Orbit Determination of 2002 KM6

The premise of this research is to determine the orbit of the asteroid 99795 2002 KM6 and predict its trajectory far in the future. Asteroids’ orbits model ellipses and can thus be described by six orbital elements: the semi-major axis, eccentricity, inclination, the longitude of the ascending node, the argument of perihelion, and the mean anomaly. Using Python, our team programmed a series of orbital determination codes, implementing the Method of Gauss to generate the orbital elements with a reasonable level of error. This required gathering data over at least three observations. We then compared these elements to those generated by JPL Horizons to ensure they were reasonable.Our team used the numerical integration program Swift to determine long-term orbital patterns over the next 50 million years. Simulations of 60 different clones of 2002 KM6, randomly sampled from a Gaussian distribution, revealed that the majority of asteroid particles will either get too far or too close to the Sun after 50 million years. A small percentage of them, however, will maintain a stable orbit.

Delta T: Polynomial Approximation of Time Period 1620–2013

The difference between the Uniform Dynamical Time and Universal Time is referred to as ΔT (delta T). Delta T is used in numerous astronomical calculations, that is, eclipses,and length of day. It is additionally required to reduce quantified positions of minor planets to a uniform timescale for the purpose of orbital determination. Since Universal Time is established on the basis of the variable rotation of planet Earth, the quantity ΔT mirrors the unevenness of that rotation, and so it changes slowly, but rather irregularly, as time passes. We have worked on empirical formulae for estimating ΔT and have discovered a set of polynomials of the 4th order with nine intervals which is accurate within the range of ±0.6 seconds for the duration of years 1620–2013.

Orbital fitting of Fomalhaut b and subsequent interaction with the dust belt

Fomalhaut harbours a moderately eccentric dust belt with a planet candidate (Fom b) imaged near its inner edge. MCMC-based orbital determination of Fom b shows that the orbit is highly eccentric (e≃0.9), nearly apsidally aligned with the belt. We study the secular interaction between the planet and the dust ring. We show that only if it is a small mass object, Fom b can perturb the belt without destroying it. But Fom b's perturbing action inevitably drives the belt to high eccentricity and apsidal misalignment. This behaviour is due to the planet's high eccentricity.This dynamical outcome contradicts both observations and orbital determination. We conclude that another, more massive and less eccentric planet (Fom c) is required to dynamically control the belt. We show that Fom b is likely to have been formerly trapped in mean-motion resonance with Fom c and that subsequent eccentricity increase caused it to cross Fom c's orbit and to jump on its present day orbit via a scattering event.

Orbital determination and dynamics of resonant extrasolar planetary systems

In this communication we review some properties and applications of mean-motion resonances in extrasolar planetary systems, with particular emphasis on the 2/1 commensurability. A first part is devoted to the dynamical structure of the 2/1 resonance, including (but not restricted to) the so-called apsidal corotations. In a second part we discuss the orbital evolution of resonant systems under the effects of non-conservative forces. Special attention is given to the use of apsidal corotations as markers of largescale orbital decay, possibly due to disk-planet interactions in primordial times. Finally, we analyze the interplay between dynamical analysis and orbital fitting. Using the HD82943 planetary system as an example, we discuss: (i) up to what point present orbital fits allow us to distinguish between different resonant configurations, and (ii) in what ways may the dynamical structure of resonances be used as a complementary part of the orbital fitting process.