tag:blogger.com,1999:blog-1644183700798263875.post8041077564009808390..comments2023-12-06T09:23:53.609-05:00Comments on Hudson Valley Geologist: The Size of the SunStevehttp://www.blogger.com/profile/14397810357022541561noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-1644183700798263875.post-31130447452146054312017-04-21T21:26:10.731-04:002017-04-21T21:26:10.731-04:00Thanks for the interesting discussion. One thing ...Thanks for the interesting discussion. One thing that dramatically simplifies calculations like this is the small angle approximation. With a small angle around half of a degree, there's virtually no difference between the result you get by doing 2*arctan((a/2)/b) and arctan(a/b). In fact, these angles are so small that you still get a very accurate answer by simply approximating the angle in radians as a/b and converting to degrees. This gives the same answer as the original calculation to 4 decimal places (which is how many significant digits are present in the measurements used above). An intuition for why this is correct is to realize that an angle in radians is simply the ratio of the arc length of a segment of a circle to the circle's radius. Drawing a picture of an extremely narrow arc as well as of a right triangle with the same angle, whose hypotenuse is the same as the arc's radius, will show that these two ratios approach each other the smaller the angle gets.lisa and damonhttps://www.blogger.com/profile/03504234799193065515noreply@blogger.comtag:blogger.com,1999:blog-1644183700798263875.post-617667872087644552013-11-29T16:50:01.757-05:002013-11-29T16:50:01.757-05:00Amazing. Now I've heard that, somehow, the co...Amazing. Now I've heard that, somehow, the comet survived it's close shave.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1644183700798263875.post-12582402346137256882013-11-29T12:36:37.045-05:002013-11-29T12:36:37.045-05:00700,000 mi is about 1.13 x 10^6 km. Plugging that...700,000 mi is about 1.13 x 10^6 km. Plugging that in above gives an angular diameter of 63 degrees. That would be as if the Sun stretched from the horizon 2/3 of the way up to the zenith.Steven Schimmrichhttps://www.blogger.com/profile/12055292815320443096noreply@blogger.comtag:blogger.com,1999:blog-1644183700798263875.post-44773744728553418532013-11-29T11:40:34.975-05:002013-11-29T11:40:34.975-05:00Interesting. What would the Sun look like from 70...Interesting. What would the Sun look like from 700,000 miles? (How close Comet ISON came as it disintegrated while whipping by the Sun?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1644183700798263875.post-23200552511374868812012-05-02T17:05:10.218-04:002012-05-02T17:05:10.218-04:00Trigonometry is cool indeed. Thanks for the calcul...Trigonometry is cool indeed. Thanks for the calculations! The graphical comparison of the Sun's angular size is really impressive.<br /><br />Due to my calculations, the angular size of Sun from the nearest star (Proxima Centauri) is ca 0.007 seconds of arc. Not much, to say the least.Maxnoreply@blogger.com