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Science Forum

  1. Standard member 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. Subscriber joe shmo
    Strange Egg
    27 Nov '08 02:53 / 1 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. Subscriber AThousandYoung
    Do ya think?
    27 Nov '08 03:20 / 1 edit
    Arcsecond = 4.8481368 µrad

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

    Yes, you are correct.
  4. Standard member sonhouse
    Fast and Curious
    27 Nov '08 04:42 / 1 edit
    Originally posted by AThousandYoung
    Arcsecond = 4.8481368 µrad

    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'
    I only need maybe 4 significant figures for my scribbling.
  5. Standard member 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.