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Einstein Nemesis # 2: As Camelpardis Apsidal motion Puzzle solution: By Joe Nahhas

The Physics Problem that Einstein Harvard MIT Cal-Tech Stanford and NASA and all other 100,000 Space-time Physicists could not solve by space-time Physics including 109 years of Nobel Prize winner Physics and physicists and 400 years of astronomy and dedicated to: National Philosophy Alliance Members and DRS KH. F.Khailullin and V.S. Kozyreva of Moscow University Who posted this motion Puzzle in 1983 as not solvable by any Physics and still posted as motion puzzle on Smithsonian-NASA website SAO/NASA. And it is the most studied motion puzzle in all of Physics.
Universal Mechanics Solution: For 350 years Physicists Astronomers and Mathematicians missed Kepler's time dependent equation introduced here and transformed Newton's equation into a time dependent Newton' equation and together these two equations explain Quantum - Relativistic effects; it combines classical mechanics and quantum mechanics into one mechanics and explains "relativistic" effects as the difference between time dependent measurements and time independent measurements of moving objects and in practice it amounts to "Visual" effects.

All there is in the Universe is objects of mass m moving in space (x, y, z) at a location
r = r (x, y, z). The state of any object in the Universe can be expressed as the product

S = m r; State = mass x location:

P = d S/d t = m (d r/dt) + (dm/dt) r = Total moment
= change of location + change of mass
= m v + m' r; v = velocity = d r/d t; m' = mass change rate

F = d P/d t = d²S/dt² = Total force
= m(d²r/dt²) +2(dm/dt)(d r/d t) + (d²m/dt²)r
= m? + 2m'v +m"r; ? = acceleration; m'' = mass acceleration rate

In polar coordinates system

r = r r(1) ;v = r' r(1) + r ?' ?(1) ; ? = (r" - r?'²)r(1) + (2r'?' + r?")?(1)

F = m[(r"-r?'²)r(1) + (2r'?' + r?")?(1)] + 2m'[r'r(1) + r?'?(1)] + (m"r) r(1)

= [d²(mr)/dt² - (mr)?'²]r(1) + (1/mr)[d(m²r²?')/dt]?(1) = [-GmM/r²]r(1)

d²(mr)/dt² - (mr)?'² = -GmM/r² Newton's Gravitational Equation (1)
d(m²r²?')/dt = 0 Central force law (2)

(2) : d(m²r²?')/d t = 0 <==> m²r²?' = [m²(?,0)?²(0,t)][ r²(?,0)?²(0,t)][?'(?, t)]
= [m²(?,t)][r²(?,t)][?'(?,t)]
= [m²(?,0)][r²(?,0)][?'(?,0)]
= [m²(?,0)]h(?,0);h(?,0)=[r²(?,0)][?'(?,0)]
= H (0, 0) = m² (0, 0) h (0, 0)
= m² (0, 0) r² (0, 0) ?'(0, 0)
m = m (?, 0) ? (0, t) = m (?, 0) Exp [? (m) + ì ? (m)] t; Exp = Exponential
? (0, t) = Exp [ ? (m) + ? ? (m)]t

r = r(?,0) ?(0, t) = r(?,0) Exp [?(r) + ì ?(r)]t
?(0, t) = Exp [?(r) + ? ? (r)]t

?'(?, t) = {H(0, 0)/[m²(?,0) r(?,0)]}Exp{-2{[?(m) + ?(r)]t + ì [?(m) + ?(r)]t}} ------I
Kepler's time dependent equation that Physicists Astrophysicists and Mathematicians missed for 350 years that is going to demolish Einstein's space-jail of time

?'(0,t) = ?'(0,0) Exp{-2{[?(m) + ?(r)]t + ?[?(m) + ?(r)]t}}

(1): d² (m r)/dt² - (m r) ?'² = -GmM/r² = -Gm³M/m²r²

d² (m r)/dt² - (m r) ?'² = -Gm³ (?, 0) ?³ (0, t) M/ (m²r²)

Let m r =1/u

d (m r)/d t = -u'/u² = -(1/u²)(?')d u/d ? = (- ?'/u²)d u/d ? = -H d u/d ?
d²(m r)/dt² = -H?'d²u/d?² = - Hu²[d²u/d?²]

-Hu² [d²u/d?²] -(1/u)(Hu²)² = -Gm³(?,0)?³(0,t)Mu²
[d²u/ d?²] + u = Gm³(?,0)?³(0,t)M/H²

t = 0; ?³ (0, 0) = 1
u = Gm³(?,0)M/H² + Acos? =Gm(?,0)M(?,0)/h²(?,0)

mr = 1/u = 1/[Gm(?,0)M(?,0)/h(?,0) + Acos?]
= [h²/Gm(?,0)M(?,0)]/{1 + [Ah²/Gm(?,0)M(?,0)][cos?]}

= [h²/Gm(?,0)M(?,0)]/(1 + ?cos?)
mr = [a(1-?²)/(1+?cos?)]m(?,0)

r(?,0) = [a(1-?²)/(1+?cos?)] m r = m(?, t) r(?, t)
= m(?,0)?(0,t)r(?,0)?(0,t)

r(?,t) = [a(1-?²)/(1+?cos?)]{Exp[?(r)+?(r)]t} Newton's time dependent Equation --------II

If ? (m) ? 0 fixed mass and ?(r) ? 0 fixed orbit; then

?'(0,t) = ?'(0,0) Exp{-2ì[?(m) + ?(r)]t}

r(?, t) = r(?,0) r(0,t) = [a(1-?²)/(1+?cos?)] Exp[i ? (r)t]

m = m(?,0) Exp[i ?(m)t] = m(0,0) Exp [? ?(m) t] ; m(0,0)

?'(0,t) = ?'(0, 0) Exp {-2ì[?(m) + ?(r)]t}

?'(0,0)=h(0,0)/r²(0,0)=2?ab/Ta²(1-?)²

= 2?a² [? (1-?²)]/T a² (1-?) ²; ?'(0, 0) = 2? [? (1-?²)]/T (1-?) ²

?'(0,t) = {2?[?(1-?²)]/T(1-?)²}Exp{-2[?(m) + ?(r)]t

?'(0,t) = {2?[?(1-?²)]/(1-?)²}{cos 2[?(m) + ?(r)]t - ? sin 2[?(m) + ?(r)]t}

?'(0,t) = ?'(0,0) {1- 2sin² [?(m) + ?(r)]t - ? 2isin [?(m) + ?(r)]t cos [?(m) + ?(r)]t}

?'(0,t) = ?'(0,0){1 - 2[sin ?(m)t cos ?(r)t + cos ?(m) sin ?(r) t]²}

- 2? ?'(0, 0) sin [? (m) + ?(r)] t cos [? (m) + ?(r)] t

? ? (0, t) = Real ? ? (0, t) + Imaginary ? ? (0.t)

Real ? ? (0, t) = ?'(0, 0) {1 - 2[sin ? (m) t cos ?(r) t + cos ? (m)t sin ?(r)t]²}

W(ob) = Real ? ? (0, t) - ?'(0, 0) = - 2 ?'(0, 0){(v°/c)? [1-(v*/c) ²] + (v*/c)? [1- (v°/c) ²]}²

v ° = spin velocity; v* = orbital velocity; v°/c = sin ? (m)t; v*/c = cos ? (r) t

v°/c << 1; (v°/c)² ? 0; v*/c << 1; (v*/c)² ? 0

W (ob) = - 2[2? ? (1-?²)/T (1-?) ²] [(v° + v*)/c] ²

W (ob) = (- 4? /T) {[? (1-?²)]/ (1-?) ²} [(v° + v*)/c] ² radians
W (ob) = (-720/T) {[? (1-?²)]/ (1-?) ²} [(v° + v*)/c] ² degrees; Multiplication by 180/?

W° (ob) = (-720x36526/T) {[? (1-?²)]/ (1-?) ²} [(v°+ v*)/c] ² degrees/100 years
The circumference of an ellipse: 2?a (1 - ?²/4 + 3/16(?²)²- --.) ? 2?a (1-?²/4); R =a (1-?²/4)
v (m) = ? [GM²/ (m + M) a (1-?²/4)]
v (M) = ? [Gm² / (m + M)a(1-?²/4)]
As Camelopardis Apsidal motion solution:
v° = v°(m) + v°(M) = 70 km/sec
v* = 2v(cm) + ? =
2[m v(m) + M v(M)]/(m + M) + ?{{[v(m)-v(cm)]² + [v(M)-v(cm)]²}/2} = 346km/sec
W° = 14.6°/century