Orbit-averaged perturbation equations of celestial mechanics with applications to Saturn’s E ring particles

• Main Author: Haanpää, V.-J. (Veli-Jussi)
• Format: Others
• Language: English
• Published: University of Oulu 2018
• Subjects: Physics
• Online Access: http://urn.fi/URN:NBN:fi:oulu-201812053229; http://nbn-resolving.de/urn:nbn:fi:oulu-201812053229

Following Burns 1976, we study the effect of a variety of perturbing forces on a set of orbital elements—semi-major axis a, eccentricity e, inclination i, the longitude of pericenter π, the longitude of the ascending node Ω, and the time of pericenter passage τ. Using elementary dynamics, we can derive the time rates of change of these quantities to produce the perturbation equations of celestial mechanics, which are written in terms of the perturbing forces. If the perturbing forces on a dust particle are small in comparison to a planets gravita- tional attraction, the change in (the first five) orbital elements is slow and on timescales much longer than the dust particle’s orbital period. We can average the effects of perturbations over a single Keplerian orbit (assumed constant). This “orbit-averaging” has both analytical and numerical advantages over non-averaged perturbation equations, which can be seen for example in processing times of computerised orbital models. We can sum the individual perturbation equations of perturbing forces to account for the cumulative effect of all perturbations on an orbital element: 〈dΨ/dt〉_{total} = ∑_{j}〈dΨ/dt〉_{j}, where Ψ is any one of the six osculating orbital elements. These orbit-averaged equations equations are on the order of hundreds of times faster to numerically integrate than the Newtonian equations. To demonstrate the orbit-averaged equations, we can use the orbit-averaged perturbation equations to model paths of dust particles in Saturn’s E Ring. Saturn’s moon Enceladus’ orbit is approximately at the same distance from Saturn as the E Ring, and it has been suggested that the E Ring—made of icy dust—originates from cryovolcanic activity on Enceladus’ south pole. Following Horanyi et al. 1992, we will explore the effects of higher order gravity, radiation pressure, and electromagnetic forces as perturbing forces in the Saturnian system to show the individual effects of perturbing forces on Enceladus-originated ice dust, as well as the cumulative effect of these perturbing forces on orbital equations of the dust.