4r^2 = (T_S/T_P)^4
where T_S = 5778 K is the effective temperature of the Sun. We get
- Earth: distance D = 500 light seconds = 1 AU, r =220, T_P= 5778/21 = 275 K (288 K)
- Mars: D =1.5, r = 330, T_P = 275 / 1.22 = 229 K (232 K)
- Jupiter: D = 5.2, T_P = 275/2.28 = 120 K ( 134 K)
- Saturn: D = 9.5, T_P = 275/3.08 = 90 K (103 K)
- Uranus: D = 19.2, T_P = 63 K ( 73 K)
- Neptune: D = 30.1, T_P = 48 K ( 63 K)
- Venus: D = 0.72, T_P = 312 K (465 K)
- Mercury: D = 0.39, T_P = 443 K ( 400 K)
where in parenthesis we give observed mean surface temperatures. We see a close fit for Mars, which has a thin atmosphere of 95% CO2. The atmospheres of the Earth and Venus increase surface temperatures substantially above the black body temperature. The very cold Saturn, Uranus and Neptune give off more heat than receieved, from some internal source of heat. Jupiter is estimated to give off about 2 times what is received from the Sun. The day and night temperatures of Mercury vary between -100 K and 700 K and a mean temperature is difficult to define.
For the Earth, the 275 K fits well with the temperature of the stratopause, while the surface temperature of an Earth without an atmosphere is commonly estimated to the lower value -18 C (instead of 2 C) as a result of certain assumptions on albedo and emissivity modifiying the black body aspects. So the -18 C is speculation and not observation.
The most interesting feature is the close fit for Mars, with seemingly small heating from
its CO2 atmosphere.
Inlägg
Solar radiation incident at top of atmosphere = 1367W/m^2 (approximately).
SvaraRaderaSolar radiation reflected =30% (approximately).
Therefore solar radiation absorbed averaged over the surface of the earth = S/4 (1-A) = 239W/m^2 or 255K.
If I understand this interesting article right the CO2 in the atmosphere on Mars is 15 times the CO2 on Earth!
SvaraRaderaSimple calculation using Daltons law re partial pressure and using 360 ppm CO2 on earth versus 95% CO2 on Mars.
"..while the surface temperature of an Earth without an atmosphere is commonly estimated to the lower value -18 C (instead of 2 C) as a result of certain assumptions on albedo and emissivity modifiying the black body aspects."
SvaraRaderaClimate science doesn't reached the conclusion that the surface temperature without an atmosphere would be -18'C. Instead the surface temperature would be -18'C without an atmosphere that absorbs and re-emits longwave radiation.
Without an atmosphere the albedo of the earth is around 10% (haven't looked up the numbers). With an atmosphere the albedo of the earth/climate system is much higher, mainly from clouds but also aerosols.