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Thomas
approved users
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Posted: Sat Oct 7th, 2006 04:46 pm |
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Hi Lyndon,
First of all congratulations for getting your book published.
Here is something you might want to consider to include in your next edition:
I found that the well known acceleration Pioneer anomaly, which has given rise to all sorts of exotic theories including cosmological ones, can simply be explained by uncertainties for the value of the earth's rotation:
the earth's rotation corresponds to an acceleration at the equator of about 3 cm/sec^2. With the acceleration vector always directed towards the earth's center, this means that its projection on the direction towards the space craft always results in an apparent acceleration towards earth, as observed. As the space craft is not always near the zenith but on average presumably in all parts of the sky (and furthermore the observing station not at the equator), the projected acceleration will be somewhat less, let's say 1.5 cm/sec^2 (the actual diurnal variation will not be evident as the data analysis uses 5-200 day batch averages). Now although the earth's rotation is obviously being taken into account in the model, the point is that both the earth's radius and angular velocity are only known with relative accuracies of 1.5*10^-8 and 1.4*10^-8 respectively (see http://hpiers.obspm.fr/eop-pc/models/constants.html ). Combined, this results in a relative error for the rotational acceleration of about 3*10^-8, and if one assumes that this is in the sense of an underestimation, this would thus correspond to an absolute acceleration of 4.5*10^-8 cm/sec^2 towards earth. If one multiplies this by two (because the analysis uses two-way Doppler data and the error will occur both for the up- and down-link), this yields an acceleration of 9*10^-8 cm/sec^2 towards earth , in good agreement with the measurements.
See also my webpage Explanation of the Explanation of the Pioneer 10 and 11 Acceleration Anomaly in this respect.
Thomas
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lyndonashmore
Administrator
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Posted: Sat Oct 7th, 2006 05:45 pm |
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Hi Thomas,
Thanks for the thoughts on the book.
I agree wth you that there is nothing exotic about the Pioneer 10 acceleration. More likely something they have missed somewhere.
I had a look at your page on it. Not sure how the Earth's rotation explains an acceleration towards the sun.
Radio metric data from the Pioneer 10/11, Galileo, and Ulysses spacecraft indicate an apparent anomalous, constant, acceleration acting on the spacecraft with a magnitude $\sim 8.5\times 10^{-8}$ cm/s$^2$, directed towards the Sun
http://www.arxiv.org/abs/gr-qc/9808081
Any thoughts?
Cheers,
Lyndon
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Thomas
approved users
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Posted: Sat Oct 7th, 2006 05:59 pm |
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Hi Lyndon,
Due to the beamwidth of the Pioneer antenna, it can not be distinguished whether the acceleration is towards the sun or towards the earth (as pointed out in Anderson's et al.'s paper). It is merely an assumption in those papers that it is towards the sun.
On the other hand, the ground station can obviously only collect data when on the near side of the earth as seen from the space craft, and thus there will be a net acceleration towards the earth which will not be completely removed by filtering out any sinusoidal diurnal variations.
Thomas
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lyndonashmore
Administrator
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Posted: Sat Oct 7th, 2006 06:34 pm |
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lyndonashmore
Administrator
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Posted: Sat Oct 7th, 2006 08:09 pm |
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Rght Thomas,
I am getting there now.
the earth's rotation corresponds to an acceleration at the equator of about 3 cm/sec^2
Is this the centripetal acceleraton of an object on the Equator? If not then they have the same value - just worked it out!
If so, are we saying that the observing station is accelerating at this rate towards the centre of the Earth i.e. away from the Pioneer. Wouldn't this appear as the space ship accelerating away from the sun and not towards it?
Cheers,
Lyndon
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lyndonashmore
Administrator
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Posted: Sun Oct 8th, 2006 08:46 am |
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Thinking about this, if it is the centripetal acceleration we are looking at, then wouldn't it not show up at all?
Centripetal acceleration will just change the direction of the observing station, not its speed. Doppler only measures radial velocities or speeds and this acceleration will not change the radial speed.
Am I on the wrong track?
Cheers,
lyndon
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Thomas
approved users
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Posted: Sun Oct 8th, 2006 05:31 pm |
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Hi Lyndon,
The centripetal acceleration vector of the observing station varies of course also sinusoidally: it always points from it to the centre of the earth, that is (on average) away from the space craft (because obviously there aren't any data when the observing station is on the far side of the earth). As seen from the observing station, the space craft will therefore show the opposite acceleration. In principle this is of course being taken into account in the model, but the point is that the constants assumed for this have only a limited accuracy, and the accepted error for this (as for instance given in http://hpiers.obspm.fr/eop-pc/models/constants.html ) results practically exactly in the observed discrepancy (this is actually if the assumed centripetal acceleration is fractionally larger than the actual one , not smaller as I suggested before). So for instance, assuming the earth's radius just a few centimters too large produces the observed effect.
Thomas
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Peter Carroll
Guest
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Posted: Mon Oct 9th, 2006 09:18 am |
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If the Anderson deceleration can account for redshift then it may arise from something more fundamental and cosmological than you suggest.
If the universe consists of a vorticitating hypersphere (ie a 3-sphere undergoing the higher dimensional analogue of rotation about all 3 dimensional axes simultaneously) then we could perhaps apply a modified form of Godel's rotating universe model:
W2 = 2piGM/Vh for angular velocity, where Vh equals hysperspherical surface volume,
This yields a centrifugal acceleration of c2/L to match the centripetal effect of the gravity GM/L2, which also equals c2/L. This yields a non expanding universe with an omnidirectional deceleration parameter for linear motion, ie the Anderson deceleration.
For the derivation see The Hyperspin Conjectures on my http://www.specularium.org
Pete Carroll
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lyndonashmore
Administrator
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Posted: Mon Oct 9th, 2006 03:09 pm |
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Hi Peter,
This is my interest in pioneer 10 (and everyone else's) - is the 'acceleration' tied up with our redshift theories! Trouble is of course the signals are blueshifted! However, I have an idea and am working on it!
I have had a look at your website but I think I need a gentle introduction to get me thinking along the right lines.
Cheers,
lyndon
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lyndonashmore
Administrator
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Posted: Mon Oct 9th, 2006 03:15 pm |
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Hi Thomas,
I am still not with you on this. The ground station does not measure accelerations it measures doppler shifts in the signals and equates these to velocities. It is from the change in these velocities over time that they come up with the decceleration.
see page 5 of
http://www.arxiv.org/PS_cache/gr-qc/pdf/9808/9808081.pdf
the Earths rotation will have no effect on these velocities as it is not radial (even though the acceleration is)
Cheers,
Lyndon
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Peter Carroll
Guest
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Posted: Tue Oct 10th, 2006 03:19 pm |
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Lyndon there's basically two major threads running in parallel on specularium, firstly, 3 dimensional time as part of a 6 dimensional spacetime geometry that explains many aspects of quantum and particle physics, hopefully.
Secondly I believe that its possible to interpret most of the data of cosmology in terms of our ocupying a 3 dimensional hyperspherical surface of fixed size which undergoes a sort of higher dimensional analogue of rotation. The rotation prevents gravitational collapse and between them the balanced forces of rotation and gravity create the retarding effect on linear motion that we observe as galactic redshift and the Pioneeer anomaly. Furthermore, hyperspherical lensing creates the further illusion that the illusory expansion is acellerating by skewing the apparent magnitude of type 1 supernovae and hence their distance estimates.
The hypothesis has grown as the papers were added, the earlier ones contain only parts of it.
The CMB presumably represents merely the temperature of the diffuse local intergalactic gas.
In my model the universe is basically finite and unbounded in both space and time, it has no start or finish or edge, but it has limited extent because it curves round in both space or time to close itself.
Pete.
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