Question

1) Every second the Sun outputs 3.90* 10^26 Joules of energy. Power is energy output per unit

time and is given in units of Watts (W) where 1 W = 1 Joule per second. The Sun's power

output is therefore 3.90*10^26 Watts. This is called the solar luminosity. As this energy travels

outward from the Sun it is spread (fairly evenly) over a spherical surface that increases in area

with distance from the Sun (recall the area of a sphere is proportional to its radius squared).

The energy received each second by an area of 1 m2 is called the energy flux.

a) Calculate the energy °ux from the Sun at a distance of 9:54 AU (that is, Saturn's mean

distance) from the Sun. How does this compare with the solar flux received at the Earth's

mean distance from the Sun?

b) Suppose we place a perfectly black sphere with radius 2600 km at a distance of 9:54 AU from

the Sun. How much direct solar energy does the sphere absorb in one second?

c) If the sphere in part (b) is in thermal equilibrium, what is its temperature?

d) Titan re°ects approximately 20% of the light that strikes its surface, and absorbs the rest.
Titan's radius is roughly 2600 km. How much energy from sunlight does Titan absorb each
second? What is the temperature of Titan if it has no internal heat sources of significance?

Answer 1

These are exercises in using the inverse square law of luminosity and the blackbody law of thermal radiation. You will be helped if you first make an effort and show your work.