Equations needed:
(1.) Wien's Law:  T= 3 x 10⁶nm/l
The temperature is in Kelvin (Degrees Celsius +273.15).

For the rest of the problem set you will need to consider intensity:

Intensity is the power per area. I=P/A
I, the intensity, is the power (Watts) per unit area (m²).

Note: Power and Luminosity are the same thing. (We tend to call the power of a luminous object luminosity)
Intensity from a "black body":

(2.) I=constant T⁴

note that T⁴ is TxTxTxT !!!!

(the constant, named sigma, or s in the book pg. 366, is equal to 5.67 x 10^-8 Watt / (m² K⁴).)

We don't really need to know what the constant is. Rather, for two hot objects, indexed 1 and 2, of different areas with the same temp we get:

(2.1) P₁/P₂ = Area₁ / Area₂

And both constant and temp. cancel out.

For the two balls with the same areas, but different temperatures:

(2.2) P₁/P₂ = T₁⁴/T₂⁴

And both constant and area cancel out.

If the two objects have DIFFERENT temperature AND DIFFERENT area the ratio of intensities is

(2.3) P₁/P₂ = Area₁T₁⁴/(Area₂T₂⁴).

The area of a sphere is:

(3) A=4pr²

Where r is the radius of the sphere.

Problem #2:  I have two spheres, one with a radius of 0.2 m and the other with a radius of 0.5 m. I heat the small one to a temperature of 2400 K, and the big one to a temperature of of 2100 K.
a) What is the ratio of the intensities of the two spheres? Answer:  0.586
b) What is the ratio of the total power emitted by these spheres? Answer: 3.66

Problem #3: Calculate the total power emitted at all wavelengths by a star whose surface temperature is 7300 K, and whose radius is 2.5 solar radii. (You may assume that the star radiates as a blackbody.) Answer in units of solar power and solar radius.

Problem #4: Calculate the radius of a Main Sequence B0 star (which has a surface temperature of 3 x 10⁴ K, and a luminosity of 1 x 10³ Lo, where Lo means "solar luminosities"). Answer in units of solar radius.

Problem #5: (For extra credit only, so that you may get 12.5/10 for this HW assignment) A spherical planet of radius 6 x 10⁶ m and surface area 4.5 x 10¹⁴ m^2 is 1.5 x 10¹¹ m from a G2 star, with 1 Lo. One side of the star is always facing the sun. Assume that the albedo is 100%, that is: all light from that star is absorbed by the planet, and then re-emitted as black-body radiation.
a. What is the intensity (power/area) of light from the star at the surface of the planet?
b. What is the surface temperature of that planet?
c. What is the total luminosity of the reflected light in units of Lo?
d. What may be the implications of this result for the search for extra-solar planets similar to earth?