## lrr-2010-4

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20–70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of $latex \sim 6\times 10^{-9}$ Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of $latex a_P = (8.74 \pm 1.33)\times 10^{-10}$ m/s$latex ^2$. This apparent violation of the Newton’s gravitational inverse square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.

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### 7 Responses to “lrr-2010-4”

1. Klaus Wilhelm says:

To whom it may concern,

since some time I try to find out the magnitude and sign of the ’so-called’ Pioneer Anomaly from the literature(see emails appended), without any reply yet. The recent Living Reviews article by S.G. Turyshev and V.T. Toth does not help either considering the following statements, which appear to be inconsistent:

Abstract — … constant sunward deceleration
7.2.1 — … anomalous acceleration … is Sun-pointing
8. Conclusion — … direction of acceleration remains unclear: the four principle directions (sunward, earthward, along the spin axis, or along the velocity vector) fall within a few degrees of each other …

Do these statements imply that it is even unclear whether an anomalous acceleration or a deceleration is the result of a certain interpretation? The original frequency measurements are needed, I feel.

With best regards,
Klaus Wilhelm

2. Viktor T. Toth says:

Dear Dr. Wilhelm,

Please allow me to try to respond to your inquiry that was forwarded to us by Living Reviews.

In our Living Reviews paper, we discuss in some detail the actual measurement process. You are correct that what is measured are neither velocities nor accelerations, but it’s not instantaneous frequencies either; what is being measured is a pulse count over a given time period. This can be the actual number of zero crossings when a modern (Mark V) receiver is used, or a differential pulse count after the received signal is mixed with a synthesized signal of known frequency.

This pulse counting is performed using specific periods of time ranging (typically) from 0.1 to 1980 seconds, and the results are recorded in a data file. So the “raw data” is a time-stamped collection of Doppler counts. You indicate that it should be possible to present the observational facts without leaving room to misinterpretations. That is true; but that presentation would include lines of data such as

-811208608.000 63 63 -112611.053138973 21984700.000 1980.00

(The fields in this case are the J2000 timestamp, transmitting and receiving DSN station ID, Doppler count expressed as a frequency, the receiver reference frequency, and the Doppler count duration.) The file from which I took this particular line contains about 680,000 such records, encoded in a binary format. That is the unambiguous raw data, which can only be used in conjunction with additional data records that tell us the transmitting station’s frequency, records such as

DSS12: -555050940.000000000 – -555050800.000000000 0021987041.199951000 -0.500000000

(the fields are: DSN station ID, start time stamp, end time stamp, exciter frequency at start, ramp rate per second.)

So there is no simple answer in the form of something like, “the received frequency is X, the expected frequency is Y, X-Y is the residual and that indicates a red/blue shift.” What we have instead is an orbital model with adjustable parameters (such as the initial state vector or the anomalous acceleration) that are optimized (e.g., using a least squares optimization algorithm) to provide a “best fit” match against the data points.

We can then compare different models by comparing the residual difference between observed and modeled frequencies at each Doppler data point. We find that if we assume the existence of a constant sunward acceleration (or equivalently, a frequency shift), the residuals are low, as expected. Without this fictitious acceleration, the residuals are significantly higher. From this, we can derive the conclusion that a constant sunward acceleration is consistent with the data and produces a significantly better fit than the assumption of no acceleration. This statement does not exclude other models (e.g., time-varying acceleration, acceleration in the direction of the Earth.)

Just to be clear, this does NOT mean that we are uncertain as to whether the acceleration is an acceleration or a deceleration. The uncertainty is more subtle. The directions of the Earth and the Sun, as seen from the spacecraft, are separated by only a few degrees or less. So when we see an approximately sunward acceleration, that does not exclude the possibility that the acceleration is in the Earth direction. Similarly, the magnitude of the acceleration being what it is, the expected error is significant. So even though a constant solution fits the data well, we cannot exclude the possibility that the actual acceleration was slowly changing (decaying) with time.

So to summarize, the observational data are consistent with an approximately constant, approximately sunward acceleration. The observational data are NOT consistent with a zero-acceleration model, nor are they consistent with a model in which the acceleration points away from the Sun. And, of course, it is up to us to decide if we interpret this apparent acceleration as an actual change in velocity, an effect on the radio signal, an acceleration of clocks, or some other physical process.

I hope I was able to address your questions in full and that you find this information helpful.

Sincerely,

Viktor

3. Klaus Wilhelm says:

Dear Dr. Toth,

thank you very much for your detailed response to my questions. I have, of course, not in mind to get into an evaluation of the the raw data. What I had hoped was to understand the sign conventions in the various anomaly papers in a consistent way. With your reply, I will try again.

With best regards,
Klaus Wilhelm

4. Viktor T. Toth says:

Dear Dr. 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

5. Klaus Wilhelm says:

Dear colleagues,

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

6. Viktor T. Toth says:

Dear Dr. Wilhelm,

- 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

7. Slava G. Turyshev says:

Dear Dr. Wilhelm:

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

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