Moving objects in retarded gravitational potentials of an expanding spherical shell/Table with computed results

Table with computed results

In the following table you will find different computed values based on the linear mass density of the black shell $\lambda _{M}$. The values had been numerically computed by a Java program.

The points in time of the generation of the cosmic microwave background (CMB) at around 380,000 years after Big Bang as well as the creation of the oldest observed galaxy JADES-GS-z14-0 (in the year 2024) at around 290,000,000 years after Big Bang are marked in bold.

Note that from 290,000 to 380,000 years after the Big Bang, the slope of the Schwarzschild radius was a little bit unstable in the table data with respect to the increasing mass of the black shell at values around 0.17 and 0.18 (marked in bold). This is due to the limited precision of the numerical computation of the Schwarzschild distances and their strong effect on the slope. However, the Schwarzschild distance was grewing much faster than the mass of the black shell during this period.

Linear mass density $\lambda _{M}$ in ${\frac {\text{kg}}{\text{m}}}$	Mass of shell $M_{S}$ in ${\text{kg}}$	Mass of shell in units of mass of visible universe ${\frac {M_{S}}{M}}$	Effective mass of shell $M_{eff}$ in ${\text{kg}}$	Schwarzschild distance $d_{S}$ in ${\text{m}}$	Schwarzschild distance in units of Hubble radius ${\frac {d_{S}}{R}}$	Schwarzschild distance $d_{S}$ in ${\text{ly}}$	Radius of the visible universe in units of the Hubble radius ${\frac {R-d}{R}}$	Slope of the Schwarzschild radius ${\frac {\mathrm {d} d_{S}}{\mathrm {d} \lambda _{M}}}$ in ${\frac {1}{\text{kg}}}$
3.3663E+26	2.87655E+53	0.96853	2.25E+47	3.34E+20	2.46E-06	35,300	0.9999975	-
3.3664E+26	2.87663E+53	0.96856	2.92E+47	4.34E+20	3.19E-06	45,900	0.9999968	0.010
3.3665E+26	2.87672E+53	0.96859	5.98E+47	8.88E+20	6.53E-06	93,900	0.999993	0.045
3.36660E+26	2.87680E+53	0.968621	1.39E+48	2.05E+21	1.51E-05	217,000	0.999985	0.116
3.36661E+26	2.87681E+53	0.968624	1.49E+48	2.22E+21	1.63E-05	234,000	0.999984	0.164
3.36662E+26	2.87682E+53	0.968627	1.60E+48	2.38E+21	1.75E-05	252,000	0.999982	0.166
3.36663E+26	2.876830E+53	0.968630	1.72E+48	2.55E+21	1.88E-05	270,000	0.999981	0.170
3.36664E+26	2.876838E+53	0.968632	1.83E+48	2.72E+21	2.00E-05	287,000	0.999980	0.168
3.36665E+26	2.876847E+53	0.968635	1.95E+48	2.89E+21	2.13E-05	306,000	0.999979	0.173
3.36666E+26	2.876855E+53	0.968638	2.07E+48	3.07E+21	2.26E-05	325,000	0.999977	0.182
3.36667E+26	2.876864E+53	0.968641	2.19E+48	3.25E+21	2.39E-05	343,000	0.999976	0.173
3.36668E+26	2.876873E+53	0.968644	2.31E+48	3.43E+21	2.52E-05	363,000	0.999975	0.185
3.36669E+26	2.876881E+53	0.968647	2.43E+48	3.61E+21	2.66E-05	382,000	0.999973	0.181
3.36670E+26	2.876890E+53	0.968650	2.56E+48	3.80E+21	2.80E-05	402,000	0.999972	0.189
3.3668E+26	2.87698E+53	0.96868	3.85E+48	5.71E+21	4.20E-05	604,000	0.99996	0.191
3.3669E+26	2.87706E+53	0.96871	5.20E+48	7.73E+21	5.68E-05	817,000	0.99994	0.20
3.3670E+26	2.87715E+53	0.96874	6.61E+48	9.81E+21	7.21E-05	1,040,000	0.99993	0.21
3.368E+26	2.8780E+53	0.9690	2.24E+49	3.33E+22	2.44E-04	3,510,000	0.99976	0.23
3.369E+26	2.8789E+53	0.9693	4.03E+49	5.98E+22	4.40E-04	6,320,000	0.9996	0.27
3.370E+26	2.8797E+53	0.9696	5.96E+49	8.86E+22	6.51E-04	9,360,000	0.9993	0.29
3.380E+26	2.8883E+53	0.972	3.05E+50	4.53E+23	3.33E-03	47,900,000	0.997	0.36
3.390E+26	2.8968E+53	0.975	6.17E+50	9.16E+23	6.74E-03	96,800,000	0.993	0.46
3.400E+26	2.9053E+53	0.978	9.84E+50	1.46E+24	1.07E-02	154,400,000	0.989	0.54
3.410E+26	2.9139E+53	0.981	1.40E+51	2.08E+24	1.53E-02	220,000,000	0.985	0.62
3.420E+26	2.9224E+53	0.984	1.87E+51	2.78E+24	2.04E-02	293,400,000	0.980	0.69
3.430E+26	2.9310E+53	0.987	2.39E+51	3.55E+24	2.61E-02	374,800,000	0.974	0.77
3.440E+26	2.9395E+53	0.990	2.96E+51	4.39E+24	3.23E-02	464,400,000	0.968	0.85
3.450E+26	2.9481E+53	0.993	3.58E+51	5.32E+24	3.91E-02	562,600,000	0.961	0.93
3.460E+26	2.9566E+53	0.995	4.27E+51	6.34E+24	4.66E-02	669,800,000	0.953	1.01
3.470E+26	2.9652E+53	0.998	5.01E+51	7.44E+24	5.47E-02	786,900,000	0.945	1.11
3.475E+26	2.9694E+53	1.000	5.41E+51	8.04E+24	5.91E-02	849,300,000	0.941	1.18
3.480E+26	2.9737E+53	1.001	5.83E+51	8.65E+24	6.36E-02	914,500,000	0.936	1.23
3.490E+26	2.9823E+53	1.004	6.71E+51	9.97E+24	7.33E-02	1,054,000,000	0.927	1.32