# Pioneer Anomalous Acceleration

Anderson etal [gr-qc/0104064] have announced an anomalous acceleration of the Pioneer spacecraft toward the Sun. This acceleration is not seen in the planets and would be easily detectable. The acceleration of Neptune toward the Sun is 6*10-4 cm/sec2 while the anomalous acceleration is 8*10-8 cm/sec2. The increased acceleration would lead to an increased orbital velocity with dv/v = 0.5*da/a = 0.7*10-4, which would shorten the orbital period by the same fraction, and lead to a mistake in the distance of Neptune of dD/D = (2/3)*dP/P = 4*10-5. But when the Voyagers went past Neptune Doppler ranging established that the distance determined from the orbital period was correct to parts per million: Anderson etal (1995, ApJ, 448, 885) give -2 +/- 1.8 ppm for da/a compared to the 133 ppm this anomalous acceleration would produce.

Aladar Stolmar claims that the anomalous acceleration of the Pioneer 10 and 11 is due to a tired light explanation of the Hubble law. If this were true the redshift produced would be

```v = cz = HD
```
and the time derivative of this effect would be
```a = dv/dt = cdz/dt = d[HD]/dt = Hv
```
The Pioneer 10 is moving outward at v = 12.24 km/sec and H = 1/[15 Gyr] so the redshift changes by cdz/dt = 2.6*10-12 cm/sec2. The observed value is a = -8*10-8 cm/sec2. Thus Stolmar is wrong by a factor of -(c/v) or 4.5 orders of magnitude and the wrong sign.

Note that the gravitational redshift effect on the clocks has no effect on this measurement because the data are from two-way Doppler ranging. In any case the Pioneers do not carry clocks that are good enough to measure this effect.

The two-way ranging doubles the size of the frequency shift produced by any cosmological effect, but it also doubles the frequency shift produced by an acceleration. Thus the ratio of anomalous acceleration to H is just as computed above.

The anomalous acceleration implies a thrust on the spacecraft that corresponds to the force produced by a desk lamp: a "photon rocket" with a power of just 60 watts. The radioactive thermoelectric generators [RTGs] on the Pioneers produce 2000 watts of thermal power. Most of this is radiated as waste heat. If this were radiated slightly anisotropicly, with 1030 W going outward and 970 W going inward, the whole anomalous acceleration would be explained. The radiator fins have been exposed to space for many years, with one side always in sunlight and the other side always in shadow. I think that a difference in the emissivity of the radiator fins of this magnitude is quite possible. No tests were done on the spacecraft to measure this anisotropy before launch, and there is no way to retrieve them for a calibration measurement.

The Cassini spacecraft shows a LARGER non-gravitational acceleration than the Pioneer's. But since it was designed to radiate RTG waste heat primarily out the back, this is not considered to be anomalous.

```Spacecraft       Mass    Acceleration    P(rtg)    mac/P
Cassini       5200 kg    -3E-9  m/s^2    10000 W     50%
Pioneer        258 kg    -8E-10 m/s^2     2000 W      3%
```
F = ma is the force, and Fc = mac is the power needed to give this force in a photon rocket. Cassini is radiating its waste heat with a 50% asymmetry factor, while Pioneer only needs to be 3% asymmetric to explain its "anomalous" acceleration.

Therefore this extraordinary claim is not supported by extraordinary evidence and should be treated with caution.

Update 19 Apr 2008: Turyshev et al. (2008) have done a thermal model of the Pioneer 10 & 11 spacecraft and get a 23 W asymmetric flux, which explains part of the anomaly. They presented this work at the April 2008 American Physical Society meeting.

Update 15 Jul 2011: Turyshev et al. (2011, PRL accepted) have recovered and analyzed old tracking files on Pioneer 10 and 11, more than doubling the time span of the available data. They find that the anomalous acceleration is decaying with time in a manner consistent with the anisotropic waste heat emission model.