Pioneer anomaly and the helicity-rotation coupling

Abstract

The modification of the Doppler effect due to the coupling of the helicity of the radiation with the rotation of the source/receiver is considered in the case of the Pioneer 10/11 spacecraft. We explain why the Pioneer anomaly is not influenced by the helicity-rotation coupling.PACS: 03.30.+p ; 04.20.Cv Keywords: Pioneer anomaly; helicity-rotation coupling 1 The Pioneer 10/11 Missions were launched about three decades ago and have been the first to explore the outer solar system. The analysis of radio tracking data since about two decades ago -when the effective acceleration away from the Sun due to the solar radiation pressure on the spacecraft decreased below 5 × 10 −8 cm/sec 2 -has persistently indicated the existence of an anomaly in the Doppler navigational data [1,2,3]. This Pioneer anomaly is a Doppler drift that may be interpreted as being due to a small constant acceleration a P = (8.74 ± 1.33) × 10 −8 cm/sec 2 of the spacecraft toward the Sun. The source of the anomaly is suspected to be a systematic effect associated with the spacecraft; however, no definitive answer is known as yet [1,2,3].In a recent paper [4], the modification of the Doppler effect due to the coupling of photon spin with the rotation of the emitter/receiver has been elucidated. This result is of interest for the Doppler tracking of spacecraft, since circularly polarized radiation is routinely employed to communicate with spacecraft and, moreover, the Earth as well as the spacecraft rotate. The question then naturally arises whether the helicity-rotation coupling contributes to the Pioneer anomaly. It is the purpose of this Letter to explain why there is no such contribution, since the main effect has already been phenomenologically incorporated in the analysis of Doppler data.Let ω and k be the frequency and wave vector of a photon according to inertial observers at rest in a global inertial frame. The photon is received by a noninertial observer with velocity v and rotation frequency Ω such that Ω << ω. According to this rotating observer, the frequency of the photon iswhere ω = ck, γ = (1 − v 2 /c 2 ) −1/2 is the Lorentz factor andĤ = ±ck/ω is the unit helicity vector of the photon. The upper (lower) sign refers to a positive (negative) helicity photon [4,5]. The photon helicity is related to its intrinsic spin S by S =hĤ. A beam of positive (negative) helicity electromagnetic radiation is such that inertial observers at rest along the beam looking down at the approaching wave will see the electric and magnetic fields both rotate counterclockwise (clockwise) with frequency ω about the direction of propagation. Equation (1) expresses the standard relativistic Doppler effect together with an extra term due to the helicity-rotation coupling (−γĤ · Ω) that may be neglected for Ω/ω → 0; otherwise, for a small but nonzero Ω/ω << 1, ignoring helicity-rotation coupling would lead to a systematic Doppler shift of magnitude ∆v = cΩ/ω along the beam. It is possible to illustrate the contribution of helicity-rotation coupling to the ...

Is the Physics Within the Solar System Really Understood?

“…Not included here is the spin-rotation coupling [22] Dust The interplanetary medium consists of (i) interplanetary dust and of (ii) interstellar dust. The first one consists of hot wind plasma (mainly protons and electrons) distributed within the Kuiper belt (from 30 AU to 100 AU).…”

“…Spin-rotation coupling A coupling of the helicity of the radio waves with the rotation of the spacecraft and the rotation of the Earth also leads to an effect which simulates a changing velocity [22]. This, however, applies to the two-way Doppler data only.…”

Nonlocal electrodynamics of accelerated systems

“…Here γ is the Lorentz factor of the observer and takes due account of time dilation. The intuitive account of helicity-rotation coupling presented here emerges from the simple kinematics of Maxwell's theory [17] and has a solid observational basis [17][18][19][20]. In particular, it is responsible for the phenomenon of phase wrap-up in the GPS system [18,19].…”

The Pioneer Anomaly

“…However, Anderson and Mashhoon [30] note that this effect cannot account for the Pioneer anomaly. The effect of rotation on the radio signal is already phenomenologically incorporated into the Doppler data analysis (see Section 4.5.4).…”