Lecture 2 - Symmetries
I always forget how hard lecturing is. When preparing, it seems so daunting to have enough material to fill and hour and a half and then, during the lecture, the time just flies by. Today was the first time I lecturing power point (well, actually keynote) slides. I’m nost sure they added much as my talking always seems to run aehad of the slides.
Symmetries is a tough topic: it is really the first major abstraction of the course. In 8.01 and 8.02, we keep things very specific and very physical. Understanding symmetries means you really have to step back from the specific and think in general terms. It is very to convey how imporant they are: I can see the students thinking, “Yeah, yeah” for foruth time I tell them.
There have been several questions about Problem 1 on the pset. Operationally, it is a very simple problem: the measurment of the speed of light comes from taking into account how long it takes the ligth to cross the diameter of the Earth’s orbit. The specifics of the problem are tough to state: the orbit period of Io is 1.8 days, of the Earth is 360 days. Say we call t=0 when the Earth is closest to Jupiter and Io goes behind Jupiter. An astronomer on Earth 1.8 days later will see Io go behind Jupiter a little later; over the 1.8 days since the first occlusion, the Earth has moved 1% along it’s orbit and is a little further alway, so it takes the light a little longer to get there. The next day, a little longer, etc.
Wait 180 days (six months). Now the Earth is furtherest away from Jupiter, about 300 million km further than t=0. Io has gone through 100 orbits of Jupiter (180 days/1.8 days/orbit). Now, it takes the light from Io just as is goes behind Jupiter 22 minutes longer to reach Earth, so the 100th occlusion occurs at t=180 days + 22 minutes.
I hope this helps. Astronomers to really amazing things like this all the time using the Earth’s orbits to measure distances and time things.
