NavList:

A collection of intriguing numbers related to time and distance, some of which are relevant to celestial navigation. They all involve the number of sexagesimal units in a unit angle (also known as one radian). The number of degrees in one radian is 180°/pi or 57.3°. Minutes of arc in one radian is 60'·180/pi or 3438'. Seconds of arc in one radian is 60"·60·180/pi or 206265".

• The "average" radius (in some sense of average) of the Earth is 3438 nautical miles which is also the number of minutes of arc in a unit angle (a one radian angle so 60·180/pi). That makes sense if you think about it. It's not an accident.
• The "average" distance to the Moon (in some other sense of average) is 206265 nautical miles. This is also the numer of seconds of arc in a unit angle (3438·60, nearly). That's weird! And actually this one is just an accident. It also implies that the mean HP of the Moon is 57.3 minutes of arc, which is also weird, accidental, and occasionally confusing. :)
• The number of seconds in one year is "pi times ten million". Though accurate to better than 99.5%, this one is little more than a mnemonic for back-of-the-envelope calculations.
• The number of AU's in one parsec is 206265. This one follows directly from the definition.

A reminder of two definitions: 1 AU or "astronomical unit" is the average distance from the Earth to the Sun, which is about 150 million km or 500 light-seconds. 1 parsec is a stellar distance at which a star would have an annual parallax of one second of arc and is approximately equal to 3.26 light-years.

• One more: since the Earth's orbital radius (approximating it as circular) is 500 light-seconds, its circumference is pi·1000 light-seconds. But since the Earth orbits the Sun in nearly pi·10,000,000 seconds, that makes the Earth's orbital speed almost exactly 0.0001 light-second/second. Equivalently, if v is the orbital speed of the Earth and c is the speed of light , then v/c is almost exactly 1/10000. And finally the annual aberration of starlight is 206265·(v/c) or 20.6 seconds of arc.

Frank Reed
PS: Holy Numerical Coincidence, it's PI DAY (3.14)! I wrote this entire post without being aware that it was Pi Day!!