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borman
2011-Feb-14, 06:12 AM
Coincidence suggests connection between anomalous secular trends

Krasinsky and Brumberg report a secular increase in the Astronomical Unit of 15cm/yr + or – 4cm. The AU is about 1.49 X 10^11 m. So, over a revolution of one orbital period, the fractional addition due to the anomaly is 1 yr X d(AU)/dt/AU, as an approximation ranging from 1.275 down to .738 X 10^-12

Williams & Boggs report a secular trend of about 3.5 mm/yr + or - 1.2 mm in the moon’s eccentricity. The semi-major axis distance to the moon is about 384,399 km. So, over a revolution of one orbital period of one month or 1/12 yr, the fractional addition due to the anomaly ranges from 1.019 down to .499 X 10^-12.

Within errors these numbers represent a possible coincidence where various families of theories that look for a uniform cause for both anomalies may find support.

An example is the 2009 Li and Chang paper considering a constant space deformation parameter within a special Finsler structure.

Of possible note is that systematic associated with time delay inside electronics of orbiters returning a signal is not a significant contribution of error in regard to LLR off a mirror on the moon.


Astrometric Solar-System Anomalies
http://arxiv.org/abs/0907.2469

Kinematics in Randers-Finsler geometry
And secular increase of the astronomical unit
http://arxiv.org/abs/0911.1890

Ken G
2011-Feb-14, 04:35 PM
One must of course first eliminate the possibility of coincidence. What about GPS satellites? Surely their orbits are also known to that kind of accuracy. Also, at the level of 1 part in 1012, have we really made contact with new physics, or do we first make contact with limitations in the assumptions of the old physics? (Neglect of gravitational perturbations from other bodies, assumptions of spherical symmetry of the objects, general relativistic effects from rotation or maybe even differential rotation, etc.). It's just not clear to me that these systems are "clean" enough, nor is the effect widespread enough, to warrant a search for new physics based on this-- other than the basic human desire to see every opportunity as a window to new physics.

baric
2011-Feb-14, 05:16 PM
How do they measure the increase in the AU?

borman
2011-Feb-16, 04:28 AM
The putative anomalies only could be noticed with confidence after improved instrumentation became available that allowed more precise measurements. Basically the measurements are all radiometric using Landers on Mars as well as orbiters and signals bounced off the surface. Soon we will have data from CASSINI and later from MESSENGER. Some of these craft have older electronics in them which may introduce a small systematic latency in signal return which could be interpreted as a portion of the AU increase. The moon just has a mirror though, so its signal could be considered freer of this systematic.

Finding a theory that can reproduce a physical secular signal consistent with observations remains an open challenge. Recently, Iorio put a paper on the arXiv regarding the LLR anomaly that looked not only to the mainstream theory of General Relativity for effects including oblate ness and frame dragging, but also over 30 alternative or exotic theories. None of them could reproduce the anomaly to the observed magnitude.

The Li and Chang idea doesn’t so much consider the anomaly as a true physical signal but more like a “Riemannian Illusion” where the observed secular trends would vary for each planet being more noticeable the more deeper into the gravity well it is measured. Mercury would be almost 50% higher than Earth. Because of this feature, it may be possible to test their hypothesis locally. The equation for R-dot is fairly straightforward where the square of the local space deformation parameter is 4/3 10^-12. This is multiplied by ¾ R/T in meters and years.

For a craft in geostationary orbit, R is approximately 42,164 km and T is one sidereal day. This creates the “illusion” of R-dot of approximately 15.39 mm/yr. The delta t of additional round trip delay per year is 1.026 X 10^-10 sec or 0.281 trillionth of a second per day. The precision of the newer quantum atomic clocks may be able to measure this fine scale.

'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise

http://www.nist.gov/pml/div688/logicclock_020410.cfm

On the anomalous secular increase of the eccentricity of the orbit of the Moon
http://arxiv.org/abs/1102.0212

baric
2011-Feb-16, 03:00 PM
The putative anomalies only could be noticed with confidence after improved instrumentation became available that allowed more precise measurements. Basically the measurements are all radiometric using Landers on Mars as well as orbiters and signals bounced off the surface. Soon we will have data from CASSINI and later from MESSENGER. Some of these craft have older electronics in them which may introduce a small systematic latency in signal return which could be interpreted as a portion of the AU increase. The moon just has a mirror though, so its signal could be considered freer of this systematic.


How is the position of Mars used to measure an AU? Are they inferring it indirectly by the Mars-Earth distances at various points in their orbits?

I guess I originally assumed that the AU was being measured from Earth to Sun and wondered how they could deal with the uncertainties of the photosphere, which also could be expanding.

Hornblower
2011-Feb-16, 11:28 PM
How is the position of Mars used to measure an AU? Are they inferring it indirectly by the Mars-Earth distances at various points in their orbits?

I guess I originally assumed that the AU was being measured from Earth to Sun and wondered how they could deal with the uncertainties of the photosphere, which also could be expanding.As far as I know there is no means of getting any kind of radar echo off of the Sun directly. It is the telemetry from various spacecraft that has enabled super precise measurements of the planetary orbits.

dtilque
2011-Feb-17, 07:40 AM
Krasinsky and Brumberg report a secular increase in the Astronomical Unit of 15cm/yr + or – 4cm. The AU is about 1.49 X 10^11 m. So, over a revolution of one orbital period, the fractional addition due to the anomaly is 1 yr X d(AU)/dt/AU, as an approximation ranging from 1.275 down to .738 X 10^-12

The most likely explanation for this is tidal drag: Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law (http://arxiv.org/abs/0905.3008)

As is well known, this is the same mechanism for the Moon retreating from the Earth. I wouldn't expect it to change the eccentricity of the Moon, though.

borman
2011-Feb-19, 11:35 PM
How is the position of Mars used to measure an AU? Are they inferring it indirectly by the Mars-Earth distances at various points in their orbits?

I guess I originally assumed that the AU was being measured from Earth to Sun and wondered how they could deal with the uncertainties of the photosphere, which also could be expanding.

Some information regarding telemetry can be found at the Wiki site, http://en.wikipedia.org/wiki/Astronomical_unit
Note the increased accuracy from 1976 to 2009.

In a paper by Arakida that explored whether dark matter density could account for the signal, he stated that the 15 cm/yr was one hundred times the error determination. However the needed dark matter density would need to be that of water to cause the signal delay.

It should be remembered that the evaluation of the d(AU)/dt is not based on a tape measure to the sun or a planet, but the round trip light signal.

Lammerzahl was able to rule out Dark Energy or cosmic expansion, dot G/G and dot c/c as putative causes. Clock drift was still not ruled out at the time of the paper. Orbital expansion is not ruled in as ephemeris do not readily collaborate this.

I have not yet found a paper that investigated whether a secular change in the (Vera) Rubin speed that preserves orbital radius and the coincidence could account for d(AU)/dt.

Is the physics within the Solar system really understood?
http://arxiv.org/abs/gr-qc/0604052

Influence of Dark Matter on Light Propagation in Solar System
http://arxiv.org/abs/0810.2827

borman
2011-Feb-20, 12:14 AM
The most likely explanation for this is tidal drag: Secular increase of the Astronomical Unit: a possible explanation in terms of the total angular momentum conservation law (http://arxiv.org/abs/0905.3008)

As is well known, this is the same mechanism for the Moon retreating from the Earth. I wouldn't expect it to change the eccentricity of the Moon, though.


The Miura et al paper considers the anomaly as physical, so there would need to be collaborating evidence from ephemeris for example. When we get data from Cassini, we can see if tidal exchange applies to Saturn as well or if it is only an inner solar system observable form mass loss due to radiation and wind.

Unlike the earth and moon where the rotation is determined by noting the rocky surface rather than noting the speed of clouds, the rotation rate of the sun is not that well constrained. The speed of the photosphere varies depending on latitude monitored.

Chang and Li mentioned the paper but thought it will need more work than the introductory paper.

Perhaps an approach that tries to improve constraints using multiple and simultaneous constraints that try not to use the sun directly but would clue in that the sun was involved without requiring knowledge of its rotation rate might improve the hypothesis. For instance, Jupiter raises tides on the sun and these might contribute a small percentage to the Earth’s putative AU drift in the manner suggested by Miura et al to support their mechanism.

A recent paper by Iorio using an extended data set that constrained a once putative anomaly in Saturn’s perihelion advance to within error bars, used multiple simultaneous constraints to greatly improve constraints on Milgrom’s External Field Effect from Milgrom’s initial .01 to .3 down to .01 to .04. These methods can assist in seeing if they are on path that has better merit.

Constraints on the location of a putative distant massive body in the Solar System and on the External Field Effect of MOND from recent planetary data

http://arxiv.org/abs/1101.2634

astromark
2011-Feb-20, 12:24 AM
When we are making fine measurements of the distances to objects that are thousands of km away. No that's hundreds of thousands of km away. I do not see 15cm as any way significant. Its less than the margin of error... The distance to a gaseous fire ball is 149 million km... how can you be so precise to a ball of gas... with a boiling surface heaving and convulsing a lot more than 15cm... I can understand a error of hundreds of km. Not 15cm.
No gentleman, please stop indulging the whim of some over educated pounce... Go get a real job...

and No. I will not apologise and withdraw that.. It is a real and obvious conclusion of what I see as a load of rubbish.
These fellows and their paper are little more than a excuse for more funding... For them, I feel sorry.
Am I really being too hard... or just real. ?
Look at what 'borman' has said.. 'dtilque','Hornblower'.. 'Ken' asks of new physics ?
There is something wrong with this whole idea. Than I can throw mud at.

borman
2011-Feb-20, 12:41 AM
Your critisism was valid in 1964.

Hornblower
2011-Feb-20, 02:49 AM
When we are making fine measurements of the distances to objects that are thousands of km away. No that's hundreds of thousands of km away. I do not see 15cm as any way significant. Its less than the margin of error... The distance to a gaseous fire ball is 149 million km... how can you be so precise to a ball of gas... with a boiling surface heaving and convulsing a lot more than 15cm... I can understand a error of hundreds of km. Not 15cm.
No gentleman, please stop indulging the whim of some over educated pounce... Go get a real job...

and No. I will not apologise and withdraw that.. It is a real and obvious conclusion of what I see as a load of rubbish.
These fellows and their paper are little more than a excuse for more funding... For them, I feel sorry.
Am I really being too hard... or just real. ?
Look at what 'borman' has said.. 'dtilque','Hornblower'.. 'Ken' asks of new physics ?
There is something wrong with this whole idea. Than I can throw mud at.

In my opinion, to categorically dismiss the quest for such precision as rubbish is a bum rap.

Of course we do not attempt a direct measurement of the distance to the photosphere, and if I am not mistaken we never have done so. We measure the distances to the planets and calculate the size of Earth's orbit from those measurements. With active spacecraft on the surface of Mars and in orbit around it and other planets, we can get enormously improved precision from the telemetry, compared with what we formerly did by optical means and more recently with radar echoes from the inner planets. We should be able to infer the annual 15cm increase in Earths mean semimajor axis from secular changes in the relative motions over the past 40 years. Even if a single measurement cannot get the necessary precision by itself, the averaging of zillions of measurements over those 40 years can greatly reduce the uncertainty of the overall pattern.

baric
2011-Feb-20, 03:06 AM
Your critisism was valid in 1964.

ok, regardless of the validity (or lack thereof) in Astromark's objections, I have to admit that was a funny comeback. :P

Jerry
2011-Feb-20, 11:14 AM
One must of course first eliminate the possibility of coincidence. What about GPS satellites? Surely their orbits are also known to that kind of accuracy. Also, at the level of 1 part in 1012,

Nope. There is an anomaly, apparently periodic. GPS re-syncs on Earth-time and using Earth-based stations. The residuals are small and could be, for example, temperature variations.


... It's just not clear to me that these systems are "clean" enough, nor is the effect widespread enough, to warrant a search for new physics based on this-- other than the basic human desire to see every opportunity as a window to new physics.

I wish the 'old physics' were comprehensive, that is, internally consistent.

grapes
2011-Feb-20, 12:37 PM
Coincidence suggests connection between anomalous secular trends

Krasinsky and Brumberg report a secular increase in the Astronomical Unit of 15cm/yr + or – 4cm. The AU is about 1.49 X 10^11 m. So, over a revolution of one orbital period, the fractional addition due to the anomaly is 1 yr X d(AU)/dt/AU, as an approximation ranging from 1.275 down to .738 X 10^-12

Williams & Boggs report a secular trend of about 3.5 mm/yr + or - 1.2 mm in the moon’s eccentricity. The semi-major axis distance to the moon is about 384,399 km. So, over a revolution of one orbital period of one month or 1/12 yr, the fractional addition due to the anomaly ranges from 1.019 down to .499 X 10^-12.

Within errors these numbers represent a possible coincidence where various families of theories that look for a uniform cause for both anomalies may find support. Yahbut, one is calculated on a per year basis, the other on a per month basis. If you're going to look for a uniform cause across the solar system, shouldn't it be the same amount of time?
It should be remembered that the evaluation of the d(AU)/dt is not based on a tape measure to the sun or a planet,I always have trouble with that one! :)


I wish the 'old physics' were comprehensive, that is, internally consistent.Comprehensive means internally consistent?

astromark
2011-Feb-21, 12:10 AM
Oops... I would seem I was in conflict with a bunch of rules... and that I may have offended some body...
Well believe it or not. I never did intend that. and now have had time to think about my view and the way I expressed it...
I was wrong... and should try not to call people names...:razz: but am pleased to have amused some.
I would take back what I said but not what I meant. As I still claim that 15cm is not worth arguing about...
and as I am not the brightest candle on the cake...would someone tell me what the 1964 remark is about ?
and NO... I am not offended and wont be. Mumbling into the distance..."I must not be taken seriously... I must not be taken seriously..." and how did they know my age....

borman
2011-Feb-22, 01:39 AM
Yahbut, one is calculated on a per year basis, the other on a per month basis. If you're going to look for a uniform cause across the solar system, shouldn't it be the same amount of time?

To put them on the same time scale of 1 yr, that is why the factor of 1/12 yr is included or else the coincidence would be off by an order of magnitude. AFAIK, Chang and Li essentially discovered the coincidence when they postdicted the LLR anomaly using the same space deformation constant for both LLR and d(AU)/dt. Since they did not write a separate paper for the LLR anomaly, but just added a paragraph to the AU paper to test their hypothesis, the coincidence may not be generally known from the paper title unless one reads the whole abstract.

The tape measure comment is to underscore that it is the time of the light signal round trip that is the essential data. Whatever can cause a delay in that time signal is a suspect for the anomaly. It might be an increase in the length of the AU, an artifact of Finsler geometry, clock drift, callibration issues, or something we have not thought of yet. The coincidence, if it is not serendipitous, might allow one to constrain the error budget.

Suppose that callibration issues (Arakida) add to increase the actual anomaly slightly. Note that while the values overlap, it is not exact. The slightly higher value center for the AU could be due to callibration issues that would be absent from the LLR value because a laser is bounced off a mirror and so callibration issues are minimized if not altogether absent leaving the LLR result as being somewhat "cleaner" than the AU value.

borman
2011-Feb-22, 01:48 AM
Astromark,

At one time we did not have the precise instruments and clocks that we have now. There then would not be sufficient sigma at that time then for a theorist to wirte on the topic. Arakida states that we can now measure one hundred times more accurate than 15cm/yr. The signal is a hundred times larger than the measuring error. This is sufficient sigma to warrant their time to investigate.

astromark
2011-Feb-22, 01:54 AM
Thank you Borman.. just what I needed.

borman
2011-Feb-22, 02:03 AM
Jerry,
Do you have a cite for which GPS anomaly you are refering to? There are a few of them.
Thanks

grapes
2011-Feb-22, 03:59 AM
To put them on the same time scale of 1 yr, that is why the factor of 1/12 yr is included or else the coincidence would be off by an order of magnitude. That's why I am asking. It looks to me like they are not on the same time scale, that one is computed on a per month basis, and the other on a per year basis. And when you compute them both on a per year basis (instead of a per revolution basis), they do differ by an order of magnitude.

borman
2011-Feb-23, 11:15 PM
That's why I am asking. It looks to me like they are not on the same time scale, that one is computed on a per month basis, and the other on a per year basis. And when you compute them both on a per year basis (instead of a per revolution basis), they do differ by an order of magnitude.

Another theorist notes the coincidence

Today, on the arXiv, Iorio makes a suggestion that empirically may explain the coincidence:

Empirical explanation of the anomalous increases of the astronomical unit and of the lunar eccentricity

http://arxiv.org/abs/1102.4572

I will read the paper in more detail as time allows.

Note that the Boggs number is about 3.5 mm/yr which is about 0.3 mm/ revolution. The reason for considering revolutions has to do with one of Kepler’s Laws regarding equal area swept out by equal times. When you multiply the period, T, by R-dot/R and compare the AU anomaly to the LLR anomaly, the value is unity within error which is a remarkable coincidence if the anomalies are unrelated.

borman
2011-Mar-15, 10:34 PM
New Arakida paper reaffirms AU increase is not caused by cosmological expansion. Such expansion falls 9 orders of magnitude too small to account for the AU anomaly.

Application of Time Transfer Function to McVittie Spacetime:
Gravitational Time Delay and Secular Increase in
Astronomical Unit

http://arxiv.org/abs/1103.2569

Gravitational time delay associated with Dark Matter density was also ruled out because the required density would be that of liquid water throughout the solar system.

grapes
2011-Mar-15, 11:44 PM
The reason for considering revolutions has to do with one of Kepler’s Laws regarding equal area swept out by equal times.What is that reason?
When you multiply the period, T, by R-dot/R and compare the AU anomaly to the LLR anomaly, the value is unity within error which is a remarkable coincidence if the anomalies are unrelated.T the period of revolution, R the radius, and R-dot is the change in R per unit time (not per revolution), correct?

borman
2011-Mar-16, 02:57 AM
FWIW, when I first did the calculation, I made the same mistake you make and got a factor of 12 difference. A month and year are not the same time interval.

grapes
2011-Mar-16, 05:44 AM
FWIW, when I first did the calculation, I made the same mistake you make and got a factor of 12 difference. A month and year are not the same time interval.I didn't make a mistake, I did that on purpose. :)

I used the same time interval for both calculations, because it seems reasonable that the expansion will be the same for the same time interval, but be different for different intervals. You said you had an explanation for why that is not the case? that involves Kepler's laws?

borman
2011-Mar-17, 03:39 AM
The answers to your questions can be found in equations 12-19 in the second reference of the first post. The equation 19 is the postdiction giving the LLR anomaly.

It may be possible to further test for validity of the deformation parameter idea by seeing if a postdicition can be made for Gravity Probe B anomalies assuming the magnitude can be sensed by Gravity Probe B’s measurements. They got the eidetic signal but were really hunting for the frame-dragging signal. It may have been that the anomalies drowned out the desired signal; sort of looking for a particular raindrop in a rainstorm.

If the Li and Chang signal should have been clearly present in the proper range but is not there, this would undermine their hypothesis. They have tried to extend their Finsler approach to other problems such as Dark Energy and recovering MOND. However they also went after the Pioneer Anomaly and since the deformation parameter is gravity well dependant, they postdict that the apparent acceleration is not constant which is contrary to observations over 40+AU. This postdiction bears a similarity to another 5 dimensional proposal by Gerrard and Sumner who also postdicted a non-constant Pioneer Anomaly.

Earth Flyby and Pioneer Anomalies
http://arxiv.org/abs/0807.3158

Debye entropic force and modified Newtonian dynamics
http://arxiv.org/abs/1005.1169

A possible scenario of the Pioneer anomaly in the framework of Finsler geometry
http://arxiv.org/abs/0909.3713

Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
http://arxiv.org/abs/0806.2184

grapes
2011-Mar-17, 08:42 PM
I used the same time interval for both calculations, because it seems reasonable that the expansion will be the same for the same time interval, but be different for different intervals. You said you had an explanation for why that is not the case? that involves Kepler's laws?
The answers to your questions can be found in equations 12-19 in the second reference of the first post.
OK, I spent several hours with that paper (http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.1890v1.pdf). It's interesting stuff, but bogus.

They derive (formula 17, p.7) lambda as the square root of 4/3 times R-dot times T divided by R, and hypothesize that it is constant.


\lambda = \sqrt{\frac{4 \dot{R}}{3 R}T}

There is no real justification for it. The paper mentions that it is not in accord with Kepler's second law (page 6). The only attempt to justify that it might be constant is from an analysis of their Table 1, but then only by ignoring the outer planets. Table 1 was generated by assuming R-dot constant (I was able to duplicate their table, all ten digits of each value), but that means that it assumes that T is proportional to R! Kepler's third law says it is not, but it will be close for the inner planets, especially when T is expressed in years, and R is in AUs. They apparently use the values for the inner planets to calculate a constant lambda, but I'm not clear on how they do that (the table has a steady increase in lambda).

They do a calculation for the moon based upon this result that is barely within the error, and conclude that they have supported their hypothesis. But had they used the value of lambda for Earth from Table 1, it would not have supported their hypothesis (actually, I don't agree with their calculation anyway, I get bigger (worse, for them) values, but I'm not going to look into it right now.*)

Ridiculous, it seems to me.


* OK I'm looking into it. If you assume their value of lambda (1.0776 x 10-6, p.7) and use their Table 1 values for Mercury (T=0.240840253 years, R=0.38709893 AU) and plug that into the formula mentioned above, formula 17, I get R-dot = 37.228 m/century which is greater than their value of 21.0 in Table 2 (p.9). My values are bigger than theirs by about the square root of pi.

Can somebody check my work?

Kinematics in Randers-Finsler geometry and secular increase of the astronomical unit (http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.1890v1.pdf), by Xin Li and Zhe Chang

borman
2011-Mar-18, 10:45 PM
The Gravity Probe B test of equation 17

Polar orbit of Semi major Axis of 7,027.4 km and orbital period of 97.65 minutes are the required information. Equation 17 can be helplessly forced to predict an anomaly of an increase of 0.1036 mm/orbit which amounts to 538.25 mm/year. Gravity Probe B went up on April 20th, 2004. Seven years totals to about 3.77 meters and so the delta t of a round trip signal to Gravity Probe B now should take around 25 nanoseconds longer on average than when it went up.

The main science mission was only a little over a year long, but supposedly it is still up there. A few well placed readings now could test and possibly falsify the hypothesis.

Gravity Probe B
http://en.wikipedia.org/wiki/Gravity_Probe_B

grapes
2011-Mar-19, 12:48 AM
The equation for R-dot is fairly straightforward where the square of the local space deformation parameter is 4/3 10^-12. This is multiplied by ¾ R/T in meters and years.

For a craft in geostationary orbit, R is approximately 42,164 km and T is one sidereal day. This creates the “illusion” of R-dot of approximately 15.39 mm/yr.Using that 4/3 x 10-12 x 3/4 R/T, and since T = 1/366.256 year, I get 15.44 mm/yr, which is close to your value (I only get 15.39 mm/yr if I use T = 1/365). However, I don't see why we'd use a value for lambda that is measured over the length of the distance from the earth to the sun, and apply it to an earth satellite. They don't make a case for it being local, or, for that matter, constant.

borman
2011-Mar-19, 03:19 AM
Using that 4/3 x 10-12 x 3/4 R/T, and since T = 1/366.256 year, I get 15.44 mm/yr, which is close to your value (I only get 15.39 mm/yr if I use T = 1/365). However, I don't see why we'd use a value for lambda that is measured over the length of the distance from the earth to the sun, and apply it to an earth satellite. They don't make a case for it being local, or, for that matter, constant.

Yes, for consistency I have been using 60 minute hours, 24 hour days and 365 days for a year throughout. This also applies to the GP-B calculation.

From Table 1 they get their premise that Lambda is constant and test it for both the AU increase and the LLR anomaly. Since it worked, they see this as support for their assumption of constant lambda. Further, from this premise they calculate the R-dot for each planet noting along the way that R-dot is proportional to R^(-1/2). So R-dot for Mercury is much higher than for Earth. The moon is near enough to the Earth to have the same value. Spacecraft in orbit about the Earth are also close to Earth and can have the same Lambda. Note the rather high value for GP-B; the closer to Earth the craft is, the higher the anomaly and the shorter the period to stay in orbit. We may get eventual test results from MESSENGER and CASSINI that will test their premise, but the large values for close orbit spacecraft should continue to use their Lambda to test their hypothesis.

This begins to get to the really interesting question if the Randers-Finsler approach is the right mathematical "clothing" to analyze the anomalies: What is the source of Lambda? Is it larger or smaller for other systems? Can it be altered and how is this accomplished? It is one thing to try to find it from empirical values from Table 1, but it remains to be explained how those values come into existence.

Note that they have gone after both the AU and LLR anomaly, but have less success with the Pioneer Anomaly which, though different for each spacecraft, remain constant over the period of observation while their postdiction is that it is not constant. Note the absence of any paper dealing with the flyby anomaly which is some 6 orders greater than the Pioneer and hence quite inconsistent by as many magnitudes with their Lambda. Until they face the source problem, they won't be able to make a unified theory for all 4 astrometric anomalies.

An important hint is another undernoticed coincidence. The AU, LLR, and orbital spacecraft anomalies are all sub-hyperbolic while the Pioneer and flyby involves initially hyperbolic orbits where the acquired anomaly is just sufficient to close the orbits. Even the New Horizons anomaly closes the orbit even though it is the fastest craft we have "tried" to send out of the system.

grapes
2011-Mar-19, 04:29 AM
From Table 1 they get their premise that Lambda is constant and test it for both the AU increase and the LLR anomaly. Since it worked, they see this as support for their assumption of constant lambda. That's exactly how they seem to have come to their conclusion that lambda was constant--but the Table 1 was created by assuming that R-dot was the same for all the planets! Go ahead and use the R and T values for each planet and 1 x 10-12 for R-dot for all the planets, and see if you don't recreate their values for lambda in Table 1 (to ten decimal places). Since this is the formula,


\lambda = \sqrt{\frac{4 \dot{R}}{3 R}T}

in order for their conclusion that lambda is constant to be true, from that table, R would have to be proportional to T (since R-dot is held constant), but we know that R2 is proportional to T3, from Kepler's Law! Lambda cannot be constant, based upon that table!

borman
2011-Mar-21, 02:11 AM
R-dot is proportional to R^-(1/2) and not to R.

Yes the values in the far column of Table 1 are what Lambda would be if R-dot were always 1 trillionth of the orbit for all planets. But this would violate Kepler as some planets are deeper in the well than others.

What is done is to take the one empirical value we actually do have at present which is d(AU)/dt for R-dot for Earth at its distance from the Sun and period of 1 year and solve for Lambda using equation 17. This value is used to compute the R-dots for the other planets in Table 2. Note they are not 10^-12 of their semi-major axis except for Earth.

Likewise if R-dot were proportional to R, being 10^-12 in particular, then the values for the geostationary R-dot would be 42 micrometers instead of 15.4 mm and in the more extreme case of GP-B it would only be 7 micrometers instead of 538 mm.

These evaluations are done assuming a uniform Lambda whose square is 4/3 X 10^-12, rather than a constant R-dot.

The issue with the incorrect post-diction for the Pioneer Anomaly should be approached cautiously as regards falsification. They may be over-reaching or misusing the approach or not “climbing the right tree”. One must be careful not to “throw out the baby with the bathwater” in haste to falsify.

To be explored is whether the Lambda seen by a spacecraft can be altered during the periapsis of a hyperbolic gravity assist.

grapes
2011-Mar-21, 06:15 AM
R-dot is proportional to R^-(1/2) and not to R.Why? I get two different results from that, each depending upon a different erroneous assumption from the paper. Is there one I am missing?


Yes the values in the far column of Table 1 are what Lambda would be if R-dot were always 1 trillionth of the orbit for all planets. But this would violate Kepler as some planets are deeper in the well than others.And yet their main conclusion seems to be based upon it. That's why their paper is bogus.

borman
2011-Apr-12, 12:50 AM
Why? I get two different results from that, each depending upon a different erroneous assumption from the paper. Is there one I am missing?
And yet their main conclusion seems to be based upon it. That's why their paper is bogus.
Are you assuming that both Lambda and R-dot are constant? Only Lambda is constant. If both were constant, then the ratio T/R would be a constant slope, violating Kepler's third law that T^2 is proportional to R^3.

grapes
2011-Apr-12, 03:52 PM
Are you assuming that both Lambda and R-dot are constant? Only Lambda is constant. If both were constant, then the ratio T/R would be a constant slope, violating Kepler's third law that T^2 is proportional to R^3.I'm not assuming anything! :)

I was just pointing out their assumptions, which are bogus as near as I can tell. I'd like to find out differently.

I'd asked you where you got the following:
R-dot is proportional to R^-(1/2) and not to R.