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The Pioneer Anomaly
Mongo
post Jun 27 2007, 02:27 PM
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The big difference between the Pioneer spacecraft and any solar planet is that the planet is in a bound orbit, while the Pioneers are in an unbound trajectory.

What if the 'Pioneer Anomaly' is dependant on radial velocity from the Sun, being zero if the object's radial velocity is zero, increasing in a linear fashion towards the Sun for objects moving outwards, and increasing in a linear fashion away from the Sun for objects moving inwards.

A planet in a bound orbit would by definition have equal amounts of inward and outward movement, so over the whole orbit the 'Pioneer Effect' would be canceled out. The amount of displacement over the orbit would be impossible to detect, due to its small magnitude (because of the small radial velocities), working over short timespans (half an orbital period).

The Pioneers, by contrast, have much higher outward radial velocities, causing the anomalous effect to be larger, unbound trajectories, allowing the magnitude of the effect to build up over time instead of being canceled out, and were tracked by radio, allowing for much smaller effects to be noticed than is the case with the planets, whose positions must be optically observed. If the planets deviate by a few km at most, then return to the calculated positions every orbit, the deviation would go un-noticed. (Radar may change this in the future, at least for the nearby planets -- but are they looking for the effect?)

edit -- In addition, the 'Pioneer effect' would simply slightly decrease the eccentricity of a planetary orbit, pushing the perihelion out a few km, and the aphelion in a few km. It might have been already detected, but misinterpreted as a slightly lower 'true' eccentricity for that planet than the actual value.

Bill
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ngunn
post Jun 27 2007, 03:13 PM
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QUOTE (Mongo @ Jun 27 2007, 03:27 PM) *
A planet in a bound orbit would by definition have equal amounts of inward and outward movement, so over the whole orbit the 'Pioneer Effect' would be canceled out.

Bill


If this were true a planet would gain less potential energy on the outward path than it lost on the inward one, making a net energy gain on every orbit. Over a long enough period of time I think this would produce fairly spectacular results.
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Littlebit
post Jun 27 2007, 03:20 PM
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Interesting comment within the article:
http://space.newscientist.com/article/dn12...y-in-doubt.html
QUOTE
Myles Standish, who calculates solar system motions at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California, says most scientists suspect the asymmetrical radiation of heat from the spacecraft is to blame.

But he also acknowledges that the orbits of Uranus, Neptune and Pluto have not been measured as precisely as those of the inner planets, suggesting the new study by Tangen cannot rule out modified gravity as a cause. "The measurements are not able to support any definite conclusions," he told New Scientist.


Tangen did not consider the cases which would involve violation of the equivalence principle, so Tangen has only addressed a small subset of possible scenarios, establishing modest constraints.

If the anomaly is a function of the radial velocity relative to the sun as Mongo supposed; if I remember right, Pioneer 11's last gravitational assist swung it initially on a vector that passed closer to sun than the Saturn orbit. The extended data set retrieved by the Planetary Society includes this period, so any radial dependance may be apparent in this extended data set.
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Mongo
post Jun 27 2007, 04:35 PM
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QUOTE (ngunn @ Jun 27 2007, 03:13 PM) *
If this were true a planet would gain less potential energy on the outward path than it lost on the inward one, making a net energy gain on every orbit. Over a long enough period of time I think this would produce fairly spectacular results.

I am not sure I follow here. A planet on the 'outward' half of its orbit would be pulled slightly inward, as if the Sun's gravitational pull were slightly stronger, and on the 'inward' half of its orbit would be pushed slightly outward, as if the Sun's gravitational pull were slightly weaker. The sum of the inward and outward phases would be the same as if the Sun's gravitational pull were constant at its true value, provided that the effect is linear with radial velocity -- as can be proven using elementary geometrical arguments.

There is one possible observable effect: because of the slight difference in the Sun's effective gravitational pull between bodies moving toward or away from the Sun, the 'outward' phase of the planet's orbit would last slightly less long than the 'inward' phase (in order for the energy transfer to balance between the two phases, and also because the planet would 'decelerate' moving outwards more quickly than it would 'accelerate' moving inwards). This difference would be very small -- perhaps a few minutes? -- but might possibly result in a detectable deviation from a perfectly elliptical orbit. Although the deviation would be extremely small.

Bill
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ngunn
post Jun 27 2007, 04:41 PM
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Energy is the integral of force over distance, so if the force is greater going one way than the other then energy is not conserved around a closed orbit.
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Mongo
post Jun 27 2007, 05:02 PM
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I am not sure that this applies here, though. Force is defined as mass times acceleration, and the Pioneer effect could be viewed as if the inertial mass of the planet were slightly lower on the outbound phase of its orbit than on the inbound phase. (Hence the increased apparent gravitational pull of the Sun -- the acceleration would be determined by the Sun's gravitational acceleration at that distance times the ratio between the planet's standard mass and its inertial mass. If the inertial mass were half the standard mass, the planet would decelerate at twice the 'expected' rate) The slightly higher deceleration of the planet, times the slightly smaller inertial mass, would result in the same force due to gravity being applied to the planet as there would be under standard physics.

Bill
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ngunn
post Jun 27 2007, 05:15 PM
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Are you saying it's inertia would be different in the radial direction from what it would be at 90 degrees to that direction? I'm not at all happy with that idea. Mass is a scalar property - or are you saying not in this case? I'm off home now but will continue to mull it over . .
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Mongo
post Jun 27 2007, 06:49 PM
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Well... (thinking about it) ...I would assume that the gravitational force exerted on the orbiting body always remains the same as it would be under 'standard' physics, for the reason that you had mentioned. But in addition to the the 'standard' effect that varies with radial distance, approaching zero as radial distance R approaches infinity, and inversely proportional to the square of the radial distance:

1) f1 = G1*m1*m2*R^-2

Where f1 is the 'actual' gravitational force exerted on the body, and G1 is Newton's gravitational constant. A second-order effect of that force on the object's trajectory would vary with radial velocity (distance over time), reaching zero as radial velocity reaches zero, and linearly proportional to (the negative of) the radial velocity:

2) f2 = -Ga*m1*m2*v

Where f2 is the pseudo-force exerted on the body, v is the radial velocity and Ga is a second gravitational constant, possibly equal to G1. f2 would be much smaller than f1 at non-relativistic velocities, reaching zero as v reaches zero, but I would not be surprised if it approached f1 as v approaches c, so that Ga equals G1. Combining the two:

3) f1+f2 = (G1*m1*m2*R^-2) - (Ga*m1*m2*v)

The 'Pioneer effect' can be viewed as a modification of the well-known Newtonian force f1:

4) f2 = f1*R^2*v*G2 where G2 = Ga/G1

Resulting in:

5) f1+f2 = (G1*m1*m2*R^-2)*(1 - R^2*v)

if G1 = Ga, as I think it could be.

So, again assuming that Ga = G1, the change in the second-order 'force' must be proportional to v, with the inertial mass equal to the first object's rest mass times (1-v) in natural units (c = 1). This is of course the opposite effect as that described in special relativity, in that with special relativity, the inertial mass equals the rest mass times the square root of (one over (1-v))

Bill
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ngunn
post Jun 27 2007, 09:56 PM
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QUOTE (Mongo @ Jun 27 2007, 07:49 PM) *
This is of course the opposite effect as that described in special relativity
Bill


Have you worked out what that would do to the perihelion of Mercury? wink.gif
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Mongo
post Jun 27 2007, 10:25 PM
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I was looking at a paper discussing modified-inerta MOND theories, and came across the following (MI = Modified Inertia, MG = Modified Gravity):

http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0510/0510117v1.pdf

MOND as Modified Inertia

QUOTE
Closer to home, the Pioneer anomaly, if verified as a new-physics effect (Anderson et al. 2002), might provide a decisive test. It can be naturally explained in the context of MOND as MI but is difficult to explain in the context of a MG theory (Milgrom 2002): The Pioneer anomaly has no match in planetary motions for which a constant, unmodelled acceleration of the magnitude shown by the spacecraft is ruled out by a large margin. The planets probe heliocentric radii smaller than where the Pioneer anomaly has been found. So a MG theory may still have a little leeway by having the anomaly set in rather abruptly with distance just at the interim heliocentric radii (e.g., Sanders 2005). A MI explanation will build on the fact that the orbits of the spacecraft differ greatly from those of the planets: the former are close to linear and unbound, the latter quasi circular and bound. It is intriguing in this connection that the analysis for Pioneer 11 (Anderson et al. 2002) shows an onset of the anomaly just around the time where the spacecraft was kicked from a bound, nearly elliptical orbit to the unbound, almost linear orbit on which it is now (the corresponding event for Pioneer 10 is not covered).
The onset still wants verification, but if real, it would be a signature of MI.


If the Anderson analysis of the anomaly is correct, then the 'Pioneer effect' will never be detected in the orbits of the planets. A radio transponder (or possibly a laser reflector) placed on an unbound Solar-escape trajectory would be needed to study it.

Bill
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frankm
post Aug 9 2007, 03:39 AM
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The Deen report provides a different way to present the telemetry blueshift.

Although the Pioneer 10/11 anomaly is presented as a "sunward acceleration", the actual data is the continuing blueshift of the telemetry signal. A researcher prepared a report that proposed a mechanism for the blueshift, it being caused by a changing "index of refraction" in what amounts to a segmented cosmic lens about the sun.

http://www.vip.ocsnet.net/~ancient/Deen-20...-10-Anomaly.doc

It should be noted that the author inverted the algorithm normally used to calculate the index of refraction, n, see Para. 4 of the report. He held v constant (inside 20 AU) and allowed c to change as the spacecraft went outbound, thus resulting in an increasing value for n. The increasing n is directly proportional to the increasing blueshift with distance.

Para. 1 of the report states the effect quite directly, "A photon emitted by a spacecraft outside the entire onion would experience successive speed reductions as it crossed successive shell boundaries moving inwards towards the Sun."

I hold a slightly different view than Deen, as I doubt the volume surrounding the Sun is layered, it has a constantly changing index of refraction, starting at the Sun's surface and extending outward to the limit of the heliosphere (or beyond). It is easier to visually present the constantly changing density as a series of layers, otherwise the density at a given point in space will be a function of the inverse square of the distance.

The detected blueshifted telemetry frequency is a reflection of the average value of the velocity of the telemetry signal as received at earth from the spacecraft at any given point in time.

We know the index of refraction for EM waves has a value of 1 as measured in a vacuum on the earth's surface. (diffraction index)^2 = (relative permittivity)
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Littlebit
post Aug 9 2007, 02:36 PM
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An increasing blueshift, due to a change in the index of refraction implies that the speed of light is increasing with increasing distance from the sun. We should expect this to a very small degree, because the solar wind is thinning (the absolute vacuum of space is becoming more absolute). I don't recall that the calculations used by Anderson & Co. including any terms for the decreasing density of the helosphere.

There is a problem with this interpretation: The rate of blueshifting should decrease with increasing distance; but the anomally, on the scale that it has been detected, is quite linear. Still thinking out loud, this does not rule out a refractive solution if the density of the solar wind is roughly constant in the same region. Its too bad we do not have a pioneer-like probe well beyond the helopause. It would be easy to rule out / rule in such a solution simply by looking at the redshift of the sun.
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frankm
post Aug 9 2007, 04:00 PM
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The rate of blueshifting is decreasing with distance. Each segment, Figure 4 or Figure 5, represents the same acceleration magnitude but the time required to achieve the same magnitude, and same blueshift, of the previous period is increasing. Under Figure 4 of the article, Deen states,
QUOTE
Each of the slanting curves corresponds to the falling off by the inverse square of the distance.

I haven't found any mention in any of the Anderson&Co reports that the density of "something" is changing outbound from the sun.

I thought the Deen report was an interesting way to present the acceleration (blueshift) data. It makes it easier to visualize the persistence of the shift.
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frankm
post Aug 12 2007, 04:35 PM
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In order to see the progression of the spherical shells illustrated in Deen's report, I replicated his nine pair of data points in a spreadsheet and extended the shells inward and outward. Deen's spherical shells follow the standard formula for such volumes.

What I really need is a spreadsheet algorithm that uses the primary anomaly variable, the value of the blueshift. I would like to see is how close the blueshift converges to zero at the Earth 1 AU distance.

Is there a report that gives the actual blueshift value at 20 AU?
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frankm
post Aug 14 2007, 10:54 PM
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I found a neat site that allows one to put in a set of values and it returns the regression results.

http://people.hofstra.edu/stefan_waner/Rea...sionframes.html

My first set used R in and the refraction index and the second set R out and the refraction index. I didn't get a good fit with any regression process for R in, but had a near perfect fit with R out.

The best fit for the outer R gave an r = 1 the equation being y = ax^b with y =.000124956x^2

I suspect the way Deen extracted his data influenced the R in vs R out data sets, the actual refraction index being tied to the R out value.

This indicates that whatever is causing electromagnetic waves to change their velocity has a near perfect fit to the square of the distance.
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