Re: ATM Formula

[Anthony Stillman <atmer@flash.net>]

>...image of ...Jupiter, ...2 inches in diameter.
>...Jupiter is say 30 seconds of arc

Joe,

As we are dealing with small angles, we can make a simplifying
approximations.  Namely, tan(x) = x  where x is in radians.

Now, 30 arc seconds is

30 arc seconds = 1/2 arc minutes = 1/2 * 1/60 degrees

An angle in degrees can be converted to radians by multiplying by pi and
dividing by 180.

  x radians = 3.141592653... * y degrees / 180

Hence 30 arc seconds is 0.145 milliradians  (0.000145 radians)

Now for the answer to your question.  How far away (L) must you place a 2"
(d) diameter object such that is subtends 30 arc seconds?

The tangent of an angle in a right triangle is defined as the length of the
side opposite the angle divided by the length of the side adjacent to the
angle (d/L)  However, we can let the tan(x) equal x, so, in this instance:

    0.000145 radians = 2 / L

therefore

    L = 13793 inches   (1149.4 feet) (a bit more than a fifth of a mile)



Anthony