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
13 ...
View
Full Document
 Fall '09
 dion
 Dot Product, Ry, unit vectors, Solid angle, cartesian unit vectors

Click to edit the document details