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
where
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