We numerically integrate the equations of motion of the Sun in Galactocentric Cartesian rectangular coordinates for -4.5 Gyr \leq t \leq 0 in Newtonian mechanics with two different models for the Cold Dark Matter ( CDM ) halo , in MOdified Newtonian Dynamics ( MOND ) and in MOdified Gravity ( MOG ) without resorting to CDM .
The initial conditions used come from the latest kinematical determination of the 3D Sun ’ s motion in the Milky Way ( MW ) by assuming for the rotation speed of the Local Standard of Rest ( LSR ) the recent value \Theta _ { 0 } = 268 km s ^ { -1 } and the IAU recommended value \Theta _ { 0 } = 220 km s ^ { -1 } ; the Sun is assumed located at 8.5 kpc from the Galactic Center ( GC ) .
For \Theta _ { 0 } = 268 km s ^ { -1 } the birth of the Sun , 4.5 Gyr ago , would have occurred at large Galactocentric distances ( 12 - 27 kpc depending on the model used ) , while for \Theta _ { 0 } = 220 km s ^ { -1 } it would have occurred at about 8.8 - 9.3 kpc for almost all the models used .
The integrated trajectories are far from being circular , especially for \Theta _ { 0 } = 268 km s ^ { -1 } , and differ each other with the CDM models yielding the widest spatial extensions for the Sun ’ s orbital path .