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EP3

EP3. Determining the Equilibrium or Planck temperature of a Planet in the absence of an atmosphere. Energy Balance. T s. Shortwave (visible) radiation emitted by sun heats up surface of the Earth. Earth then radiates IR radiation as a blackbody

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EP3

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  1. EP3

  2. Determining the Equilibrium or Planck temperature of a Planet in the absence of an atmosphere.

  3. Energy Balance Ts Shortwave (visible) radiation emitted by sun heats up surface of the Earth. Earth then radiates IR radiation as a blackbody with temperature Ts.. For equilibrium, shortwave energy in = IR radiation out.

  4. As seen from the Sun, the cross-sectional area of a planet is where r is the radius The (average) reflectivity of the planet is the albedo, a, where a = 1 means a perfectly white planet.

  5. Planck Temperature Calculation Energy Balance Solar Power Absorbed: Power radiated by Planet R (Assume rapidly rotating Planet.)

  6. Equating the two quantities, and solving for Ts, the surface temperature of the planet, we find:

  7. Planck Temperatures

  8. Surface temperature considering the effect of an atmosphere

  9. Infrared Absorptivity of the Earth’s atmosphere

  10. 290 K Blackbody

  11. Latitudinal Energy Balance Equation Energy radiated from a latitudinal zone: Energy flow between latitudinal zones: The following equation must be iterated to find the temperature for each zone:

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