1
Homework 1
Due: Sep.11
Problem 1 (20 Points)
Assume that the Sun radiates as a blackbody at T=5783 K and is a uniform sphere with a
radius of 6.96x105 km. Calculate total solar radiance and irradiance at the orbits of Venus
and Earth. The distance between the Earth and Sun is 1.5x108 km and between the Sun
and Venus is 1.08x108 km.
Problem 2 (20 Points)
You are observing a cloud that occupies the portion of the sky defined by π/4<θ<π/2 and
0< φ< π/8.
i) What is the solid angle subtended by the cloud?
ii) What percentage of the sky is covered by this cloud?
Problem 3 (10 Points)
The net flux is defined as the integral of a normal component of the intensity over the all
solid angles (over 4π). Starting with this definition, show that ↓
↑−=
λλ
λ
FFFnet ,.
Problem 4 (10 points)
For blackbody radiation, flux is proportional to intensity:
λ
π
λ
IF
=
Derive this equation starting with Eq.(3.7) in Lecture 3.
Problem 5 (40)
Using the result of Problem 3 and the expression of Planck function derived in Appendix A
of your textbook, derive the Stefan –Boltzmann law F =
π
B(T).