'energy budget'. In effect, what it implies is that if there is more 'hot' energy around, such as generated by stars and galaxies, then there is more of that vacuum energy budget around, but less gravity energy, to balance out. But conversely, if there is less hot energy, such as on the edge of our solar system, or at the galaxy outer arms, then there is more gravity energy in the budget, with less vacuum energy to balance out. I don't know how to test for this, since at this time we cannot test for 'vacuum energy' in the outer solar system. But we can test for 'inertial mass' in the energy budget, to see if it is different at the solar system's edge versus here, to see how it balances out. The MOND idea then becomes, if this were true, that a_0 is the factor that accounts for where we are in the total energy budget, balancing out 'hot energy' in the vacuum energy budget with 'gravity energy' in that same budget. Just a thought, really a muse, but thought to mention it, because it's fun.

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