Pioneer Anomaly

 

A report[1] on the acceleration anomaly with respect to Pioneer 10 and 11 suggests another situation where considering that light has a constant speed can lead to inconsistent and/or incorrect conclusions.

 

As a spacecraft travels away from any source of gravity, it is traveling through a time gradient that is becoming less dense as the craft gets further away from the gravity source. Assuming that the craft is not undergoing deliberate acceleration, it should continue traveling at a constant velocity, which might be modified by gravitational attraction, contact with space debris, or emissions from the craft. After factoring in any such modifying conditions, the craft would be expected to have some particular predictable velocity, which may or may not be uniform.

 

Measurement of this velocity would depend upon establishing the average time over periodic trials for an electromagnetic signal to reach the craft and return. This is essentially what has to be done regardless of the form of the trials. It appears that in the case of the subject craft a signal is sent and a new signal is generated by the craft for return to earth. This average time should increase for each trial as the craft gets further away from the observer. The distance of the craft at each trial can then be determined by using the speed at which the signal travels. The problem with the results with Pioneer 10 and 11 is apparently that this calculated distance is not the same as the distance predicted from other considerations for each trial, which is the same thing as the calculated velocity not being the same as the predicted velocity. The difference is such that the velocity of a craft appears to be different than it ought to be, which is cast in terms of acceleration in a direction other than that in which the craft is traveling (i.e. towards the sun, which is essentially toward the observer).

 

So what might be happening? As the craft travel away from the gravity source, the clock rate in the region of each craft is increasing. Thus the speed of the electromagnetic signals in that region is increasing, and the average speed of a signal between the craft and earth would be increasing for each trial[2]. This means that the signal time would be less than would be expected if the signal speed remained constant, and thus that the calculated distances at each trial would be less than would be expected with constant signal speed. This could then be interpreted as an unexpected acceleration toward the observer. This type of discrepancy is consistent with the reported results.

 

If the gravitational attraction acting on the craft can be accurately predicted, which would seem to be the case if its effect on the craft can be predicted, then it might be possible to also determine what the clock rate would be at the position of the craft. If that is the case, then it should be possible to determine what the relative change in average signal speed should be from trial to trial. By incorporating this into the calculations, it may be possible to resolve the anomaly as being one of current interpretation rather than craft behavior. Such a simple approach might suffice for a few trials over small periods of time. Over an extended period of time it would probably be necessary to consider the clock rates along the entire signal path as the proximity of the path to various bodies might be continuously changing.