3. The four final Venus states

The remaining question is to know under which initial conditions (period of rotation, and orientation of the axis at the end of the phase of formation of the solar system) a planet can reach such an equilibrium state?

One can show that for a large amount initial conditions, under the effect of tidal forces, but also of the dissipation that occurs at the core-mantle border, the obliquity of the planet (angle between the plane of equator and the orbital plane) will slowly evolve towards 0 or 180 degree, while its rotation reaches an equilibrium position under the various tidal torques, with only four possibility, two correspondant to a prograde state (F0+, Fp+) and two with a retrograde state (F0-, Fp -) (fig. 4). Once the rotation period of one of the final states is known, one can deduce the rotation period of the three others. Assuming that the current state is close to equilibrium, one can then deduce that the two retrograde states have 243.0 days period, and the two prograde states 76.8 days period.

Figure 4: The four final Venus states.

It should be stressed that retrograde states F0- and Fp- correspond both to the current observation of planet, but with completely different histories: in the first case, (F0 -), the planet, supposed to be initially in prograde rotation, will slow down under the influence of the dissipative effects, while its obliquity evolves to zero degree, then it stops its rotation, and starts to turn in the opposite direction to reach its final 243 days final period.

In the second scenario, (fig. 5), the planet which can be initially with an obliquity of almost 0 degrees, will see its obliquity increasing considerably under the influence of the planetary perturbations, at the point of being able to be turned over, while slowing down, for finally reaching also a retrograde final rotation period of 243 days..