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Rg. 9-4. The Electromagnetic Spectrum. The expanded view highlights visible and Infrared wavelengths frequently exploited by satellites. Sample space missions across the entire spectrum are listed above the band region.

30 WAVELENGTH, Pm

Rg. 9-4. The Electromagnetic Spectrum. The expanded view highlights visible and Infrared wavelengths frequently exploited by satellites. Sample space missions across the entire spectrum are listed above the band region.

For all electromagnetic radiation in a vacuum, the relation between the wavelength, A, and the frequency, v,* is c = Av = 2.997 924 58 x 108 m/s (9-1)

where c is the speed of light Thus, in terms of frequency, the usable electromagnetic spectrum ranges from radio waves measured in kilohertz (kHz) to gamma rays with

* Both V and/are commonly used to represent frequency. We use V throughout this chapter to avoid confiision with focal length, which is also represented by/.

frequencies in the tens of exahertz (EHz). (1 kiloheitz = 1,0(X) cycles/s = 300-km wavelength; 1 exahertz = 109 GHz = 1018 cycles/s = wavelength of 3 angstroms or 3 x 10"IO'm.)*

At any temperature above absolute zero (0 K), all matter continuously emits electromagnetic radiation. This is called thermal radiation or Hackbody radiation. For a perfect blackbody, the rate of total energy emission and the energy distribution by wavelength or frequency is a function only of the temperature, T. The actual spectrum of emitted radiation from a real object will depend on the surface characteristics for small objects, such as a spacecraft, or on the atmosphere for large objects, such as the Earth or Sun. Nonetheless, in practice the blackbody energy distribution is a good starting point for analysis. The spectral energy distribution of a blackbody is given by Planck's Law.

2jiAC

A5 ech,m-l

where E^ is the energy per unit wavelength (also called the spectral irradiance and typically measured in W*nr2,nnr1),A is the wavelength, h is Planck's constant (6.626 075 5 x IO-34 W-s2), T is the absolute temperature, c is the speed of light, and k is Boltzmann's constant (1.380 658 x IO"23 W-s/K). Figure 9-5 shows typical energy distribution curves for various blackbody temperatures. When E^ is divided by the solid angle (in steradians) leaving an extended source in a given direction, it becomes L\ the spectral radiance (typical units, W-nr2'pmr1*sr-1).

Frequency (Hz) 1014 1010

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