The Pioneer Anomaly described here is a clear indication that currently accepted theory is seriously flawed. One could try postulating the existence of whatever is required to overcome the problem, but what would be the point?

The anomaly between current theory and the available evidence from the Pioneer missions defied explanation for around 30 years, until a recent computer simulation demonstrated that the anomaly was due only to an asymmetry in the spectrum of thermal radiation off all parts of the spacecraft. According to the simulation the residual acceleration was exactly equal to the Pioneer anomaly and pointing away from the earth, accelerating Pioneer in the direction of the earth.

But how was the thermal radiation spectrum for the simulation derived? How can it differ from the results from all previous analyses which treated every relevant component of the spacecraft individually and thoroughly (e.g. the above link)? The information plugged into the computer simulation obviously didn't compare with the results from other studies. Why didn't it?

A computer simulation based on ill defined methodology is not a valid argument for the removal of the Pioneer anomaly. The anomaly still remains a very significant thorn in the side of current theory.

And why do the outer planets exhibit a similar anomalous acceleration toward the sun if such an anomaly doesn't exist?

The Pioneer Anomaly is of course not an anomaly in nature, but an illusion which stems from an error in our current understanding of the universe.

The following graph shows the gforce differences between current theory and the Zero Origin Concept (ZOC). The two theories do not compare, so at least one of them is wrong. Since the anomaly manifests itself in current theory, that theory is automatically flawed, and if the difference between current theory and ZOC is equal to the Pioneer anomaly, ZOC complies with what is observed.

The light blue curve represents the normal gforce change per radius from the sun, while the black curve, which follows almost the same path, gives the gforce change according to ZOC. The red curve is the difference between the blue and black curves. Even on the Sun's surface the difference would be barely noticeable. The gforce at that radius is 273 m/sec^2 while the difference is only .54 m/sec^2.

All of the graphs in this article were mathematically generated using Qbasic. They are not artistic impressions.

In order to compare with the Pioneer Anomaly, the sun's mass is necessarily increased from 1.99e30 to 1.990156e30 kg, which is an increase of around 26 times the mass of the earth, while the apparent radius between the sun and the Pioneer spacecraft is not as it seems.

G*M/r/c^2 gives the unit time difference between a clock in deep space and a clock within a gravity well. If 1 is the time unit in deep space, for a clock on the earth's surface where G = 6.67e-11, M = 5.97e24 and r = 6400000, the time unit increases to 1 + G*M/r/c^2 = 1.00000000069132 units. The time unit increases by 6.9132e-10 units.

The value of c for any circumstance can be derived from the transposed equation; c = sqr(G*M/r/t). The equation can even be used to determine the time rate attributable to the gravitational potential of the universe. i.e. If t =.5 and the radius of the universe is 1.26e26 meters (13.3 billion light years), the required effective mass of the universe is 8.48e52 kg. "effective mass" because the rest of the universe will have evolved to much the same level as the local universe, but only what is observed of the past universe can be of consequence here. The resultant light speed is; sqr(6.67e-11*8.48e52/1.26e26/.5) = 299633639 m/sec, which is near enough. This sets the maximum rate for the passage of time anywhere in this part of the universe.

The radius and mass of the universe can be juggled to achieve the required outcome. For which there are unlimited combinations. But fiddling with (t =.5) leads to errors which are later described.

The Earth, Sun and Milky Way galaxy also contribute significantly to the local speed of light.

c on the earth's surface (ce) 
G=6.67e-11 : Me=5.97e24 kg : re=6400000 meters
ce = sqr(G*Me/re/.5) = 11155 m/sec

c per Sun at 1 AU radius (cs)
G=6.67e-11 : Ms=1.99e30 kg : rs=1.5e11 meters
cs = sqr(G*Ms/rs/.5) = 42069 m/sec

c per galaxy at the galaxy radius (cg)
G=6.67e-11 : Mg=2e41 kg : rg=6e20 meters) 
cg = sqr(G*Mg/rg/.5) = 210871 m/sec. 

The sum of the lot including the input from the universe gives the speed of light on the earth's surface.

The input to the speed of light from the sun at any point along Pioneer's trajectory depends on its distance from the sun. That's the only significant variable in the Sun-Pioneer relationship. The inputs from the galaxy and universe remain constant. The earth is of no consequence in this case.

The measuring unit used to measure Pioneer's distance from the sun is dependent on the speed of light, and because light speed varies with radius from the sun, so too does the measuring unit. With cu representing c for the universe, cg for the galaxy, cs for the sun, the measuring unit variation is according to
1*((cs+cg+cu)^.5 / (cg+cu)^.5)
cu and cg remain constant in this case (299633639 and 210871 respectively). So every meter close to the sun along the trajectory of a Pioneer spacecraft is longer than it seems. In order to compare with the Pioneer anomaly, the mass of the sun is increased from 1.99e30 to 1.990156e30 kg (+ 26 earth masses).

Note that precise masses are unnecessary here. 
If the sun's mass is presumed to be 2e30 for 
example the added mass required to achieve a 
common result changes only slightly (+++++++). 
    (1) (1.99e30 sun mass) 
(1.99e30 + 1.56e26) / 1.99e30 = 1.0000784 
    (2) (2e30 sun mass)
(2e30 + 1.568e26) / 2e30 = 1.0000784 

Next are the results from step 1 of the attached program based on this logic. The program runs in Qbasic, which had the potential to be one the greatest communication tools of the 20th century. And it's not supported by Windows 7 !!!

 299633638.7328991 c per universe.
 210871.2087191295 c per galaxy.
 1.990156D+30 kg sun mass (increased from 1.99e30).
 616880.7484418404 c per sun at 4.650666666666667D-03 AU radius.
 300461390.69006 total c at this point in space.
 1.001028139204314 measuring unit variation.
 697600000 meter normal segment length.
 698317229.9089295 adjusted segment length.
 697600000 normal radius (1).
 698317229.9089295 adjusted radius (2).
 272.7507581695564 gforce(1) m/sec^2  (M = 1.99e+30).
 272.2121080085851 gforce(2) m/sec^2  (M = 1.990156e+30).
-.5386501609713719 gforce(2) - gforce(1) (real-phony).

At a distance equal to the average orbit radius of the earth around the sun, the sun's mass gives a gforce of GM/r^2 : 6.67e-11 * 1.99e30 / 1.5e11^2 = .00589924 m/sec^2. According to the next graph, the gforce error at that radius is -1.1e-6 m/sec^2, which is more than 5000 times less than the gforce from the sun. Slight estimation errors in solar radiation pressure would also help conceal the error this close to the sun.

The error curve from the original graph is now magnified 100000 times. A simulation of the Pioneer anomalous acceleration curve from this address is also included. The horizontal line representing zero error by current theory and the curved line, which is the true zero error according to ZOC, coincide at around 12.5 AU from the sun, where the result switches from negative to positive.

The relationship between the zero error line per current theory and the true zero error curve is the difference between current theory and ZOC, and for these circumstances it will never change. Forced errors resulting from aligning either theory with what is observed will alter the curve alignments but won't alter the relationship at all.

The current mass for the sun is determined by orbit radii and orbital speeds, and will naturally provide the best fit with the available evidence, according to predictions of the chosen theory.

Local to the earth the gforce error per current theory is negative, so in order to reduce the error the chosen sun mass will be greater than if there was no error. The zero line on the graph is shifted downward, in the direction that reduces the error. But whatever mass is chosen to cancel the error for one orbit radius, it's still going to show up at other orbit radii. The Pioneer anomalous acceleration curve soundly supports that view.

But if the full extent of the -1.1e-6 m/sec^2 gforce error local to the earth is counteracted by the presumption of an appropriate mass increase for the sun, the error in planetary orbital speeds, or orbit radii, would become very apparent.

G = 6.67e-11
M = 1.99e+30
r = 1.5e11 (1 AU)
gforce at 1 AU: G*M/r^2 = 5.9e-3 m/sec^2
error = -1.1e-6 m/sec^2
M2 = (gforce - error) * r ^ 2 / G = 1.9903711e+30 kg
(G * M / r) ^ .5  = 29747.045 m/sec orbital speed
(G * M2 / r) ^ .5 = 29749.818 m/sec orbital speed
2.77 m/sec orbital speed difference.

Because the error adjustment required to align the two curves is 5.5e-10 m/sec^2, the orbital speed error for the earth is only 1.39e-3 m/sec.

Evidence from observation at all radii would naturally be juggled to achieve the best fit.

Qbasic is currently not supported by Microsoft, but finding a copy shouldn't be too difficult. Any Windows version prior to Windows 7 will run it. The following program is easily accessed by Qbasic if it's stored in the same folder as Qbasic. Simply Copy-Paste the program into Notepad directly off this screen and save it per "All Files" with a .BAS extension.

Microsoft Qbasic.exe and Qbasic.hlp are now available in the form of a self extracting zip file that can be downloaded from this address.

The graphics attached to the end of the program are set so that all presumed errors resulting from aligning current theory with what is observed have been accounted for (false zero is set, etc.)

'-----The Program----
' Ctrl_Break halts the program. ESC exits. 
DEFDBL A-Z   ' sets 16 digit precision. 
f$ = "  Press 'f' for fast forward"
c = 300000000#
G = .0000000000667# ' gravitational constant.
Mu = 8.48D+52       ' kg universe mass.
ru = 1.26D+26       ' meters (13.3 billion light years).
tu = .5             ' Time constant for the universe.
cu = SQR(G * Mu / ru / tu) ' Light speed contribution
                           ' from the universe.
PRINT cu; "c per universe. "
Mg = 2D+41          ' Galaxy mass.
rg = 6D+20          ' Galaxy radius.
cg = SQR(G * Mg / rg / tu)
              ' Light speed contribution from the galaxy.
PRINT cg; "c per galaxy. "
au = 150000000000#  ' meters (1 earth orbit radius)
Ms = 1.99D+30       ' Original sun mass.
Mx = Ms + 1.56D+26  ' Mass error is 26 times the mass of
                    ' the earth.
PRINT Mx; "kg sun mass (increased from 1.99e30)."

rs = 697600000#     ' Sun radius.
ds = rs 
' The segment length added to the Pioneer radius from the 
' sun for each step along its trajectory is equal to the 
' sun's radius. Increasing the segment length reduces the 
' number of steps needed to negotiate a sufficient 
' distance to highlight the anomaly, but the outcome is 
' affected slightly. In order to eliminate the need for 
' tediously stepping through the program, a fast forward 
' option is provided. 


DO: s$ = INKEY$: LOOP UNTIL s$ <> ""
IF s$ = CHR$(27) THEN END

aa: LOCATE 1, 1
cs = SQR(G * Ms / rs / tu)
PRINT cs; "c per sun at"; rs / au; "AU radius.               "
totlc = cs + cg + cu
PRINT totlc; "total c at this point in space.     "
mtr = (cs + cg + cu) ^ .5 / (cg + cu) ^ .5

' Light speed and the measuring unit are not directly
' comparable. Comparison can only be made by taking the
' square root of the light speed calculation. Or by
' squaring the measuring unit if the result is to be
' compared in the realm of light.

PRINT mtr; "measuring unit variation.    "
PRINT ds; "meter normal segment length.  "
PRINT ds * mtr; "adjusted segment length.  "
st1 = st1 + ds * mtr  'st1 holds the adjusted radius
PRINT rs; "normal radius (1).  "
PRINT st1; "adjusted radius (2).  "
gf1 = G * Ms / rs ^ 2
PRINT gf1; "gforce(1) m/sec^2."
gf2 = G * Mx / st1 ^ 2
PRINT gf2; "gforce(2) m/sec^2."
PRINT gf2 - gf1; "gforce(2) - gforce(1) (real-phony)."

IF rs > 5E+11 THEN GOSUB ax
       ' lesser radii are beyond the graphics limit

  'Remove the next switch to compare the 100 X magnification.
'CIRCLE (100 + rs / 1.5E+10, 200 - (gf2 - gf1) * 1.25E+08), 0, 11
  'Compare the gforce multipliers used in the CIRCLE statements.
  'The 100000 X magnification scale doesn't apply of course.

IF f4 <> 1 THEN PRINT f$: DO: s$ = INKEY$: LOOP UNTIL s$ <> ""
IF s$ = CHR$(102) THEN f4 = 1
IF s$ = CHR$(27) THEN END
rs = rs + ds
IF rs > 7E+12 THEN END

ax: 'This has been shifted here to avoid word wrapping lines.
CIRCLE (100 + rs / 1.5E+10, 200 - (gf2 - gf1) * 1.25E+11),0,11

ad: COLOR 7
LOCATE 21, 27: PRINT "100000 X magnification (y scale)"
FOR s = 1 TO 17: READ a, b
LINE (100 + aa * 10, 280 - bb *12.5)-(100+a*10, 280-b*12.5),12
aa = a: bb = b
LINE (90, 280)-(500, 280)
LINE (90, 380)-(220, 380), 7
LINE (90, 180)-(220, 180), 7
LOCATE 12, 9: PRINT "8e-10"
LOCATE 24, 8: PRINT "-8e-10"
LOCATE 13, 9: PRINT "m/s^2"
LOCATE 20, 9: PRINT "False"
LOCATE 21, 9: PRINT "scale"
LOCATE 18, 46: PRINT " False zero "
LOCATE 18, 12: PRINT "00"
LOCATE 18, 25: PRINT "10"
LOCATE 18, 36: PRINT "20 AU"
LINE (110, 240)-(110, 420)
LOCATE 27, 14: PRINT "Earth"
LINE (100, 100)-(400, 100)
LINE (100, 150)-(400, 150)
LINE (100, 200)-(400, 200)
LINE (100, 250)-(400, 250)
LINE (100, 300)-(400, 300)
LINE (100, 350)-(400, 350)
LINE (80, 400)-(400, 400)

LINE (100, 100)-(100, 400)
LINE (150, 100)-(150, 400)
LINE (200, 100)-(200, 400)
LINE (250, 100)-(250, 400)
LINE (300, 100)-(300, 400)
LINE (350, 100)-(350, 400)

  'The following data generates 
  'the recorded Pioneer anomaly. 
DATA 5.2,.6,9.6,1.5,12.4,6.4,14,8,17,8.1,19,9,22,8
DATA 23,8.8,26,8.6,28,8.8,31,8.4,34,8.3,35,7.8,37,8.4
DATA 40,7.5,43,8.2,45,8.4

'-----Program end------

Note the number of calculations required to determine the predicted variants from current theory. And every one of those calculations become the quantitative data value determining the position of each dot on the graph.

A mismatch between current theory and the zero origin concept is guaranteed. The fact that the mismatch can so closely resemble the Pioneer anomaly is nothing short of a miracle if ZOC is wrong.

The Pioneer anomaly has far reaching consequences for all theories which attempt to describe the universe.

The effect of the sun's mass on the speed of light at any point along a Pioneer trajectory is easily determined. But light speed variations for any point in space within the local galaxy are not so clear. Orbit speeds are noted to remain reasonably constant for any radius around the galaxy center, so a graph of the average matter density enclosed within all orbit radii can be readily plotted. But the required enclosed matter densities don't compare with what is observed.

This graph shows the expected orbital speeds for different radii from the galaxy center according to the apparent observed distribution of matter.

Precise matter distribution isn't required to demonstrate my point here. An approximation is all that's needed.

With a galaxy mass of 2e41 kg enclosed within a radius of 6e20 meters, matter in a circular orbit around its perimeter will be traveling at 149 km/sec. If that orbit speed is maintained throughout the galaxy, this is the resultant graph of enclosed average matter densities.

The next graph is a close match to what is observed. The galaxy mass is necessarily increased to 4.34e41 kg, so enclosed average matter densities will be too high. But such orbital speeds can't be generated with anything less (outer orbital speeds are noted to be slightly faster than inner speeds).

The next graph is according to ZOC. The estimated galaxy mass and observed radius are necessarily altered. In this case, mass is increased from 2e41 to 5.08e41 kg, while the galaxy radius is increased from 6e20 to 7.02e20 meters.

The galactic center is in a more advanced stage of evolution than the frame at the galaxy perimeter from which all measurements are taken. The higher speed of light at the center generates an added depth of dimension to be attached to what is observed from the perimeter. Everything at the center exists for a longer time than can be comprehended from the perimeter. The radius to the center is compressed into the limit of that comprehension and the distance appears closer than it really is.

The zero mark is necessarily shifted to the limit of our comprehension.

The galaxy mass and radius can be whatever is required to comply with observation. That's the only way the true galaxy properties can be revealed in a zero origin universe.

In the big bang universe, only the space-time between non gravitationally bound systems is expanding. The expansion rate is noted to be almost constant at around .0233 m/sec per light year (9.46e15 meters).

This multi scaled graph shows the consequences of the stretching space-time from the big bang to the present day as a galaxy with the properties of the Milky Way galaxy is shifted between those two boundaries. Orbit speed refers to a mass in orbit around the perimeter of the galaxy (mass = 2e41 kg : radius = 6e20 meters).

Everything in the galaxy frame remains constant, but the stretch of space-time over the distance to the big bang has diminished every detail to the point of non existence from where we are in the present. Over the 13 billion light years the expansion rate has reached the speed of light. Everything within the galaxy frame at that distance is retreating from the present at light speed. From a viewpoint in the present, nothing in the galaxy will move. Light speed will be zero.

Orbit speed, redshift and the speed of light all alter at the same linear rate in a big bang universe. Space-time is simply stretched.


The zero origin universe naturally emerged from non existence where, light speed, mass, gforces, the gravitational constant, dimension and any form of relativity were all meaningless. As was "were", and "was".

For either universe, its radius is measured in a linear fashion according to redshift. But the observed redshift in a zero origin universe is only a measure of the frequency change in the natural harmonics of the elements as the universe evolves. The simple graph for the big bang universe cannot apply here. i.e. The natural resonance of the Caesium atom configuration used in atomic clocks is known to alter proportionally to GM/r/c^2 and, sqr(1-v^2/c^2) or sqr(c^2-v^2)/c, depending on the application. A proper analysis of the Pound and Rebka shot tower experiment shows that the frequency generated in the radioactive iron sample used in the experiment altered proportionally to GM/r/c^2 as well. Nowhere has it ever been demonstrated to be otherwise.

Next is the ZOC graph comparison with the previous multi scaled graph for the big bang universe. All courtesy of Qbasic, and Windows 98 where the resulting graphics can be copy-pasted.

In the following set of formulas, the value of cx is incremented from zero until it equals the value of c, at which point the redshift rate is equal to c, and the universe ceases to exist.

1 * (c - cx) / c   relative meter (mtr). 
G * (c - cx) / c   gravitational 'constant' (G').
r * (c - cx) / c   radius of the universe (r'). 
rg * (c - cx) / c  relative galaxy radius (rg'). 
M * (c - cx) / c   relative mass of the universe (M'). 
Mg * (c - cx) / c  relative mass of the galaxy (Mg'). 
Acceleration is the only test for mass, and is unidirectional. 

sqr(G'*M'/r'/tu) gives the value of c at each stage of 
evolution (tu=.5). 

Orbital speed is according to (G'*Mg'/rg')^.5 
At the 50% redshift stage of evolution; 
(3.335e-11 * 1e41 / 3e20)^.5 = 105436 m/sec orbital speed. 
For the big bang universe; 
(current speed / 2) = 149000 / 2 = 74500 m/sec orbital speed. 

Orbital speed discrepancies between the two universes are starkly obvious, and the true universe is revealed.

The formula I've used to determine the redshifting of spectral lines is based on the formula for the slowing of natural atomic oscillators within any gravity well; redshift = 1 - (G*M/r/c^2) / (G'*M'/r'/c'^2). The Hubble Constant demands that the redshift graph be a straight line connecting the present and the infinitely distant origin of the universe, which is only 13 billion light years away as measured by the measuring units of the present.

Even infinity is within the scope of our comprehension. But we can only perceive the universe according to our circumstances of existence.

Other consequences of the zero origin.

From the Zero Origin Concept; everything that exists in the present is advancing through the past of everything else in the universe. The rate of advance toward all matter in the universe in every direction is the speed of light. The matrix of the universe in the present holds all matter in a reasonably constant distance relationship so that everything follows through the past of everything else in the drive toward the future.

On the earth's surface, the matter density of the universe is reasonably uniform. Apart from the earth, sun and local galaxy, there are no spikes of consequence in the distribution of matter. The most significant local spike is the gravity well of the earth. Everything on the earth's surface is driving toward all of earth's matter at the rate of sqr(G*M/r/tu) = 11155 meters per second.

If the second' time unit in deep space is equal to 1 second here on earth, the clock slowing at 6400000 meter radius from the earth's center of mass per G*M/r/c^2, is 6.913e-10 sec'/sec'.

1/sqr(1-v^2/c^2) gives the unit time rate change when clocks are in motion relative to the ECI frame. Giving v in the equation the value of earth's input to the speed of light (11155) results in 1.0000000006913 increase in the localized time unit. The difference is, 1/SQR(1-v^2/c^2)-1 = 6.913e-10 sec/sec. Which is the same result as above.

If matter is moving in any direction relative to the ECI frame, including up or down, 1/sqr(1-v^2/c^2) applies. The fact that it applies in this case is evidence that anything fixed with the ECI frame is still somehow moving relative to that frame, at the rate of 11155 m/sec.

(v=11155) changes with altitude, and the two equations compare for any radius. And the rate of change is linear.

If the time constant "tu" is not .5 those numbers will NOT compare.

It's also essential that the numbers compare at every stage of evolution.

Since clock time rates alter in a linear fashion per distance from a gravitating body and are never directly related to light, i.e. GM/r/c^2, sqr(1-v^2/c^2), sqr(c^2-v^2)/c, the appropriate equation for the relative universal time unit (.5) change rates as the universe evolves is; tu' = tu*(G'*M'/r'/(c-cx)^2) .

At first glance, the time rate graph may seem to be wrong because it doesn't match the straight line graph depicting the degree of redshift. But that's not so. At the 100% redshift mark, time stops altogether, so the graph plot must rise to infinity.

The time unit at each stage of evolution would necessarily remain constant relative to all measurements at the time; tu' = tu*(G'*M'/r'/c'^2) .

The proportionality between everything in the universe is maintained.

Near the truly infinitely distant origin, where distance is measured according to a measuring unit which is barely more than 0/1 by comparison, all length measurements in that realm, which encompass relatively enormous distances, are all compacted into the 13.3 billion light year limit of our perception. Within that compacted dimension is where the Cosmic Microwave Background Radiation resides.

Observed galaxy formations at distances less the limit of perception are very much part of the present relative to the background.


The Schwarzchild radius for the black hole generated by a 4.3178e33 kg mass (2GM/c^2) is equal to the earth's radius (6400000 meters). If that mass is housed within earth's radius the speed of light increase at the surface is sqr(G*M/r/tu) = 299998572 m/sec. 1/SQR(1-v^2/c^2) extends the time unit to infinity. Time will stop. But the speed of light generated from all sources has changed. It's now c + 3e8 = 6e8 m/sec. If v = 3e8 the relative time unit increases to only 1.155 (per 1/SQR(1-v^2/c^2)). Our rate of existence is based on the speed of light, and the event horizon of the presumed black hole is the current comprehension limit. But there is no physical boundary.


The Zero Origin Concept