Near Earth Asteroid 2002 AA29 Chris Williams, HET617, Student 1607421 email: [email protected]

Abstract Quasi-satellite Phase Simulation Stability Asteroid 2002 AA29 is one of three 2002 AA29, from time to time, en- Tests of simulation stability were per- known examples of horseshoe orbit be- ters into an Earth quasi-satellite state in formed to ensure that results are reliable. haviour. The asteroid is co-orbital with which it stays within 0.2 AU of Earth Shorter integration time steps, 0.00027 Earth; the only substantial difference in for several decades. During the quasi- vs. 0.001 years, produced grossly differ- orbital parameters being a 10.7◦ inclina- satellite phase the asteroid occupies the ent results beyond approximately 5000 tion. From time to time, 2002 AA29 region normally excluded by its horse- years elapsed. An alternate, commonly- leaves the horseshoe behaviour and en- shoe motion. Fig. 2 shows consecutive used solar system starting state (Standish ters a quasi-satellite relationship with close approaches to Earth; one resulting et al. [2] vs. JPL HORIZONS) lead Earth (Connors et al. [1]), the next in- in several quasi-satellite orbits. to behavioural changes within the first

0.95 stance being approximately 2580 AD. Near 385 Yrs 500 years. Simulation without the outer 0.96 Near 483 Yrs 0.97 Near 605 Yrs Using the SWIFT simulation suite run- 0.98 planets rapidly diverges from the base X (AU) 0.99 1 ning on the Swinburne supercomputer -0.3 -0.2 -0.1 0 0.1 0.2 0.3 behaviour indicating that their distant ef- this project investigates the orbital be- Y (AU) fect is significant. The simulations are haviour of 2002 AA29, in particular the Figure 2: Three consecutive close approaches, the clearly very sensitive to starting state, quasi-satellite phase. The investigations third leading to quasi-satellite behaviour. and less so to simulation time step. The confirm the presence of quasi-satellite To get out of the horseshoe pattern, primary simulation is sufficiently stable behaviour and discount the possibility of 2002 AA29 must gain enough energy to over the 1200 years analysed in detail. resonances with Jupiter causing the tran- climb the potential barrier near Earth. To sition. investigate possible sources of that boost Conclusions the following checks were done: The orbital dynamics of 2002 AA29 Horseshoe Orbit are interesting as an example of horse- Alignment of Jupiter at Earth- 1 • shoe interaction with Earth. The quasi- L4 100 asteroid close approaches. No consis- 80 0.5 60 satellite behaviour is unique among 40 20 tent alignment was found at the on- 0 known examples of horseshoe orbits. 0 L3 Sun Earth -20 Y (AU) -40 set or termination of quasi-satellite Ecliptic latitude (deg) -60 Jupiter, and the outer planets, play a part -0.5 -80 60 70 80 90 100 110 120 130 phases. Elongation from Sun (deg) L5 in the evolution of the inner solar system -1 Approaching Receding -1 -0.5 0 0.5 1 Resonance between Jupiter and but do not appear to be the trigger for X (AU) • Years 0-95 Years 95-191 oscillation in semi-major axis during entry or exit to the quasi-satellite stage. Figure 1: 2002 AA29 annual average position over 192 quasi-satellite phase (Fig. 3). Subse- The asteroid’s oscillatory motion about years in co-rotating frame (left), and close approach quent phases showed varied oscilla- Earth seems to be purely the result of in- near 2190 AD as seen in the morning sky (right). tion periods; 13 to 16.8 years. No teractions with Earth near the asteroid’s The equations of motion for gravita- convincing resonance was found. nodes. tional systems with three or more bod- Sensitivity to position of Future work on the nature of the quasi- ies are not generally analytically inte- 2002• AA29’s nodes (potential close satellite phase could look in more detail grable. A number of tractable three- approaches). Changing the asteroid at the nature of nodal interactions be- body restricted cases exist for which mo- orbit orientation slightly changes the tween Earth and 2002 AA29. tions have been determined analytically. onset of quasi-satellite phase.

Examination of such systems in a frame 1.012 1.008 1.004 that co-rotates with the planet led to 1 a (AU) 0.996 0.992 the derivation of Lagrangian equilibrium 0 200 400 600 800 1000 1200 points (L1–L5) at which a light object 1.012 1.008 References 1.004 1 may be dynamically stable. The ob- a (AU) 0.996 0.992 [1] M. Connors, P. Chodas, S. Mikkola, P. Wiegert, ject may be seen as trapped in a horse- 560 570 580 590 600 610 620 630 640 650 C. Veillet, and K. Innanen. Discovery of an aster- Elapsed time (Yrs) shoe shaped gravitational well along the 2002 AA29 Earth oid and quasi-satellite in an Earth-like horseshoe or- planet’s orbit, bounded by high walls bit. Meteoritics and Planetary Science, 37:1435–1441, Figure 3: 2002 AA29 semi-major axis vs. time for October 2002. near the planet. 2002 AA29 oscillates simulation (top) and quasi-satellite period (bottom). [2] E. M. Standish, X. X. Newhall, J. G. Williams, and about the potential well generated by the The most likely cause of the quasi- D. K. Yeomans. Explanatory Supplement to the As- Earth-Sun system over a period of 190 tronomical Almanac, chapter Orbital ephemerides of satellite behaviour is interaction with the Sun, Moon and planets. University Science Books, years (Fig. 1). Annual motion appears Earth, and this is very sensitive to align- Mill Valley, CA, 1992. as a spiral about the Earth’s orbit. ment near the nodes.