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Unformatted text preview: 2.1.3 Angular separations from coordinates in Sky
First convert from latitudelongitude style coordinates to Cartesian unit vectors, e.g., rz = z = sin b
^
rx = x = cos b cos l
^
ry = y = cos b sin l
^
Then use vector formulas to get the angle between the two unit vectors.
cos = r r
^^
1 2 is ok when is not small, but for small separations it becomes inaccurate
(angles pile up around cos = 1). In that case use the construction
^1
r (1/2) ^  ^2
r1 r (1/2)θ ^
r2
length =(
1/2) ^1 + ^2
rr which yields ^r
^
tan 1 = jr + r j :
2 jr ^ j
^
1 2 1 2 2.1.4 Solid angles
When observing an object from a point, the solid angle subtended by the
object refers to the fraction of all \lines of sight" that the object covers. In
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This note was uploaded on 12/29/2011 for the course AST 350 taught by Professor Dion during the Fall '09 term at SUNY Stony Brook.
 Fall '09
 dion

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