1. Astronomy 340 Fall 2005
Class #4
18 September 2007

2. Announcements HW #1 due Thursday A little out of order
Last time  radiation (notes available today)
This time  tides

3. Solar Heating and Transport
Why?
Astrophysics is all about how energy gets from point A to point B
Sun responsible for most of energy in solar system
Surface temperature
Atmospheric temperature
Mass loss from comets
Temperature
Measure of kinetic energy; E=(3/2)nkT
n = # cm-3
k = Boltzman’s constant
T = temp
Thermal  E = (1/2)mv2  so temp is related to velocity (consider simple case of escape velocity of an atmosphere from a planet a given distance from the Sun

4. Radiation Bf(T) = (2hf3/c2)[1/(ehf/kT-1)]
Λmax = (0.29/T)  wavelength at the maximum of the BB curve
f = frequency
Units = erg s-1 cm-2 Hz-1 ster-1
In limit hf << kT, then
Bf(T) ~ (2f2/c2)kT
True in the radio regime

5. Radiation What do we measure? F = ΩB(T) (erg s-1 cm-2 Hz-1)
Integrate over frequency and solid angle
F = 4π∫Bf(T)df = σT4 – this is a measure of the effective temperature – the flux emitted by any source can be described by a single temperature. Similarly, the Sun emits radiation as a function of its temperature

6. What happens when solar radiation meets a planetary surface?
Fin = (Lo/4πD2)πRp2
This heats the surface and the surface radiates….how much?
In general
L = 4πR2σT4
So if the planet’s luminosity arises solely from incoming solar flux, then
Teq = [(L0/4πD2)(1/4σ)]1/4  equilibrium temperature just balances radiation in with radiation out.

7. Complications
Albedo – the amount of radiation that is actually absorbed as opposed to being reflected or hitting at non- incident angles
Fin=(1-Ab)(L0/4πD2)πRP2
But it’s even more complex…
Albedo
Rotation period  what do you think the effect is
angle of Sun

8. ∫0∞(1-Av)(L0/4πr2)cos(α(t)-α)cos(δ0(t)-δ)dv
Heating of planetary surfaces via conduction…
depends on the characteristics of the surface material
Depends on temperature gradient
Q = heat flux = -ζ (dT/dx)  this is empirical
X= distance
ζ = thermal conductivity (erg s-1 cm-1 K-1

9. Properties of surfaces – thermal heat capacity and specific heat
CP = (dQ/dT)P = thermal heat capacity = amount of heat needed to raise the temp of one mole of matter by 1 degree K at constant P (can also do the same for volume)
Specific heat = amount of energy needed to raise temp of 1 gram of material by 1 degree K at constant temperature and pressure. Usually shown as cP or cV.
Related via: cP = (CP/mm) where mm is that mass of a mole of the stuff  can substitute V for P.