Greenhouse effect Masatsugu Sei Suzuki Department of Physics (Date: September 21, 2018) 1. Solar constant ( 0 p ) The solar constant is a flux density measuring mean solar electromagnetic radiation (solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (AU) from the Sun (roughly the distance from the Sun to the Earth). It is measured by satellite as being 1361 W/m² at solar minimum and approximately 0.1% greater (roughly 1362 W/m²) at solar maximum. Solar constant is the energy flux from the Sun to the Earth, energy per unit area per unit time. The luminosity of the Sun (which is the total energy per unit time from the Sun) is given by 6 4 2 0 2 2 3.828 10 4 4 sun sun B sun L R T dp W. So we have 2 4 0 2 4 sun B sun R T p d =1361.17 W/m 2 The luminosity of the Earth is 2 4 4 earth E B E L R T which is equal to 2 0 E R p ; 2 2 4 0 4 earth E E B E L R p R T or 4 0 0 4 B E p J T The real temperature of the Earth is determined from the relation 2 2 4 0 0 (1 )( ) 4 E E B r R p R T
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Greenhouse effect Masatsugu Sei Suzuki Department of ...bingweb.binghamton.edu/~suzuki/ThermoStatFIles/6.5 PD Greenhou… · greenhouse effect, even though most greenhouses depend
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Greenhouse effect
Masatsugu Sei Suzuki
Department of Physics
(Date: September 21, 2018)
1. Solar constant ( 0p )
The solar constant is a flux density measuring mean solar electromagnetic radiation (solar
irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical
unit (AU) from the Sun (roughly the distance from the Sun to the Earth). It is measured by satellite
as being 1361 W/m² at solar minimum and approximately 0.1% greater (roughly 1362 W/m²) at
solar maximum.
Solar constant is the energy flux from the Sun to the Earth, energy per unit area per unit time.
The luminosity of the Sun (which is the total energy per unit time from the Sun) is given by
64 2
0
22 3.828 104 4sun sun B sunL R T d p W.
So we have
2 4
0 2
4 sun B sunR Tp
d
=1361.17 W/m2
The luminosity of the Earth is
2 44earth E B EL R T
which is equal to 2
0ER p ;
2 2 4
0 4earth E E B EL R p R T
or
400
4B E
pJ T
The real temperature of the Earth is determined from the relation
2 2 4
0 0(1 )( ) 4E E Br R p R T
or
400(1 )
4B
pr T
where r is the reflection constant. When r = 0.3, we have 0 255T K.
The solar constant is not really constant. There is a small variation, typically less than 1W/m2,
due to the change of the solar output over an 11-year solar cycle, as well as variations on
cosmological time scales. The solar constant is defined as the amount of solar radiation received
outside the Earth’s atmosphere at the Earth’s mean distance from the Sun. The Earth’s orbit is
slightly eccentric, which leads to a variation of solar irradiance from 1412W/m2 in early January