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8 Conclusion of Volume 1 |
Print["Finished"]; |
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Print["—————————"]; --; |
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Subroutine Perihelkep This is the routine that plots the Keplerian orbit with the chosen parameters
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perihelkep:=
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Cos φ |
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ParametricPlot ,,α (1 − ec2) |
1 ec Cos[ ] φ |
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Sin φ |
+ [ |
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α (1 − ec2) |
1+ec Cos[ ] [φ] |
--, {φ, 0, 2 Pi}, AxesLabel → {x, y}, Ticks → None, |
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PlotStyle → {{Thickness[0.006]}} ; -- |
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Subroutine Perihelgr This is the subroutine for the calculation and drawing of the orbit with the same parameters in the Schwarzschild metric
perihelgr:=,, |
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Print["—————————"]; |
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Print["After ", nn, " revolutions"]; |
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1 |
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1 ec |
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QQ = NDSolve ,,uu [φ] + uu[φ] − |
3uu[φ]2== |
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, uu[0]== |
+lq |
, uu [0]==0--, |
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lq |
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{uu[φ]}, {φ, 0, 2nnπ}, MaxSteps → 500 ; |
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Sin φ |
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Cos φ |
{φ, 0, 2nnπ}, AxesLabel → {x, y}, |
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ParametricPlot Evaluate ,, uu [φ |
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uu |
[φ |
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AspectRatio → 1, Ticks → None,
PlotStyle Thickness 0.006 , RGBColor 1, 0, 0
→ {{ [ ] [ ]}} ; -
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Examples
This section contains some examples of orbits calculated with Periastro.
With a = 60 m and ε = 0.6
periastro
===========================
We make a comparison between orbits in Newton’s Theory and in Schwarzschild geometry
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Input of geometrical parameters
===========================
PLOT of the ORBIT with the following parameters: Semilatus rectum = 60 m
eccentricity = 0.6
===========================
Keplerian orbit with these parameters
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8 Conclusion of Volume 1 |
After more revolutions, Yes or No? Finished
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{Null}
In this example we see, highly emphasized by the smallness of the orbit and by its large eccentricity the phenomenon of periastron advance.
With a = 10, ε = 0.1
periastro
===========================
We make a comparison between orbits in Newton’s Theory and in Schwarzschild geometry
—————————
Input of geometrical parameters
===========================
PLOT of the ORBIT with the following parameters: Semilatus rectum = 10 m
eccentricity = 0.1
===========================
Keplerian orbit with these parameters
