# 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 ${\displaystyle \lambda _{M}}$. The values had been numerically computed by a Java program.

The Schwarzschild distance that is corresponding to the Hubble radius of the universe during the generation of the cosmic microwave background (CMB) at around 380,000 light-years (ly) is marked in bold.

The same applies to a Schwarzschild distance of 858 million light-years, where the ratio between the mass of visible universe to the mass of the black shell is equal to one. This distance corresponds to the distance between the particle horizon and the visible horizon of the cosmic microwave background (CMB) according to the ΛCDM model.

Note that to 380,000 years after the Big Bang, the slope of the Schwarzschild radius in relation to the slightly increasing linear mass density was very high. The Schwarzschild distance was grewing much faster than the mass of the black shell during this period.

Linear mass density
${\displaystyle \lambda _{M}}$
in ${\displaystyle {\frac {\text{kg}}{\text{m}}}}$
Mass of black shell
${\displaystyle M_{S}}$
in ${\displaystyle {\text{kg}}}$
Mass of black shell
in units of mass of visible universe
${\displaystyle {\frac {M_{S}}{M}}}$
Effective mass of black shell
${\displaystyle M_{eff}}$
in ${\displaystyle {\text{kg}}}$
Schwarzschild distance
${\displaystyle d_{S}}$
in ${\displaystyle {\text{m}}}$
Schwarzschild distance
${\displaystyle {\frac {d_{S}}{R}}}$
Schwarzschild distance
${\displaystyle d_{S}}$
in ${\displaystyle {\text{ly}}}$
in units of the Hubble radius
${\displaystyle {\frac {R-d_{S}}{R}}}$
3.36663E+26 2.876830E+53 0.968630 1.67E+48 2.48E+21 1.83E-05 262,000 0.999982
3.36664E+26 2.876838E+53 0.968632 1.78E+48 2.64E+21 1.94E-05 279,000 0.999981
3.36665E+26 2.876847E+53 0.968635 1.90E+48 2.83E+21 2.08E-05 299,000 0.999979
3.36666E+26 2.876855E+53 0.968638 2.02E+48 3.00E+21 2.21E-05 317,000 0.999978
3.36667E+26 2.876864E+53 0.968641 2.15E+48 3.19E+21 2.35E-05 337,000 0.999977
3.36668E+26 2.876873E+53 0.968644 2.28E+48 3.39E+21 2.49E-05 358,000 0.999975
3.36669E+26 2.876881E+53 0.968647 2.40E+48 3.56E+21 2.62E-05 377,000 0.999974
3.3667E+26 2.876890E+53 0.968650 2.53E+48 3.76E+21 2.77E-05 398,000 0.999972
3.3668E+26 2.876975E+53 0.968678 3.83E+48 5.69E+21 4.19E-05 602,000 0.99996
3.3669E+26 2.877060E+53 0.96871 5.19E+48 7.71E+21 5.67E-05 815,000 0.99994
3.367E+26 2.877146E+53 0.96874 6.60E+48 9.80E+21 7.20E-05 1,040,000 0.99993
3.368E+26 2.878000E+53 0.96902 2.24E+49 3.32E+22 2.44E-04 3,510,000 0.9998
3.369E+26 2.878855E+53 0.96931 4.03E+49 5.98E+22 4.40E-04 6,320,000 0.9996
3.37E+26 2.879709E+53 0.96960 5.96E+49 8.85E+22 6.51E-04 9,360,000 0.9993
3.38E+26 2.88826E+53 0.9725 3.05E+50 4.53E+23 3.33E-03 47,900,000 0.997
3.39E+26 2.89680E+53 0.9754 6.17E+50 9.16E+23 6.74E-03 96,800,000 0.993
3.40E+26 2.9053E+53 0.9782 9.84E+50 1.46E+24 1.07E-02 154,000,000 0.989
3.41E+26 2.9139E+53 0.9811 1.40E+51 2.08E+24 1.53E-02 220,000,000 0.985
3.42E+26 2.9224E+53 0.9840 1.87E+51 2.78E+24 2.04E-02 293,000,000 0.980
3.43E+26 2.9310E+53 0.9869 2.39E+51 3.55E+24 2.61E-02 375,000,000 0.974
3.44E+26 2.9395E+53 0.990 2.96E+51 4.39E+24 3.23E-02 464,000,000 0.968
3.45E+26 2.9481E+53 0.993 3.58E+51 5.32E+24 3.91E-02 563,000,000 0.961
3.46E+26 2.9566E+53 0.995 4.27E+51 6.34E+24 4.66E-02 670,000,000 0.953
3.47E+26 2.9652E+53 0.998 5.01E+51 7.44E+24 5.47E-02 787,000,000 0.945
3.47566E+26 2.97000E+53 1.00000 5.46E+51 8.11E+24 5.97E-02 858,000,000 0.940
3.48E+26 2.9737E+53 1.001 5.83E+51 8.65E+24 6.36E-02 915,000,000 0.936
3.49E+26 2.9823E+53 1.004 6.71E+51 9.97E+24 7.33E-02 1,050,000,000 0.927