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Astronomy 340 Fall 2005

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

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Astronomy 340 Fall 2005

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  1. Astronomy 340Fall 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.

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