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⇤ ← Revision 1 as of 2014-07-01 15:55:04
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| The Planck black body spectrum is ) $ { 2 h {\nu}^3 } \over { c^2 ( e^{h \nu / k T } - 1 $ Watts / steradian m^2^ Hz |
The Planck black body spectrum is: $ \Large { { 2 h {\nu}^3 } \over { c^2 ( e^{h \nu / k T } - 1 ) } } $ Watts / steradian m^2^ Hz |
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| $ { 2 h {\nu}^3 } \over { c^2 ( 1 + h \nu / k T - 1 ) $ | $ \large { { 2 h {\nu}^3 } \over { c^2 ( 1 + h \nu / k T - 1 ) } } $ |
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| $ { 2 h {\nu}^3 } \over { c^2 h \nu / k T $ | $ \large { { 2 h {\nu}^3 } \over { c^2 h \nu / k T }} $ |
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| $ { 2 {\nu}^2 k T } \over { c^2 } $ | $ \large { { 2 {\nu}^2 k T } \over { c^2 } } $ |
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| $ 4 \pi kT BW / {\lambda}^2 $ W / m^2^ | $ 4 \pi kT ~ BW / {\lambda}^2 $ W / m^2^ |
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| $ ( 4 \pi Rsun / \lambda )^2 kT BW $ Watts | $ ( 4 \pi Rsun / \lambda )^2 ~ kT ~ BW $ Watts |
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| If we tried to make 100 Terawatts of earth energy from space solar power, and broadcast 120 Terawatts of ISM energy to do it, the brightness of the constellation would be 3500 times the entire sun into all of space. |
If we tried to make 100 Terawatts of earth energy from space solar power, and broadcast 120 Terawatts of ISM band power to do it, the brightness of the constellation would be 3500 times the entire sun radiating into all of space. |
Solar Emission in the ISM band
The sun is 6.955e8 meters in diameter, and 1.496e11 meters away. Its effective black body temperature is 5778k.
The Planck black body spectrum is:
\Large { { 2 h {\nu}^3 } \over { c^2 ( e^{h \nu / k T } - 1 ) } } Watts / steradian m2 Hz
For h \nu << kT, this approximates to:
\large { { 2 h {\nu}^3 } \over { c^2 ( 1 + h \nu / k T - 1 ) } }
\large { { 2 h {\nu}^3 } \over { c^2 h \nu / k T }}
\large { { 2 {\nu}^2 k T } \over { c^2 } }
{ 2 kT / {\lambda}^2 }
Multiplied by half the sky, 2 \pi steradians, and the bandwidth BW , the power per square meter is
4 \pi kT ~ BW / {\lambda}^2 W / m2
Multiplied by the surface area of the sun 4 \pi {Rsun}^2 :
( 4 \pi Rsun / \lambda )^2 ~ kT ~ BW Watts
For the the ISM band, \lambda = 2.997e8 m / 5.8 GHz = 0.0517 meters and BW = 15 MHz. The Boltzmann constant k is 1.3806488 × 10-23 J/K so kT is 7.977E-20 Joules . 4 \pi Rsun / \lambda is 4 π 6.955e8 / 0.0517 = 1.69e11 (unitless). The power emission from the entire Sun in ISM is 2280 Watts / Hz or 34.2 GW for the entire ISM band.
Brighter than 1000 suns
If we tried to make 100 Terawatts of earth energy from space solar power, and broadcast 120 Terawatts of ISM band power to do it, the brightness of the constellation would be 3500 times the entire sun radiating into all of space.