Recent developments of the field are included. A few subsections and more than fifty new references are added, minor improvements and corrections of the text are made at several points, and the bibliography is updated.

Added DOIs and updated format of references, thereby reducing PDF page numbers from 107 to 103.

I believe there is a typo in equations 62 and 64. The 1+x^2 should be 1+e^2 in each case, as in http://www.lorene.obspm.fr/palma.pdf.

Karen

I wanted to suggest 3 references you might be interested: Phys.Rev. D81 (2010) 124048, Phys.Rev. D82 (2010) 124065, and http://arxiv.org/abs/arXiv:1108.2410 (just submitted to PRD)

Salvatore Vitale (a Post Doc in the Virgo group at Nickef) and I calculated the frequentist uncertainties for parameter estimations from insipiral signals detected from ligo data with asymptotic expansions of the variance and bias in terms of the inverse of the SNR.

The first order of these expansions is the well studied Cramer Rao Lower bound, while the second order has never been evaluated before (and includes effects of the non gaussiantity of the distribution of maximum likelihood estimators). The results extend all existing works with the CRLB for the estimates of intrinsic parameters and the direction of arrival and show that the second order is fundamental for medium to low SNR (for example network SNRs about 15) and realistic parameter spaces.

Regards,
Michele Zanolin

I see that there may be some difficulties as to how to interpret the DSN sign convention… Concerning your question:

“I want to repeat my main questions: what are the sign and the value of the frequency drift under the assumption of a spacecraft orbital motion as expected from all known forces.”

The frequency received at a DSN station is drifting towards higher values at the anomalous rate of f0=~6e-9 Hz/s. The inferred anomalous acceleration appears to be slowing down the spacecraft at the rate of aP. Hope this helps.

With best regards,
S. Turyshev

Let me start with a few unambiguous blanket statements about interpreting the Pioneer anomaly:

- If the anomaly is due to a fictitious force that is pushing the spacecraft, the force is directed in the approximate direction of the Sun;

- If it is a fictitious effect that is altering the frequency of the received signal, the frequency shifted up;

- If it is a fictitious effect tinkering with the transmitting station’s clock, the clock is ticking faster over time;

- If it is a fictitious effect tinkering with the receiving station’s clock, the clock is ticking slower over time;

- If any statements appear to be contrary to the above, the statements are either incorrect, ambiguous, or wrongly interpreted.

[...]

I hope this helps.

Viktor

your efforts to clarify some of my difficulties are highly appreciated. Unfortunately, I have still problems with my main questions (see letter appended) and with some formulations in the various Pioneer anomaly papers.

[...]

I want to repeat my main questions: what are the sign and the value of the frequency drift under the assumption of a spacecraft orbital motion as expected from all known forces.

With best regards,
Klaus Wilhelm

I believe that some confusion is due to the fact that when we speak of a “sunward acceleration”, we use an unsigned number, but some orbit determination software codes use a positive sign for a vector pointing away from the source, so a sunward acceleration would have a negative sign. Some authors chose to retain this convention (imposed by software) in papers, others not.

The bottom line is that the acceleration is unambiguously in the direction of the Sun; or, if one prefers to interpret the anomaly as a frequency shift instead, it would be a blueshift.

I hope this helps,

Viktor