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The Astronomers' Magic Envelope

Preface: how do envelopes come into it?

Outline of Topics

  1. The gravitational constant    Every ancient society practised something we would recognize as astronomy. But what Newton did around 1666, calculating what would happen in the sky from physical principles, was completely new. It seems appropriate to begin by noting some subtleties of the familiar gravitational two-body problem.
  2. Celestial mechanics    From Newton's miracle year of 1666 to Poincaré describing chaos in 1902, astrophysics more or less was celestial mechancs. Here we will try to understand what made the gravitational three-body problem so fascinating for so many generations.
  3. Schwarzschild's spacetime    Although the field equations of general relativity require much formalism for this level, metrics and geodesics are accessible. Here we will see how general relativity modifies Newtonian gravity slightly for weak fields, then more and more, and eventually leads to black holes.
  4. Quantum processes    This chapter explains Planckian units, and reviews the Bose-Einstein and Fermi-Dirac distributions, for later use.
  5. The Chandrasekhar mass scale    Here we introduce the idea of hydrostatic equilibrium, and see the consequences of the interaction of gravity and degeneracy pressure.
  6. Nuclear fusion    Everyone knows that stars are powered by nuclear fusion, like hydrogen bombs. But stars do nuclear fusion more subtly than bombs, with help from quantum tunnelling.
  7. The main sequence of stars    Here we see why opacity prevents stars burning up all at once.
  8. The expanding universe    On the Friedmann equation and its consequences.
  9. The microwave background    Finally, we see how fairly simple microphysics in the context of an expanding universe brings us close to frontiers of contemporary research.

Course materials

  1. Lecture notes and problems. This is the basic material for the course, being incremented as we go along. (It is, however, very brief, about a page per hour of lectures and tutorials. So it may not make much sense before the lectures and tutorials.)
  2. Orbit integrator for chapters 2 and 3.
  3. Friedmann solver for chapter 9.
  4. A puzzle spectrum. This is an animation (kindly provided by my colleague Aaron Boley) of the time-dependent spectrum of a binary star. You are invited to estimate the semi-major axis of the orbit and the star masses.