The Arizona desert is a fine place for getting reacquainted with some old friends in the night sky. The air was dry and almost chilly and moonless sky was as transparent as the dark Montana skies I knew as a kid. The mountains on the horizon cut their blackness into the sky as it slowly rotated above them. The binoculars stayed on in their case. I hadn't seen the Milky Way this well in years. Turning my attention towards Perseus I located Algol and without thinking realized I was comparing it to a few other stars to estimate its brightness.
Algol is one of those stars that amateur astronomers learned about when they got ot the point where they wanted to learn about the sky rather than just looking at it. It is easy to find and reasonably bright. Well - mostly it is reasonably bright. It has an apparent magnitude of 2.1, but every 68 hours and 49 minutes it dims by about 70%.1 It is very regular variable start.
Well - sort of ...
It is really three stars orbiting around a common center of mass. Two are very close - only about 0.06 Astronomical Units - the distance from the Sun to the Earth. The third is about 2.7 AU - still ridiculously close for stars, but most of the interesting action is between the tight pair.
Algol A is very bright blue star and its tight pair Algol B is a larger, but fainter orange star. The orbit happens to line up with a line of sight to Earth so Algol B passes in front of A effectively dropping the brightness as seen on Earth - like clockwork.
Due to the close distance some of Algol B is being sucked into Algol A - the sight must be incredible.2
Looking at it again I remembered a game I began to play as a teenager. A game that is still with me. I try to imagine what might change - history or even life itself - if something in Nature was altered. I stay away from altering the fundamental physics and chemistry, but are still many rich things to imagine. What color would plants be if the Sun had a different spectral type, what if we didn't have a moon, what if our axis was in the plane of our orbit, what if the Earth's mass was 20% more - or 20% less, what if our orbit was more elliptical, ...?
In High School we learned about the Longitude Prize in Mr Wolff's world history class. It completely captivated me at the time. Navigation requires knowing latitude and longitude. Latitude is trivial - a simple sextant will do. Longitude requires knowing what time it is. Before the prize good clocks weren't up to the task - a precision chronometer was necessary and a remarkable story unfolded.
I had been doing my little thought experiments and, on the way home from school, it struck me what if Algol had a shorter period or the apparent brightness change was greater? There would have been a clock beating in the sky. Would this have enabled precision navigation for mariners thousands of years ago? How would the world have changed?
Dozens of questions arise. Little thought experiments where you hold everything constant except one variable that gets perturbed is a powerful technique for critical thinking. Quite a bit of physics, particularly in the early stages of an investigation, use it. Of course it is fundamental to experimental science and has applications elsewhere.3 You can test any number of ideas with the technique and it can be a good out-of-the-box thinking technique. Just be sure and apply enough rigor to the ideas you generate.
Now we place our own precision clocks in the sky and have revolutionized navigtion in the process.
1 Apparent magnitude is the brightness of an object as seen by an observer on Earth. Ptolemy popularized a scheme that divided the visible stars into six magnitudes. The brightest was the first magnitude, the dimmest was the sixth. Each brighter level was considered twice as bright as the previous level. In the 19th century as photometric techniques were developed the scale was redefined such that a first magnitude star was 100 times brighter than a sixth magnitude - the fifth root of 100 is about 2.512, so the difference in brightness between a 2.1 and 3.4 is 2.512(3.4-2.1) or about 3.11. Some objects are brighter than 1 and most are dimmer than 6. The sun is about -27 and a full moon is about -13 (so the Sun is about 400,000x brighter than a full moon)
2 The figure is from a paper from the CHARA interferometer group. A fantastic instrument that does long baseline optical interferometry to resolve objects that are too close together to separate with conventional telescopes. Note that Algol B has a distorted shape - this is real. The distortion on C is an artifact.
3 FaceBook for example:-)
Everyone who is cooking this week probably has a menu firmly at hand. I'll list some vegetable roasting techniques may be useful
° Use a sheet pan. A deeply set pan holds the steam from the roasting vegetables making them mushier.
° I don't cut produce to uniform sizes. I like a bit of variation. Also carrots are often best roasted whole. Broccoli is often good split lengthwise.
° spread them out on the pan - crowding over steams them. Remember most ovens have very little airflow.
° some vegetables need more oil than others. Mushrooms take more than sweet potatoes for example.
° toss them at least once during the cooking
° crank up the temperature 425° to 450° The Maillard reaction and caramelization are your friends. Of course you have to watch the cooking more closely if you move to higher temperatures. The difference between perfect and ash can be a couple of minutes.