| |||||||

DISTANCES, SIZES AND ARCS
Recall that a circle has 2 pi radians (pi ~ 3.1416). A circle also has 360 degrees. Both degrees and radians measure arc. This means that a radian is about 57.3 degrees. 360 ---------- = 57.3 degrees in a radian. 2 * 3.14 So, we can convert back and forth easily between units of arc. Recall also that one degree is 60 arcminutes, and that one arcminute is 60 arcseconds. So one degree is 3600 arcseconds, and one radian is about 206,000 arcseconds. When looking up at the sky to measure things, it's useful to keep in mind that a fully open, outstretched hand spans about 20 degrees of arc from tip of thumb to tip of pinky. A closed hand spans about 10 degrees and a finger width is about 2 degrees. Here is one very useful thing about radians: an object that subtends one radian of arc is as wide as it is far away. For example, if you're 15 feet away from a car, and the car is 15 feet long, then the car subtends one radian of arc. Here is another very useful thing about angles and arcs: ratios are preserved when it comes to angles. So if you double your distance from an object, the projected size is cut in half. If you triple your distance, the projected angle is cut to a third. If the car above is 30 feet away, then it subtends half a radian of arc; if it's 45 feet away, it subtends a third a radian; etc. This also works for degrees of arc, arcminutes, and arcseconds. |