# How many radians = 1 arc second?

sonhouse
Science 26 Nov '08 23:56
1. sonhouse
Fast and Curious
26 Nov '08 23:56
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 1,296,000 arc seconds so if I divide that by 2 PI (6.28....) I come up with 206,264.8062... arc seconds = 1 radian. Then invert that 1/206,264... and I come up with 4.848 E -6 radians = 1 arc second. Is this correct? Thanks.
2. joe shmo
Strange Egg
27 Nov '08 02:531 edit
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.
First

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

then

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.
3. AThousandYoung
West Coast Rioter
27 Nov '08 03:201 edit

http://en.wikipedia.org/wiki/Minute_of_arc

Yes, you are correct.
4. sonhouse
Fast and Curious
27 Nov '08 04:421 edit
Originally posted by AThousandYoung

http://en.wikipedia.org/wiki/Minute_of_arc

Yes, you are correct.
Thanks, didn't see that link. Funny, it gives 8 significant figures as 'approximate'ðŸ™‚
I only need maybe 4 significant figures for my scribbling.
5. sonhouse
Fast and Curious
27 Nov '08 04:44
Originally posted by joe shmo
First

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

then

1 arc sec = 2Pi rad./(1.296x10^6)

or use conversion factors as illu ...[text shortened]... Another benifit of this method, is that it can be arranged in any way to solve for any unit.
Thanks for that, I think I can use that in my hp48 set of programs on the subject.