Plots of Results Summarized in Table 1

All plots and details of the results for r(0) = 1.186071579 10¹¹ [m]

Analysis and plots of the motion for an initial distance of $r_{(0)}=1.186071579\ {10}^{11}\left[m\right]$ , and the following initial conditions and parameters:

$G=6.67408\ast{10}^{-11}\ \frac{Nm^2}{{\rm Kg}^2}$	(the universal gravitational constant)
$M=2\ {10}^{30}\ Kg$	(the mass of the Sun)
$m=5.9\ {10}^{24}\ Kg$	(the mass of the Earth)
${\dot{r}}_{(0)}=0\ [m/s]$	(linear velocity of the center of mass m at t=0)
$\emptyset_{(0)}=0\ [rad]$	(azimuthal position of the center of mass m at t=0)
${\dot{\emptyset}}_{(t)}=\Omega$	(is the relative angular velocity between the spin of the center of mass M and the translation of the center of mass m)
Since there is a singularity for $\theta=0$ , the “zero” initial condition of the polar angle was taken close to zero as $\theta=\frac{\pi}{{10}^3}\ [rad]$ .

The polar angle of equilibrium ( $\theta_f$ ) is found for several values of the initial conditions of $\theta_{(0)}$ , $\omega_{(0)}$ , and $\Omega$ . The three vertical values of $\theta_f$ on each table cell, from top to bottom, are the results for each of the three values of from left to right. For example:

Obs.: the table is very long, and it is split over into several images (misaligned gaps between images are easy to note).

Go to Table 1 to see the summary of the results obtained here.

Plots of Results Summarized in Table 1

All plots and details of the results for r(0) = 1.186071579 1011 [m]

All plots and details of the results for r(0) = 1.186071579 10¹¹ [m]