Solar system dynamics

Abstract

This dissertation investigates the complex dynamics of planetary motion, with a specific emphasis on explaining the mechanisms governing Milankovitch cycles. The primary objective is to identify the three fundamental orbital parameters responsible for Earth’s cycle variations and to investigate their impact on fluctuations in solar insolation. To accomplish this, the Milankovitch terms — eccentricity, precession and obliquity — are introduced and their periods are calculated. The computation for the precession period relies on the foundational concept of gyroscope precession. In contrast, numerical apsidal precession is calculated based on the definition of torque and gravitational theory, incorporating gravitational forces from both outer and inner planets. Additionally, the derivation of the Milankovitch equations, highlighting variations in eccentricity and angular momentum, is achieved based on Hamiltonian theory and Poisson brackets. Moreover, this dissertation strives to establish a relationship between solar insolation and the Milankovitch cycles. A relationship between the solar constant at perihelion and aphelion is expressed as a function dependent on eccentricity. A corresponding graph illustrating the variation in solar insolation ratio between perihelion and aphelion is presented. Additionally, the solar insolation values across different latitudes are discussed by modifying one or all of the three Milankovitch terms. To present these outcomes, a brief review of conic properties, including the equation of an ellipse, and Kepler’s three laws, is provided. Additionally, the methodology to calculate planetary positions relative to the Sun and to other planets at specific times is outlined. In investigating orbital dynamics, the role of the disturbing function, in understanding how the gravitational pull from massive bodies influences the motion of other bodies, is analyzed alongside secular perturbations. Finally, the dissertation concludes by exploring the possibility that the Milankovitch parameters, accountable for Earth’s orbit variations around the Sun, could explain Earth’s current warming trend.