If you are reading this, you probably know already that the magic envelope is in fact not completely magical: only the back of the envelope has a magical ability to turn scribbles into profound statements about the universe. Like all good magic, it works even if you don't believe it to be magical. So you are free to interpret the magic envelope in a Clarkean sense.
Whatever. These notes and lectures are an introduction to astrophysics with the envelope firmly in mind. The aim is to explain a small number of physical principles and use them to discuss interesting examples, with a minimum of random factoids. So we will meet Planck units, chaotic orbits, and the sound horizon on the microwave background, but we will keep well clear of temperature axes going from right to left, logarithms to the base ten times 2.5, and frequencies expressed in kilometers per second per megaparsecs.
The topics are arranged in roughly the order that they historically first came to be studied. Thus we will start with orbital dynamics, first Newtonian, then relativistic. Next we will review some quantum phenomena and see how the interaction of microphysics and gravity leads to stars and planets. Finally, we will study the expanding universe and some consequences of the big bang. The presentation, however, is not historical at all. So for example, we will not see the three-body problem as Newton saw it, but more as a modern researcher in dynamical systems might view it.
Beyond the above broad brush, there is no attempt to be comprehensive. If your favourite topics are dark matter, or nucleosynthesis, or galaxies, please do not take it personally that dark matter appears only briefly, and the other two do not appear at all. The reason is that, to get to the interesting things to do with galaxies or nucleosynthesis, and to a lesser extent dark matter, one needs somewhat more specialized knowledge than this introduction assumes.
Of the many influences in preparing this course, the two that appealed most to the right brain have been First Principles of Cosmology by Eric Linder, and The significance of numerical coincidences in nature by Brandon Carter. Linder, near the beginning of his book, asks `how many cosmic microwave background photons hit your outstretched hand every second?' which more or less sums it up. (And variants of this very question will come up several times.) The emphasis on the interaction between gravity and microphysics, along with the casual use of Planckian units is Carter's influence.
For the left brain Astrophysics in a Nutshell by Dan Maoz has been a splendid reference. I have also learned much from Cauldrons in the Cosmos by Rolfs and Rodney and from Liliya Williams' cosmology lecture notes.