USEFUL DERIVATIONS
Contents
1
1 Solar Constant 2
2 Pressure using Hydrostatic Equation 3
3 Adiabatic Lapse Rate 5
4 Poisson’s Equation/ Potential Temperature 7
1
, 1 Solar Constant
Solar constant S is defined as the amount of energy per meter squared received at the mean
sun-Earth radius.
We assume that we are considering a black-body so the total amount of radiation emitted from
the sun is
B(T ) = σT 4 [W m−2 ]
Power of the sun can be defined as
PSun = σT 4 × 4πRSun
2
Now we can define the solar constant as
2
S= PSun
2
4πRSE
= σTs4 ( RR2s )
SE
Contents
1
1 Solar Constant 2
2 Pressure using Hydrostatic Equation 3
3 Adiabatic Lapse Rate 5
4 Poisson’s Equation/ Potential Temperature 7
1
, 1 Solar Constant
Solar constant S is defined as the amount of energy per meter squared received at the mean
sun-Earth radius.
We assume that we are considering a black-body so the total amount of radiation emitted from
the sun is
B(T ) = σT 4 [W m−2 ]
Power of the sun can be defined as
PSun = σT 4 × 4πRSun
2
Now we can define the solar constant as
2
S= PSun
2
4πRSE
= σTs4 ( RR2s )
SE
