Plots of Results Summarized in Table 3


All plots and details of the results for r(0) = 150 109 [m]

Analysis and plots of the motion for an initial distance of r_{(0)}=150\ {10}^9\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 3 to see the summary of the results obtained here.