## Pioneer Anomaly

A couple of matters have caused me some curiosity of late. One is the "Pioneer Anomaly", wherein exploratory spacecraft are slightly off course:

http://en.wikipedia.org/wiki/Pioneer_anomaly

The other is something I read about recently in New Scientist, about a revised theory of gravity making Dark Matter unnecessary.

http://www.newscientistspace.com/article/dn8631

Can anybody tell me more and/or give me a lowdown on whether these items are mere journalistic sensation?
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 Here's an excerpt from the New Scientist link: "It's as if gravity is stronger near the centres of galaxies", Brownstein told New Scientist. "Then, at a certain distance, the stars become sparse, and the gravitons don't contribute that much." So at larger distances, gravity returns to the behaviour described by Newton...... Furthermore, the team tested the theory against observations of NASA's 34-year-old Pioneer 10 spacecraft, which appears about 400,000 kilometres away from its expected location in the outer solar system.
 Anybody? Gravity and dark matter?

## Pioneer Anomaly

http://www.newscientistspace.com/art...ar-system.html

the-kink-at-the-edge-of-the-solar-system
 Thanks micky. I'm in the UK too.
 A couple of things about the cluster paper; -They model clusters as isothermal spheres. There are clear temperature gradients in clusters, particularly within ~200Kpc. -They make no mention of substructure within the clusters. The assumption of hydrostatic equilibrium is violated in the presence of a major merger. A quick look at the clusters in their study tells me there are quite a few there that are known mergers. A lot of these seem to fit their metric-skew-tensor model, whilst some of the more dynamically relaxed clusters seem to not fit well. I would like to see a study done on relaxed systems alone. I have a feeling that their model may not fit this revised sample so well. As for the Pioneer anomaly, I think a test specifically designed to measure the anomaly will solve the puzzle.
 Hello, here's a paper Gravitational Solution to the Pioneer 10/11 Anomaly by Brownstein and Moffat: http://arxiv.org/PS_cache/gr-qc/pdf/0511/0511026.pdf Can anybody tell me in a nutshell what metric skew tensor gravity is?

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 Quote by Farsight Hello, here's a paper Gravitational Solution to the Pioneer 10/11 Anomaly by Brownstein and Moffat: http://arxiv.org/PS_cache/gr-qc/pdf/0511/0511026.pdf Can anybody tell me in a nutshell what metric skew tensor gravity is?
From the abstract of reference 4 in that paper, http://arxiv.org/abs/astro-ph/0412195,

Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
Authors: J. W. Moffat

 Einstein gravity coupled to a massive skew symmetric field F_{\mu\nu\lambda} leads to an acceleration law that modifies the Newtonian law of attraction between particles
So this is general relativity with an additional force, carried by a massive particle which is described by a skew tensor field, $$F_{\mu\nu\lambda}$$. Skew means the same thing as anti-symmetric; if you interchange any two of the indexes the result is the same as multiplying the tensor by -1 $$F_{\nu\mu\lambda} = - F_{\mu\nu\lambda}$$ and so on. The Faraday tensor of electromagetism is a skew tensor, but that's not the same is the one describing this new force because Faraday is a rank two tensor (two subscripts) while the new Moffat tensor is defined to be rank 3 (three subscripts).

Forces in GR are described by tensor fields because tensor equations are true in every diffeomorphism class, the coefficient of the tensors change but the equations remain true.

An important point here is that Moffatt originally made up his theory to explain galactic rotation curves and now is asserting that it can account for the Pioneer anomaly too.
 Thanks selfAdjoint. I was hoping for a geometrical one liner. I found this powerpoint presentation which looked pretty good, but I don't understand the "phion field". Sorry, I can't link direct, so search google on Edinburgh Moffat Talk Gravity and it's at the top. http://www.google.co.uk/search?hl=en...G=Search&meta= I didn't know this sort of thing had been kicking around for so long. Where have I been? MOND is a modification of the usual Newtonian force law, hypothesized in 1983 by Moti Milgrom of the Weizmann Institute, as an alternative to Dark Matter.

 Quote by Farsight MOND is a modification of the usual Newtonian force law, hypothesized in 1983 by Moti Milgrom of the Weizmann Institute, as an alternative to Dark Matter.
MOND really just says that the measurements for gravitational acceleration that were taken during the time of Newton were too crude and that the crude measurement lead to an improper assumption that objects under such sparse gravitational conditions will abide by the same gravitational correlation.

For the Pioneer Anomaly, MOND is used to try and say that there is no blueshift taking place; rather, our calculations of where the probes should be are wrong because of our incorrect assumption of classical Newtonian Dynamics.

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It is important to understand what is being measured as the Pioneer Anomaly.

It is not the actual acceleration of the space craft, nor its actual position, but rather the frequency of the carrier wave repeated back from the space craft to a ground station.

See: The Pioneer Anomaly: Seeking an explanation in newly recovered data
 Doppler data is the measure of the cumulative number of cycles of a spacecraft’s carrier frequency received during a specific count interval. The exact precision to which these measurements can be carried out is a function of the received signal strength and station electronics, but it is a small fraction of a cycle. Raw Doppler data is generated at DSN tracking stations (see discussion of the present-day DSN capabilities in [11]). Count intervals for Doppler data can vary from 0.1 seconds to 10 minutes, with count times of 10 to 60 seconds being typical [3, 8]. The Pioneers used S-band (∼2.2 GHz) radio signals to communicate with the DSN. The 1-σ accuracy of S-band data is approximately 1 mm/s for a 60 second count interval after being calibrated for transmission media effects.
The acceleration and position anomalies are deductions obtained by comparing this frequency count with expectations from the classical Newtonian model.

There are two interpretations of a real effect: The Study of the Pioneer Anomaly: New Data and Objectives for New Investigation
 The anomaly can be due to a force acting on the craft that produces acceleration Eq. (2), (aP = (8.74 ± 1.33) × 10−10 m/s2) or, alternatively, this signal can also be interpreted as a time deceleration uniformly changing with rate at = (2.92 ± 0.44) × 10−18 s/s2 (see discussion of this possibility in (Anderson et al., 2002a; Turyshev et al., 2004, 2005a, 2006)).
(emphasis mine)

The PA is a deviation of the measurement of frequency with prediction, it is a comparison of two time rates.

Thus the primary measurement is one of clock drift. It is only by applying doppler does this become an anomalous acceleration and hence a deviation of velocity and position from that predicted by Newton.

Garth
 Many thanks for that Garth. I've printed the papers and will enjoy some bedtime reading.

 Quote by Garth Thus the primary measurement is one of clock drift. It is only by applying doppler does this become an anomalous acceleration and hence a deviation of velocity and position from that predicted by Newton. Garth
So what you are saying is that the PA is an (de-)acceleration of clocks? I think I read something about that, Ephemeris time time vs. atomic time.

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 Quote by PRodQuanta So what you are saying is that the PA is an (de-)acceleration of clocks? I think I read something about that, Ephemeris time time vs. atomic time. Paden Roder
It could be.
The primary measurement is the comparison of two clock rates: that received from the space-craft compared with that predicted by Newtonian physics.

If the space-craft are actually behaving as Newton predicts then the anomaly is one of clock acceleration, as you say Ephemeris v atomic time. (Incidentally as predicted by SCC)

If the two clock rates are identical then the space-craft are not behaving as Newton predicts.

In this case either there is an extra force decelerating the space-craft such as radiation imbalance, gas emission, dust drag, or Planet X (this last option being the reason the data was examined in the first place!)
or
gravity does not behave as Newton predicts at large ranges or small accelerations (MOND).

If there is an extra unaccounted force it is strange that the sun-wards acceleration is constant and the same for both space-craft.

If there is some MOND-type effect it is surprising it has not been detected elsewhere in planetary orbits.

Garth
 Recognitions: Gold Member Science Advisor Read all about it! Today's New Scientist:Have we got gravity all wrong? Garth

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 Quote by Farsight Hello, here's a paper Gravitational Solution to the Pioneer 10/11 Anomaly by Brownstein and Moffat: http://arxiv.org/PS_cache/gr-qc/pdf/0511/0511026.pdf Can anybody tell me in a nutshell what metric skew tensor gravity is?
From the abstract of reference 4 in that paper, http://arxiv.org/abs/astro-ph/0412195,

Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
Authors: J. W. Moffat

So this is general relativity with an additional force, carried by a massive particle which is described by a skew tensor field, $$F_{\mu\nu\lambda}$$. Skew means the same thing as anti-symmetric; if you interchange any two of the indexes the result is the same as multiplying the tensor by -1
$$F_{\nu\mu\lambda} = - F_{\mu\nu\lambda}$$
and so on. The Faraday tensor of electromagetism is a skew tensor, but that's not the same is the one describing this new force because Faraday is a rank two tensor (two subscripts) while the new Moffat tensor is defined to be rank 3 (three subscripts).

Forces in GR are described by tensor fields because tensor equations are true in every diffeomorphism class, the coefficient of the tensors change but the equations remain true.

An important point here is that Moffatt originally made up his theory to explain galactic rotation curves and now is asserting that it can account for the Pioneer anomaly too.
Moffat has a new paper this week where he suggests a way to falsify his theory by measuring some time-delays from probes in the outer.

http://arxiv.org/abs/gr-qc/0605141
Time Delay Predictions in a Modified Gravity Theory
J. W. Moffat
5 pages
"The time delay effect for planets and spacecraft is obtained from a fully relativistic modified gravity theory including a fifth force skew symmetric field by fitting to the Pioneer 10/11 anomalous acceleration data. A possible detection of the predicted time delay corrections to general relativity for the outer planets and future spacecraft missions is considered. The time delay correction to GR predicted by the modified gravity is consistent with the observational limit of the Doppler tracking measurement reported by the Cassini spacecraft on its way to Saturn, and the correction increases to a value that could be measured for a spacecraft approaching Neptune and Pluto."
 Recognitions: Gold Member Staff Emeritus Sounds good. From his previous paper and the original rotation curve one it looked liked he was tuning his theory to accomodate whatever "appearance" he was looking at, a la epicycles.