“Trojan asteroid orbits” by Javier Jalandoni wins second place in SOSE awards 2012 for undergraduate basic research category

Dr. Quirino Sugon Jr., Javier Jalandoni, and Dr. Toby Dayrit

In the School of Science and Engineering (SOSE) awards last March 2, 2012, 4:30 pm at the MVP Roofdeck, Javier “Javy” Jalandoni (IV BS Physics) won second place for his work on “Trojans Asteroid Orbits via Perturbation Theory in Geometric Algebra,” under the supervision of Dr. Quirino Sugon Jr. of the Department of Physics.

Trojan asteroids are asteroids that orbit at the same radius and orbital frequency as the planet, while forming an equilateral triangle with the sun and the planet. There are two points: the Lagrange points L4 and L5. The study of the orbits of Trojan asteroids at Lagrange points L4 and L5 is important because the results can be applied to any planet aside from Jupiter. In late 2009, the two STEREO (Solar Terrestrial Relations Observatory) satellites passed through Lagrange points L4 and L5 in search for earth Trojans. In 2010, the WISE (Wide-field Infrared Survey Explorer) found an earth Trojan named 2010 TK7 at the Lagrange point L4, oscillating far below and above the earth’s orbital plane. Lagrange points L4 and L5 are the most stable positions to place satellite observatories because they require less fuel to maintain in their orbits. The unstable Lagrange points L1 and L2 are reserved for the SOHO (Solar and Heliospheric Observatory) satellite and James Webb Space Telescope.

In Javy’s work, he assumed that the orbital plane of the earth Trojan is around point L4 coplanar with the earth. There were also similar works done in the literature, but they approach the problem using numerical simulations. Some also do the analytical approach via perturbation theory in Hamiltonian dynamics, which is an energy method. In Javy’s case, he also use perturbation methods, but using forces. Javy decompose the asteroid’s orbit around the Lagrange point L4 as a sum of rotating circles via exponential Fourier series, in the same way as Copernicus approximates the earth’s orbit as a sum of rotating circles of harmonic frequencies. As long as the initial position and velocity of the asteroid is given, Javy can predict its motion analytically as a function of time, as long as the orbital radius about the Lagrange point L4 is small (less than 10 percent) compared to the distance of the L4 to the sun (or to Jupiter).  The mathematical formalism Javy used is Clifford (geometric) algebra Cl(2,0) which combines scalars, vectors, and imaginary numbers in a single algebra.

Here is Javy’s thoughts the day after he received his award:

My Stay in Ateneo

by Javier Jalandoni

Javier Jalandoni in front of his poster on Trojan asteroid orbits

I was accepted by the Ateneo to study Legal Management, hoping one day that it would give me the edge in running my own business with knowledge of the law. One year later, I decided to change my concentration to physics, knowing little of differential calculus and linear algebra and knowing even less of physics itself to pursue my dream of reaching for the heavenly bodies and to satisfy this need to fulfill my curiosity of space and the stars. Who would have guessed that I would end up leaving the Ateneo, 4 years later, as RUNNER-UP for SOSE AWARDS for OUTSTANDING UNDERGRADUATE RESEARCH, where much credit should be given to my advisor, Prof. Quirino M. Sugon Jr., who provided so much guidance in the development of this research. My stay in the Ateneo is one that I shall never forget.

My world has open up so much to the quantum and to the heavenly when I shifted to physics; and I don’t regret it one bit. I hope others will take time to understand and appreciate its beauty. But aside from the academe, I will never forget my extra-curricular activities in the Ateneo. I will never forget those days playing basketball in the cov courts from early afternoon till late in the evening, inducing my predisposed migraines and forcing me to drive home half asleep. I will never forget those countless nights training and practicing for concerts with CADs, who always has a place in its heart for people with the passion to dance. They were my first org family, but definitely not my last. I will never forget block O3, for being my first Ateneo family, and definitely block VsubI, for being my adopted Ateneo family. I will never forget those nights hosted by LeaPS in the Manila Observatory, where I fell in love with the night sky the moment I saw Saturn for the first time through a telescope, invigorating me to buy my own to share this feeling with others. I will never forget my climbs with the Loyola Mountaineers, who have shown me the beauty of nature and that the walk to the top is long and hard, but the reward once you get there is so worth it.

Yes, I will never forget my stay in the Ateneo. Thank you for developing my mind, my body and my soul.