Q2.2. If the great-circle angular separation between two points on the celestial sphere with right ascension and declina

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Q2 2 If The Great Circle Angular Separation Between Two Points On The Celestial Sphere With Right Ascension And Declina 1 (100.67 KiB) Viewed 21 times

Q2.2. If the great-circle angular separation between two points on the celestial sphere with right ascension and declination values (@1,8) and (a2,82) is d, then: a. Using spherical trigonometry (see Appendix A), write down an expression for cosd. {Hint: Construct a spherical triangle with vertices at the NCP, the point (,8) and the point (a2,0z) and use the cosine rule.} [7 points). 2 b. Using the small-angle approximations (e.g. sin x = x and cos x = 1-3 show that the small-separation limit of the great-circle relation derived in (a) is ď =(18)? + cos²z (Aa)”, where A8 = 8, – 8, Aa= a, – a, , and = 8+82. Hints: { 2 i) Assume the relation: cos(x-&) cos(x+8) - cos²x-&?, (€«l); this can be derived by simplification; ii) Also, drop terms of higher order than (Aa)", (48)", or (AaAS)" for n > 2}. [8 points). n