Pioneer Spacecraft: Exploring SR Effects on Gravitational Fields

[Jeltz]

Pioneer Spacecraft: As far as I know, the "extra" apparent acceleration towards the sun is yet to be adequately explained or shown to be an empirical error. Given the ad-hoc nature of this experiment it may require a better one to resolve this, but it got me thinking about what is unique about these spacecraft where empirical science and astronomical observation is involved.

I came to the conclusion that perhaps we have discounted the effect of Special Relativity (SR) on the gravitational field of the Sun. Most experiments we do with moving atomic clocks and practically the entirety of astronomical observations are done where the "experiment" is in orbit and/or has very low radial velocity with respect to the dominant gravitational field. I know of no accurately observed experiment where this is not the case.

Direct SR effects alone due to the radial velocity of Pioneer with respect to the Sun are many orders of magnitude too small too account for the anomaly. General Relativity (GR) reverts to the weak field Newtonian solution but this is what is in possible disagreement with the Pioneer results.

But has anyone considered the effects of Special Relativity on the entire Gravitational field of the Sun? Will it not distort from a spherical shape to a non-spherical shape and cause an extra dipole acceleration towards the sun that is a function of radial velocity? My best efforts to do this show the effect may be close to the cube-root of the SR direct effects, and just about the right size to explain the anomaly. Could someone confirm or refute this please?

As far as I know, these spacecraft are the first accurate observations of accelerations due to gravity where the object has significant radial velocity with respect to the dominant gravitational field in its neighbourhood.

 

[bcrowell]

I came to the conclusion that perhaps we have discounted the effect of Special Relativity (SR) on the gravitational field of the Sun. Most experiments we do with moving atomic clocks and practically the entirety of astronomical observations are done where the "experiment" is in orbit and/or has very low radial velocity with respect to the dominant gravitational field. I know of no accurately observed experiment where this is not the case.

There are a lot of very precise experiments that explicitly measure SR and GR effects for spacecraft orbiting the Earth and in hyperbolic trajectories. The GPS satellite network has to take SR and GR effects into account in order to work. Some of the best current tests of GR come from the Cassini probes.

Although the Pioneer anomaly is unexplained, unexpected properties of gravitational interactions have been ruled out as an explanation: http://arxiv.org/abs/0912.2947

 

[Jeltz]

Thanks for the reference to that paper. They make in my opinion an unwarranted assumption:

"If the PA was due to some modifications of the
known laws of gravity, this should be due to a radial extraforce
affecting the orbits of the astronomical bodies"

But this is certainly NOT the case if the PA effect is due to radial motion of the object to the dominant gravitational field it is in. The planets and GPS satellites have NEGLIGIBLE radial velocities relative to the gravitational field they are in, and as you say the standard GR and SR effects are well understood.

If the effect is due to radial motion to the gravity field then this should certainly show up for objects in highly eccentric orbits, but the authors go on to explicitly state that such objects (notably comets) due to outgassing and other effects are not suitable objects for measuring such a small effect.

Also I do not believe the Cassini probes were ever in a period of high radial velocity for long enough periods between course corrections to prove or disprove the PA Effect.

 

[bcrowell]

Thanks for the reference to that paper. They make in my opinion an unwarranted assumption:

"If the PA was due to some modifications of the
known laws of gravity, this should be due to a radial extraforce
affecting the orbits of the astronomical bodies"

But this is certainly NOT the case if the PA effect is due to radial motion of the object to the dominant gravitational field it is in. The planets and GPS satellites have NEGLIGIBLE radial velocities relative to the gravitational field they are in, and as you say the standard GR and SR effects are well understood.

If the effect is due to radial motion to the gravity field then this should certainly show up for objects in highly eccentric orbits, but the authors go on to explicitly state that such objects (notably comets) due to outgassing and other effects are not suitable objects for measuring such a small effect.

Also I do not believe the Cassini probes were ever in a period of high radial velocity for long enough periods between course corrections to prove or disprove the PA Effect.

An effect of the type you're referring to would be parametrized by $\zeta_1$ in the PPN formalism http://en.wikipedia.org/wiki/Parameterized_post-Newtonian_formalism . A nonzero value of this parameter would cause nonconservation of momentum, and there are tight experimental bounds on how much nonconservation of momentum there can be. See http://relativity.livingreviews.org/Articles/lrr-2006-3/ , section 3.7.3.

[EDIT] Actually I think Iorio does make his assumption explicit, although it may not be obvious to someone who's not an expert. On p. 2 he explicitly says he's restricting himself to gravitational explanations that respect the equivalence principle. A nonzero $\zeta_1$ would violate the equivalence principle. Based on the equivalence principle, whatever acceleration is experienced by the probes must be experienced by other objects in that region as well; this is basically the only assumption he makes.

 

[Jeltz]

I am just trying to learn here. I am not saying GR/SR is wrong, just that the simplifications made to explore SR effects within GR weak gravitational fields may not have been fully tested or completely justified in the weak field limit.

The test is for an effect where the radial component of the velocity is high compared to its tangential component with respect to the direction of the gravitational field. GPS satellites and planets do not meet this criterion. It may be a silly test but it would be a brave theoretician who says it need not be tested because we know what the answer will be. I have seen no reference to an experiment designed to test this and which refutes the PA being caused by combined GR/SR effects on this basis.

You have pretty much convinced me except for one point. Your argument seems to be that an extra force correlated with radial velocity will break equivalence and momentum conservation.

And yet the direct SR effect (small though it is and far to small to explain the PA) says that the lorentzian mass increase of the sun due to the radial motion of the spacecraft should cause a net acceleration towards the sun. This is an acceleration that is correlated with radial velicity that does not break equivalence or conservation of momentum, which seems directly contrary to your argument.

I am not saying there is an acceleration caused by the radial motion of the craft, just that the complete combined SR effects inside a GR field in the weak limit may not yet have had a full accounting by the experts. In this case, from the suns frame of reference it would most certainly experience an equal and oppoosite PA force, which of course need not break equivalence and momentum conservation.

 

[Upisoft]

It seems we have made tests with high radial component. It was not intended as test but nevertheless there are the results: http://en.wikipedia.org/wiki/Flyby_anomaly" .

 

[Jeltz]

I disagree. These fly-by tests did not measure accelerations to the accuracy required to detect the Pioneer anomaly.

During the planetary fly-by encounter the deviations of the spacecraft from standard GR based orbit codes were of the order of 10-4 m/s2 and appear to deviate significantly from these codes only close to the actual fly-by encounter.

The pioneer anomaly is almost 6 orders of magnitude smaller than these fly-by discrepancies. To prove or disprove the pioneer anomaly we are talking meaurement accuracies of 10-10 m/s2, which can generally only be achieved by observing the spacecraft over very long periods of time.

 

[Dale]

Personally, I don't know why anyone would bother with the Pioneer anomaly. Unless something is repeatable it is impossible to really know the cause since it is impossible to try it under different conditions and thereby isolate the cause.

 

[inflector]

Based on the equivalence principle, whatever acceleration is experienced by the probes must be experienced by other objects in that region as well; this is basically the only assumption he makes.

Can you clarify specifically what about the equivalence principle implies that gravity would affect all the objects in the region equally? I don't see how that follows from inertia and gravity being equivalent.

 

[inflector]

Personally, I don't know why anyone would bother with the Pioneer anomaly. Unless something is repeatable it is impossible to really know the cause since it is impossible to try it under different conditions and thereby isolate the cause.

Isn't the idea that if we can figure out some viable theories for what is causing the anomaly then we should be able to run a test to isolate the posited cause by testing for specific effects that a specific theory predicts.

For example, let's suppose we come up with a possible change the equations of GR or the strength of the solar wind at that distance, we could send a set of probes along with some sort of telemetry device to relay data about those probes. These probes could test specifically for confirmation of any specific theory and or the absence of effects which some might believe to be causing the anomaly. Using our example, they could present different profiles of mass versus surface area exposed to the sun, and a survey of any dust particles at that distance, among other things.

We could also measure velocity and acceleration more precisely using these probes. We could send much faster lighter probes to check for an effect that is due to velocity rather than a gravitationally induced acceleration. There is a lot we could do to isolate the cause.

 

[bcrowell]

You have pretty much convinced me except for one point. Your argument seems to be that an extra force correlated with radial velocity will break equivalence and momentum conservation.

And yet the direct SR effect (small though it is and far to small to explain the PA) says that the lorentzian mass increase of the sun due to the radial motion of the spacecraft should cause a net acceleration towards the sun. This is an acceleration that is correlated with radial velicity that does not break equivalence or conservation of momentum, which seems directly contrary to your argument.

Have you looked at the Will review that I linked to? http://relativity.livingreviews.org/Articles/lrr-2006-3/ Sections 3.2 and 3.7 deal with this kind of thing. To progress beyond a certain point, you need to do the math. The $\zeta_1$ parameter refers to an effect that is in addition to all SR and GR effects, including the relativistic increase in inertia. GR predicts exact local conservation of momentum. This is because the Einstein tensor is divergenceless, and the Einstein field equations set it equal to the stress-energy tensor, so the SET is divergenceless, which means mass-energy and momentum are locally conserved. When you set $\zeta_1\ne0$, this breaks down. This is why table 2 in section 3.2 of the Will paper describes all the $\zeta$ parameters with "Violation of conservation of total momentum?"

I am just trying to learn here. I am not saying GR/SR is wrong, just that the simplifications made to explore SR effects within GR weak gravitational fields may not have been fully tested or completely justified in the weak field limit.

IMO your approach is kind of backwards. There is nothing wrong with saying that GR is wrong. GR probably is wrong. All scientific theories are just approximate models of reality. Clifford Will is a very well known relativist, and he's spent his entire career playing around with models of gravity that contradict GR. That doesn't make him a kook or a crank. Basically you can never test a theory experimentally unless you have an alternative test theory in mind that predicts something different. But you seem unwilling to accept that lots of physicists have been working for decades on tests of GR, including solar-system tests using spacecraft telemetry, and these people are not stupid. If you don't familiarize yourself with the work that has been done already, then there is zero probability that you are going to come up with a new explanation for the Pioneer anomaly that has never been thought of before. A specialist like Will or Iorio is not going to wake up one morning and say, "Gosh, I forgot to take relativity into account in my analysis of the Pioneer anomaly," as you suggested in your original post.

I am not saying there is an acceleration caused by the radial motion of the craft, just that the complete combined SR effects inside a GR field in the weak limit may not yet have had a full accounting by the experts.

What are you basing this statement on? You don't seem to have taken the trouble of reading a review article on the topic, so how would you have any idea of what has been accounted for by the experts?

In this case, from the suns frame of reference it would most certainly experience an equal and oppoosite PA force, which of course need not break equivalence and momentum conservation.

I can point you to the review article by Will, but I can't read it for you.

 

[bcrowell]

Re the flyby anomalies, it would be interesting to see a recent analysis that includes all the Rosetta flybys. Apparently Anderson's empirical formula predicted a 1 mm/s anomaly for the 2007 Rosetta flyby, but the observed anomaly was consistent with zero and inconsistent with 1 mm/s.

[EDIT] I found a paper on arxiv by Busack that lists results for the 2009 flyby, and apparently the situation was similar to the 2007. Anderson's formula has been falsified twice.