Title: Secular Perturbations Arising From the Action of Jupiter on Mars A Thesis Presented to the Faculty of Philosophy of the University of Pennsylvania Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 0484376683
ISBN 13: 9780484376686
Binding: HRD
Condition: New
Weight: 268 grams

About this title

Synopsis

Unlock the mechanics behind planetary orbits and how a giant neighbor can quietly steer Mars.

This scholarly work presents a rigorous treatment of secular perturbations in a two-body system, focusing on the gravitational influence of Jupiter on Mars. Grounded in classical mechanics, it builds from Lagrange’s canonical forms to Hamilton’s equations, and then moves through Jacobi’s transformations to reveal how the system’s constants evolve under perturbation.

The book advances through several key methods, each explained with care and applied to a concrete celestial problem. It covers the shift from second-order to first-order differential equations, the transformation to canonical variables, and the analytic path to integrating motion in multi-body contexts. It also details Hill’s modification of Gauss’s method for computing secular effects and shows how perturbations can be expressed and evaluated with practical accuracy.
A substantial portion is devoted to computation. The text discusses transforming variables, evaluating perturbing functions, and using elliptic integrals and quadrature to obtain reliable results. It includes worked examples drawn from Hill’s theories and presents data and steps used to estimate the perturbations in the Mars–Jupiter system, with references to established ephemeris work.
What you’ll experience

A clear through-line from foundational equations to practical perturbation techniques
Step-by-step derivations of canonical forms and Jacobi transformations
Methods for transforming and evaluating the perturbing function
Guidance on applying Hill’s approach to real celestial configurations

Ideal for readers who want a precise, math‑driven view of orbital perturbations and the historical methods used to tackle them, from students to researchers in celestial mechanics and astronomy history.

"About this title" may belong to another edition of this title.

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