Celestial mechanics is firmly rooted in Newton’s (and Einsteins) laws of gravity and enables us to compute the positions of planets, moons, and comets with high accuracy. Besides the solar attraction, the major gravitational perturbation of comets are caused by Jupiter. Non-gravitational forces are important to understand the dynamics and composition of our interstellar visitor ʻOumuamua, which not only followed a hyperbolic trajectory but additionally accelerated.
How does a “non-gravitational force” arise?
For asteroids and comets, the term “non-gravitational force” refers to all effects besides the standards law of gravitation. For comets the most obvious one is the force induced by the sublimation of ice. The gas molecules fly into space and carry along momentum transferred from the cometary nucleus. The momentum transfer affects cometary motion considerably:
- there is a mass loss of the comet (for comet 67P/Churyumov-Gerasimenko) of about 1/1500th of its total mass during the 2015 apparition.
- the very existence of comets millions of years after the genesis of the solar system shows that these fellows follow unstable orbits, which does hide them most of the time in shadowed regions of the outer solar system, since otherwise within short “astronomical times” (10,000 years) they would be evaporated.
- the momentum transfer affects the rotation period and rotation axis orientation of the nucleus. We have discussed this in detail in our article in Astronomy & Astrophysics “Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation-induced torques” (free arxiv version and excellent blog entry on planetary-mechanis.com by Benoît Noyelle)
- and finally the orbital evolution of the comet is altered, as discussed next (for more details see our article in Astronomy & Astrophysics “Outgassing induced acceleration of comet 67P/Churyumov-Gerasimenko”, free arxiv version)
Fortunately, Rosetta was a faithful companion of 67P/Churyumov-Gerasimenko and provided the required positions in space (accuracy better than 10 km). The accurate determination of the spacecrafts is an art by itself, as described in this report. Only this data allowed us to retrieve the non-gravitational acceleration and to deduce how much water ice sublimated during the 2015 apparition.
Flying close to the nucleus provided us with spectacular views of the surface from the OSIRIS camera, but made it more difficult to assess the overall gas production of the comet, since Rosetta moved actually across the escaping molecules and probed the density “in-situ” using the ROSINA devices. Together with the ROSINA principal scientists Kathrin Altwegg and Martin Rubin, we (Matthias Läuter and Tobias Kramer) reconstructed the surface emission rate from the in-situ data (“Surface localization of gas sources on comet 67P/Churyumov-Gerasimenko based on DFMS/COPS data“, free arxiv version). This completely independent determination of the water gas production of 67P agrees matches up nicely with the acceleration data as shown in the figure.
You can run your own experiments with various parameters for the outgassing induced acceleration by using the NASA Horizons web interface. You need to input the 6 osculating elements (an equivalent to specifying the position and velocity vector of the comet) and you can enter values for the non-gravitational parameters A1,A2,A3. Usually these parameters are determined by a careful analysis of several apparitions of a comet, since one apparition as seen and measured from Earth does not allow us to retrieve the values with enough confidence.
For 67P a good orbit representation is given by these values from our article:
Osculating elements of 67P Churyumov Gerasimenko:
Epoch 2456897.7196990740
Eccentricity 0.6410114978
Perihelion distance 1.24317813856152504
Perihelion Julian date 2454893.7138435622
Longitude Ascending Node 50.1459466115
Argument of perihelion 12.7813547059
Inclination 7.0405649967
Non-gravitational parameters:
A1 +1.066669896245E-9 au/d^2
A2 −3.689152188599E-11 au/d^2
A3 +2.483436092734E-10 au/d^2
∆T 35.07142 d
Trespassing allowed: from the classical to the quantum world (and back again) 