orbital insights

In some cases, unexpectedly deep connections allow far-reaching conclusions to be drawn from commonplace observations. This post provides an example of such an occurrence. A readily observable fact about the orbits of bound celestial objects is that they regularly repeat. Closed orbits are not only prevalent in the solar system, but can also be directly observed, for instance, in visual binary stars, as shown in the figure below. This simple observation places strong constraints on the nature of the gravitational force.  Observed orbit projected in the plane of the sky of the secondary component of the Sirius system relative to the primary (open and filled circles represent data obtained with different techniques, as detailed in the legend; the black filled circle at the origin marks the position of the primary). The best-fitting orbit is shown by the black line (data and orbital solution from Bond et al. 2017, ApJ 840, 70).   A somewhat obscure theorem of classical mecha...

I owe my first encounters with celestial mechanics to a popular science magazine and a university-level supplementary textbook. The unlikely pair consisted of a special issue of Le Scienze (the Italian edition of Scientific American), devoted to the scientific biography of Sir Isaac Newton, and of the Italian translation of Schaum's Outline of Theoretical Mechanics, which, from its dusty appearance, had spent quite some time forgotten on a shelf of a surprisingly well-stocked high school library.     Still barely halfway through high school, and equipped only with a shaky understanding of limits and derivatives, I marveled at the genius of the Man who invented Calculus, while the dusty textbook inspired, intrigued, and (more often than not!) frustrated me. These two oddly complementary readings cemented my choice of Physics as university major. More than twenty years later, the better part of which I have spent pursuing a PhD in Astrophysics and later working as a researcher,...