The temperature of a planet's surface is determined by the balance between the heat absorbed by the planet from sunlight, heat emitted from its core, and thermal radiation emitted back into space. Emissivity of a planet is determined by the nature of its surface and atmosphere. Temperature measurements Pyrometers and infrared cameras are instruments used to measure the temperature of an object by using its thermal radiation; no actual contact with the object is needed. The calibration of these instruments involves the emissivity of the surface that's being measured. Mathematical definitions Hemispherical emissivity Hemispherical emissivity of a surface, denoted ε, is defined as where Me is the radiant exitance of that surface; Me° is the radiant exitance of a black body at the same temperature as that surface. Spectral hemispherical emissivity Spectral hemispherical emissivity in frequency and spectral hemispherical emissivity in wavelength of a surface, denoted εν and ελ, respectively, are defined as where Me,ν is the spectral radiant exitance in frequency of that surface; Me,ν° is the spectral radiant exitance in frequency of a black body at the same temperature as that surface; Me,λ is the spectral radiant exitance in wavelength of that surface; Me,λ° is the spectral radiant exitance in wavelength of a black body at the same temperature as that surface. Directional emissivity Directional emissivity of a surface, denoted εΩ, is defined as where Le,Ω is the radiance of that surface; Le,Ω° is the radiance of a black body at the same temperature as that surface. Spectral directional emissivity Spectral directional emissivity in frequency and spectral directional emissivity in wavelength of a surface, denoted εν,Ω and ελ,Ω, respectively, are defined as where Le,Ω,ν is the spectral radiance in frequency of that surface; Le,Ω,ν° is the spectral radiance in frequency of a black body at the same temperature as that surface; Le,Ω,λ is the spectral radiance in wavelength of that surface; Le,Ω,λ° is the spectral radiance in wavelength of a black body at the same temperature as that surface. Hemispherical emissivity can also be expressed as a weighted average of the directional spectral emissivities as described in textbooks on "radiative heat transfer". Emissivities of common surfaces Emissivities ε can be measured using simple devices such as Leslie's cube in conjunction with a thermal radiation detector such as a thermopile or a bolometer. The apparatus compares the thermal radiation from a surface to be tested with the thermal radiation