From paleolithic shepherds to perturbation theory: the history of celestial mechanics in half an hour (perhaps it's more accurate to say the highlights rather than the history). That's a good one-line description of the video The New Shepherd's Lamp. After contemplating the night sky our guide is motivated to visit, in succession, an astronomer, a mathematician, and an engineer to learn about what he sees (including a satellite streaking across his view). The astronomer begins with the shepherds, takes him through Ptolemy and winds up with a quick Renaissance quadruple play: Copernicus to Galileo to Brahe to Kepler. The mathematician gets more time: he begins with a peek at the Principia, then a précis of perturbation theory (homage to Lagrange), and a summary of recurrence (nod to Poincaré). We also get from him the story of Leverrier's discovery of Neptune (no mention of Adams, it is a French film). We end at a French space center whose engineers tell us a little about controlling an artificial satellite's motion.
The apparent purpose is to excite high-school students about the wonders and power of university-level mathematics, especially calculus. I don't think it will do that unless it falls on already very fertile ground. A kid already excited about studying physics, astronomy, and mathematics will enjoy it, but there are too many middle- aged guys lecturing at blackboards to really inspire the blasé. This is not to say the producers didn't try: it's beautifully shot, there are some lovely locations, and nice computer enhancements, e.g., when the speaker traces in the air a cone with his fingers a cone appears and when he chops it with a wave of his hand a plane is traced out intersecting it. It is clear that the original French version (1995) was much more compelling than the English-dubbed version I viewed. The dubbing is an appallingly bad job: the music has been erased; the first time the crusty, old male French astronomer speaks we hear a lovely twenty-something female voice with a British accent, it's absurd and distracting (there are three different English voices dubbing the six or seven French ones); on several occasions the English translation ceases long before the French speaker stops moving his lips reminding one of a terrible 1950s Japanese horror movie; there were two obviously unintentional extended periods of silence on the tape I viewed, one in the middle of the explanation of perturbation theory, the other at the beginning of the explanation of recurrence, thus rendering both of those passages incomprehensible to the uninitiated. The French makers of the original really ought to have a word with the folks at Springer; these flaws make it not worth viewing in English.