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Fall 2003 Special Topics: Astrophysics (Phys 493)

Dr. I. Fernini


Homework # 3

Due Monday, October 27 - Late HW won't be accepted anymore.



Problem 1:


By expressing the unit direction vector W in Cartesian coordinates, i.e.,


W = Wx x + Wy y + Wz z



Wx = sinq cosj

Wy = sinq sinj

Wz = cosq


prove the following identities:


(a)            ò dW = 4p

(b)            ò W dW = 0

(c)            ò W (W A) dW = (4p/3) A

(d)           ò (W A) (W B) dW = (4p/3) (A B)


where A and B are any vectors which are independent of W.



Problem 2:


Show that the anisotropic factor f = K/J = 1/3 for each of the following radiation fields:


(a) I(m) = I0 + m I1 (Eddington approximation)

(b) I(m) = I0 d(m - m0) where m0 = 1/Ö3