Hill_force_txt_logger only valid for non-inclined orbits
Hallo,
maybe this is already known, but the way the Hill_force_txt_logger tracker is implemented only gives the torque for non-inclined orbits (z=0 always). The way the formula is written now, only the z component of the torque is outputted, but this may not be what one wants for inclined orbits:
Following for example Bitsch+2013, one has that a "small disturbing force dF may change the planetary orbit in size (semi-major axis a), eccentricity e, and inclination i. The inclination i gives the angle between the orbital plane and an arbitrary fixed plane [...] which corresponds to the midplane of the disc. Only forces lying in the orbit plane can change the orbit’s size and shape, while these forces cannot change the orientation of the orbital plane." The angular momentum in this frame is independent of the inclination (only it's projection on the z axis is), so only forces whose vectors lie inside the orbit plane can change the angular momentum and thus yield a torque; in fact, it's only forces in the direction of the velocity of the planet (\vec{F_T}
) that give a torque. But for an inclined orbit, the velocity of the planet does not lie on the z=0 plane, so \vec{\Gamma} = \vec{r} \times \vec{F_T}
is not parallel to the z axis.
So I think that in the Hill_force_txt_logger one should take this into account, otherwise we are outputting a projection onto the z axis of the actual torque felt by the planet, not the total torque itself?