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ay45c2-page4 - 2.1.3 Angular separations from coordinates...

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Unformatted text preview: 2.1.3 Angular separations from coordinates in Sky First convert from latitude-longitude 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 ...
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