Astronomy 340 Fall 2005 Class #4 18 September 2007

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

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

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

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

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.

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

∫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

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.