Originally posted by sonhouse
I am trying to understand the gravitational lens equation and the answer is in radians and I want to convert directly to arc seconds, check my math, see if my logic is correct:
1 radian is the angle described by the radius of any circle over the radius layed out around the circumference. That makes it 360/ 2*PI. or 57 degrees and change. 360 degrees is 1,2 ...[text shortened]... that 1/206,264... and I come up with 4.848 E -6 radians = 1 arc second. Is this correct? Thanks.
360 degrees = 1.296x10^6 arc seconds
360 degrees = 2 Pi radians
so equate the two right sides of the equation:
1.296x10^6 arc seconds = 2 Pi radians
now to get to 1 arc second divide both sides by 1.296x10^6
note: don't divide out the units as well
1 arc sec = 2Pi rad./(1.296x10^6)
or use conversion factors as illustrated below
(360deg/1,296,000 arc sec)*(2pi/360deg)*(A arc sec)
if you write these ratios vertically you will se that units divide out leaving you with radians in the numerator, Where I put "A", you plug in any number of arc seconds you would like to convert to radians. Another benifit of this method, is that it can be arranged in any way to solve for any unit.