View source for 50 out 1001 Mersury's perihelion precession advance

{{Infobox paper
| title = 50 out 1001 Mersury's perihelion precession advance
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6432.pdf Link to paper]
| author = [[Joe Alexander Nahhas]]
| keywords = [[Perihelion]], [[real]], [[time]], [[astronomy]], [[relativity]], [[Einstein]]
| published = 1973
| num_pages = 25
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6432.pdf here]

==Abstract==

Mercury's perihelion is an experimental error made on Earth and the proof is attached and I dare the human race to prove it wrong. I included 50 out of 1001 ways to caalculate Mercury's perihelion precession advance in 1970's

==Overview==

[[Joe Alexander Nahhas]] holds that the 43 arc seconds per century of anomalous perihelion advance of Mercury — the observation that made [[General Relativity]] famous — is not a physical motion of the orbit at all but an artefact of measuring a planet's orbit about the Sun from a moving Earth. His governing distinction is between what he calls '''event time''' (when something happens) and '''real time''' (when it is measured), and the '''shift time''' between them. On his account "modern and Nobel physicists and astronomers measure in present time and calculate in past time" and then attribute the difference to warped space-time. The 43 arc seconds are, in his phrase, "Einstein's numbers without Einstein = Illusions."

The paper's rhetorical form is unusual and is part of its content. Nahhas announces himself as "the founder of real time astronomy July 21 1969 at age 11," dates his mathematics to 1971 and his physics to 1973, and states that he is "not only the greatest physicist of all time but the only physicist since the beginning of time because I know/knew what time it is and all others do/did not." The body then presents fifty numbered derivations — each labelled "Modern and Nobel error # ''n''" — every one of which is claimed to yield 43 arc seconds per century. The declared purpose is to show that the figure is so easily obtained from ordinary solar-system quantities that it cannot be evidence for anything.

==The argument==

===The visual-size relation AC = BD===

The paper opens with an origin story: watching Apollo 11 rise in July 1969, Nahhas noticed the rocket appearing to shrink and concluded that apparent size encodes distance rather than physical change. If an object of true size ''C'' at distance ''A'' appears with size ''D'' at distance ''B'', then from the identity ''A'' = ''B'' + (''A'' − ''B'') he obtains (''A''/''B'')''C'' = ''C'' + [(''A'' − ''B'')/''B'']''C'', and by comparison with ''D'' = ''C'' + (''D'' − ''C'') concludes

: ''AC'' = ''BD'' = actual distance × actual size = visual distance × visual size,

with ''D'' − ''C'' = [(''A'' − ''B'')/''B'']''C'' as the "visual contraction." Differentiating ''AC'' = ''k'' and separating variables gives ''A'' = ''Be''<sup>''i''ω''t''</sup> and ''C'' = ''De''<sup>−''i''ω''t''</sup>, so that "a real object (classical) of size ''C'' has a visual (quantum) of size ''D'' = ''Ce''<sup>''i''ω''t''</sup>." Taking the real part along the line of sight yields ''D''<sub>x</sub> = ''C''√[1 − sin<sup>2</sup>(tan<sup>−1</sup> ''v''/''c'')] ≈ ''C''√[1 − (''v''/''c'')<sup>2</sup>] — the Lorentz factor recovered, on his reading, as pure perspective. The difference ''D'' − ''C'' is then labelled "visual illusions = (Einstein's relativity theory)."

===The fifty routes to 43===

The application is immediate. Nahhas defines δθ'<sub>0</sub> = 70.75, which he calls Mercury's angular velocity in arc seconds per century, and then multiplies it by a succession of dimensionless ratios drawn from solar-system data, each of which is close to 0.61:

* Distance ratio: 70.75 × [1 − 58.2/149.6] (errors #1, #7)
* Light-signal travel times: 70.75 × [(194 − 498.67)/498.67], from ''T'' = ''r''/''c'' (#2)
* Orbital velocities: 70.75 × [(48.1 − 29.8)/29.8] (#3, #8)
* Surface gravities: 70.75 × [(3.8 − 9.8)/9.8] (#4, #9)
* Photon momentum and energy shifts d λ/λ = −d''p''/''p'' (#5, #6)
* Kepler's law: 70.75 × [(88/365.26)<sup>2/3</sup> − 1] (#16)
* Newton's ''v'' = √(''GM''/''r''): 70.75 × [(29.8/47.9)<sup>2</sup> − 1] and 70.75 × [(149.6/58.2)<sup>1/2</sup> − 1] (#17, #18)
* Le Verrier: the angular-speed term ''v''/''r''<sub>0</sub> that arises if Mercury's motion is referred to the Sun but measured from a moving Earth (#21–#25)
* Angular sizes: (''D''/''C'')(29.8/29.335) − 1 using the radii of Mercury and Earth (#15)
* Earth's axial tilt: 70.75 × (1 − sin 23.44°) (#46)
* The Sun–Mercury mass ratio: π(''m''/''M'') converted to arc seconds per century (#48)

Chapters six and seven repeat the same ratios inside the complex-exponential machinery, writing each as −2 sin<sup>2</sup>[½ cos<sup>−1</sup>(ratio)]·δθ'<sub>0</sub>, and then again through a Fourier transform of ''e''<sup>''i''ω''t''</sup> over one orbital period, which returns 42.5 arc seconds per century (#42–#45).

===Newton's equation "solved wrong for 350 years"===

The final chapter is the one piece of independent derivation. Nahhas writes the state of a body as ''S'' = ''mr'' and refuses to hold mass constant, so that ''F'' = ''m''γ + 2''m''&prime;''v'' + ''m''&Prime;''r''. In polar form this gives d<sup>2</sup>(''mr'')/d''t''<sup>2</sup> − (''mr'')θ&prime;<sup>2</sup> = ''F''(''r'') together with d(''m''<sup>2</sup>''r''<sup>2</sup>θ&prime;)/d''t'' = 0. Solving by separation of variables yields ''m'' = ''m''<sub>0</sub>''e''<sup>(λ<sub>m</sub>+''i''ω<sub>m</sub>)''t''</sup>, ''r'' = ''r''<sub>0</sub>''e''<sup>(λ<sub>r</sub>+''i''ω<sub>r</sub>)''t''</sup> and θ&prime; = θ&prime;<sub>0</sub>''e''<sup>−2[(λ<sub>m</sub>+λ<sub>r</sub>)+''i''(ω<sub>m</sub>+ω<sub>r</sub>)]''t''</sup>, so that

: ''r''(θ, ''t'') = [''a''(1 − ε<sup>2</sup>)/(1 + ε cos θ)]·''e''<sup>(λ<sub>r</sub>+''i''ω<sub>r</sub>)''t''</sup>.

Setting ''t'' = 0 recovers the classical ellipse; the difference between the two is what Nahhas calls the relativistic effect. Putting λ = 0 and identifying ω<sub>m</sub>τ<sub>0</sub> = tan<sup>−1</sup>(''v''°/''c''), ω<sub>r</sub>τ<sub>0</sub> = tan<sup>−1</sup>(''v''<sub>0</sub>/''c'') gives his closed formula

: Δθ = −(720 × 36526 × 3600/τ<sub>0</sub>)·√[(1 − ε<sup>2</sup>)/(1 − ε)<sup>2</sup>]·[(''v''° + ''v''<sub>0</sub>)/''c'']<sup>2</sup>

which for ε = 0.206, τ<sub>0</sub> = 88 days and ''v''<sub>0</sub> = 48.14 km/s returns 43 arc seconds per century (#49). His summary formulation is "Real (complex numbers solution) = real numbers solution + relativistic effects," relativity thus being demoted to the imaginary part of a Newtonian solution.

==Assessment==

The paper's one substantive idea deserves to be stated plainly, because it is not absurd. Formula #49 is a genuine derivation rather than a ratio, it contains the right physical ingredients — eccentricity, orbital period, and (''v''/''c'')<sup>2</sup> — and it is of the correct order. That the anomalous advance scales as (''v''/''c'')<sup>2</sup> is not in dispute; it is why the effect is largest for Mercury. A framework in which relativistic corrections appear as the imaginary part of a complex-valued Newtonian orbit is a legitimate thing to explore, and Nahhas is entitled to insist that measurement geometry be separated from dynamics before any residual is called a new physical effect.

Almost everything else in the paper undermines that idea rather than supporting it. The central constant δθ'<sub>0</sub> = 70.75 is described as Mercury's angular velocity in arc seconds per century, but it is not: Mercury completes about 415 orbits per Earth century, roughly 5.4 × 10<sup>8</sup> arc seconds. The quantity 70.75 is produced by the expression (2π/88·24·3600)(180/π)(36526/88)(3600), which mixes radians per second with a dimensionless period ratio and a degrees-to-arc-seconds conversion; the result carries no coherent unit. Since 43/70.75 = 0.608, the entire catalogue of fifty "errors" amounts to the observation that many ratios formed from solar-system data happen to lie near 0.61 — the Mercury/Earth orbital radius ratio 58.2/149.6 = 0.389 (so 1 − 0.389 = 0.611), the velocity ratio 29.8/48.1 = 0.62, (88/365.26)<sup>2/3</sup> = 0.39, sin 23.44° = 0.398. These are not fifty independent confirmations; they are one arithmetic coincidence restated fifty times, and the coincidence exists because the same two orbits supply all the numbers.

The paper is also internally inconsistent in its own arithmetic, which matters because the arithmetic is the argument. On page 3 the Sun–Mercury distance is given as 5.82 × 10<sup>9</sup> m, a factor of ten too small (the correct value is 5.79 × 10<sup>10</sup> m); with that figure the stated ratio yields −68, not −43. In section 1.1 and again in 2.1 the same expression is written as (58,200,000,000 − 149,600,000)/149,600,000 — Mercury in metres against Earth in kilometres — which evaluates to 388, not −0.61, while the result is still reported as 43. The data table gives Earth's orbital period as 375.26 days rather than 365.26, and Earth's radius appears as 6731 km on one page and 6371 km on the next. Sections are numbered 6.12 twice and 13.14 in a chapter labelled six; error #16, #17, #18 and #24 are each printed twice with different values.

Against measurement, the decisive difficulty is that the 43 arc seconds are not the observed precession but the ''residual''. Mercury's observed perihelion advance is about 5600 arc seconds per century, of which roughly 5025 is the precession of the equinoxes — a change of reference frame — and about 532 is Newtonian perturbation by Venus, Earth, Jupiter and the rest, computed by Le Verrier and refined since. If the 43 arc seconds were an artefact of viewing Mercury from a moving Earth, that artefact would already have been removed with the 5025, since reduction to the mean equinox and to heliocentric coordinates is exactly the correction Nahhas says is missing. His fifty ratios explain a number, but not the number that survives the reductions. Nor does the paper address the modern extensions of the same test: the anomalous perihelion advances measured for Venus, Earth, Mars and the asteroid Icarus, and the periastron advance of 4.2 degrees ''per year'' in the binary pulsar PSR B1913+16, where there is no Earth-based parallax geometry of the kind invoked here and no 0.61 to be had.

Finally, the tone works against the content. A reader asked to weigh a technical claim is instead asked to accept that "everything modern and Nobel said in physics and astronomy is all wrong" and that the author is the only physicist who has ever known what time it is. The one derivation worth examining — formula #49 — is buried in the last three pages behind forty-eight arithmetic coincidences, and no error analysis, no comparison with the reduced residual, and no application to any other body is offered.

==See also==

* [[Joe Alexander Nahhas]]
* [[General Relativity]]
* [[Albert Einstein]]
* [[Simultaneity]]
* [[Aberration]]
* [[Special Relativity]]
* [[Isaac Newton]]

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