aa r X i v : . [ phy s i c s . g e n - ph ] N ov A few remarks about the Pioneer anomaly
Michael A. IvanovPhysics Dept.,Belarus State University of Informatics and Radioelectronics,6 P. Brovka Street, BY 220027, Minsk, Republic of Belarus.E-mail: [email protected] 20, 2018
Abstract
Some features of the Pioneer anomaly are discussed in context ofauthor’s explanation of this effect as a deceleration of the probes inthe graviton background. It is noted that if the model is true thenthe best parameter of the anomalous acceleration should be not thedistance to the Sun but a cosine of the angle between a velocity of theprobe and its radius-vector.
As it was reported by the authors of the discovery, NASA deep-spaceprobes Pioneer 10/11 experience an anomalous constant acceleration directedtowards the Sun (the Pioneer anomaly) [1, 2]. A possible origin of the effectremains unknown. In my model [3], any massive body must experience aconstant deceleration w ≃ − Hc , where H is the Hubble constant and c isthe light velocity, of the same order of magnitude as observed for cosmicprobes. This effect is an analogue of cosmological redshifts in the model.Their common nature is forehead collisions with gravitons. I would like toconsider here the main known features of this anomaly in context of myexplanation keeping in mind present and future efforts to verify the realityof this effect and to understand it.The observed anomaly has the following main features: 1) in the range 5- 15 AU from the Sun it is observed an anomalous sunward acceleration withthe rising modulus which gets its maximum value, leastwise for Pioneer 111see Fig. 3 in [2]); 2) for greater distances, this maximum sunward accelera-tion remains almost constant for both Pioneers [1, 2]; 3) also it is observedan unmodeled annual periodic term in residuals for Pioneer 10 [4] which isobviously connected with the motion of the Earth.If my conjecture [3] about the quantum nature of this acceleration istrue then an observed value of the projection of the probe’s acceleration onthe sunward direction w s should depend on accelerations of the probe, theEarth and the Sun relative to the graviton background. If we assume thatthe Sun moves relative to the background slowly enough, then anomalousaccelerations of the Earth and the probe will be directed almost againsttheir velocities in the heliocentric frame, and in this case: w s = − w · cosα ,where α is an angle between a radius-vector of the probe and its velocity inthe frame. For a terrestrial observer, an additional term should be taken intoaccount which is connected with its own motion relative to the background.By the very elongate orbits of the both Pioneers (see Fig. 3 in [2]), itwould explain the second (and main) peculiarity. For example, for Pioneer10 at the distance 67 AU from the Sun one has sin α ≈ .
11 (it is a visualestimate with Fig. 3 of [2]), i.e. cosα ≈ . . If for big distances from theSun we use the conservation laws of energy and angular momentum in thefield of the Sun only , then in the range 6.7 - 67 AU a value of cosα changesfrom 0.942 to 0.994, i.e. approximately on 5 per cent only. Due to this fact,a projection of the probe’s acceleration on the sunward direction would bealmost constant.As Toth and Turyshev report [5], they intend to carry out an analysis ofnewly recovered data received from Pioneers, with these data are now avail-able for Pioneer 11 for distances 1.01 - 41.7 AU. If the serious problem oftaking into account the solar radiation pressure at small distances is preciselysolved (modeled) [6], then this range will be very lucky to confront the ex-pression w s = − w · cosα of the considered model with observations for smalldistances when Pioneer 11 executed its planetary encounters with Jupiterand Saturn. In this period, a value of cosα was changed in the non-trivialmanner, and the projection of anomalous acceleration should behave itselfsimilar. For example, when the spacecraft went to Saturn, cosα was negative during some time. If this model is true, the anomaly in this small periodshould have the opposite sign . I think, it would be the best of all to comparethe two functions of the probe’s proper time: the projection of anomalousacceleration of Pioneer 11 and cosα for it. These functions should be verysimilar to each other if my conjecture is true. At present, a new mission to2est the anomaly is planned [7]. It is seen from this consideration that itwould be desirable to have a closed orbit for this future probe (or the onewith two elongate branches where the probe moves off the Sun and towardsit). Leaving for the future the question about the stability and form of theEarth orbit by such the anomalous acceleration, I note that namely this onewould cause feature 3) of the anomaly. In this case, because Pioneers 10and 11 have different trajectories, it is possible to compute a sign of theprojection of Earth’s anomalous acceleration contribution: when the Earthmoves after a probe, we should observe a minimum of the periodic term,and we should see a maximum when they move in opposite directions. Forthe twins, these maximums-minimums will appear in different time intervals,that is important to test the model.The observed very tiny anomaly in the probe motion may be the firstegress beyond the applicability limits of general relativity in the solar system.If my explanation of the one is true then this effect may turn out to be and thefirst observable macroscopic manifestation of low-energy quantum gravity. References [1] Anderson, J.D. et al.
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