Albedo & Emissivity (SL IB Physics)

• Stars are good approximations to a black body, whereas planets are not
  • This can be quantified using the emissivity
• Emissivity, e, is defined as

The the ratio of the power radiated per unit area by a surface compared to that of a black body at the same temperature

• It can be calculated using the equation

e =

• Calculations of the emissivity assume that the black body:
  • Is at the same temperature as the object
  • Has the same dimensions as the object

• For a perfect black body, emissivity is equal to 1
• When using the Stefan-Boltzmann law for an object which is not a black body, the equation becomes:

P = eσAT⁴

• Where:
  • P = total power emitted by the object (W)
  • e = emissivity of the object
  • σ = the Stefan-Boltzmann constant
  • A = total surface area of the object black body (m²)
  • T = absolute temperature of the body (K)

• Albedo, a, is defined as

The ratio of the total scattered power to the total incident power of radiation that is reflected by a given surface

• It can be calculated using the equation

a =

• More specifically, the albedo of a planet is defined as

The ratio between the total scattered, or reflected, radiation and the total incident radiation of that planet

• Earth’s albedo is generally taken to be 0.3, which means 30% of the Sun’s rays that reach the ground are reflected, or scattered, back into the atmosphere
• An albedo of 1 represents a surface that scatters all the incident radiation
• Earth’s albedo varies daily and depends on:
  • Cloud formations and season – the thicker the cloud cover, the higher the degree of reflection
  • Latitude
  • Terrain – different materials reflect light to different degrees
  • Incident angle of radiation
• It is useful to know the albedo of common materials: 
  • Fresh asphalt = 0.04
  • Bare soil = 0.17
  • Green grass = 0.25
  • Desert sand = 0.40
  • New concrete = 0.55
  • Ocean ice = 0.50 - 0.70 
  • Fresh snow = 0.85
• Albedo has no units because it is a ratio (or fraction) of power