Heat Balance

F_sun = S₀/<r_s>² S₀ ident

ident

1.37 · 10⁶ ergs/cm²

P_abs = (1 - A_b) · F_sun · sunlit area = (1 - A_b) · F_sun ·

· R_eq · R_pl

a = total area = 2

· R²_eq +

(R²_pl/e) · log_e [ (1 + e)/(1 - e)]

e =

sqrt

[R²_eq-R²_pl]/R_eq

F_abs = P_abs/a

T_eq = [P_abs/(a · sigma

sigma

)]^0.25
If the eccentricity is equal to zero, e = 0, then

a = 4

· R_eq · R_eq

F_abs = (1 - A_b) · F_sun/4

T_eq = [ (1 - A_b) · F_sun/(4 · sigma

sigma

) ]^0.25

	bond albedo	F_sun erg/s/cm²	F_abs erg/s/cm²	P_abs erg/s	T_eq K
Venus	0.750	2618462.8	163653.9	7.5299e+23	231.89
Earth	0.306	1370000.0	237414.7	1.2110e+24	254.49
Mars	0.250	590102.3	110447.6	1.5922e+23	210.18
Jupiter	0.343	50616.0	8123.3	4.9933e+24	109.45
Saturn	0.342	15011.7	2381.4	1.0167e+24	80.54
Uranus	0.300	3691.7	641.0	5.1818e+22	58.01
Neptune	0.290	1498.8	264.0	2.0141e+22	46.47
Titan	0.220	15011.7	2927.3	2.4391e+21	84.80

P_int = F_int · a

F_out = F_int + F_abs

ratio = F_out/F_abs = (F_int + F_abs)/F_abs

T_eff = (F_out/ sigma

sigma

)^0.25

	F_int erg/s/cm²	P_int erg/s	F_abs+F_int erg/s/cm²	T_eff K	out/in ratio
Venus	0.0	0.0000e+00	163653.9	231.89	1.0000
Earth	62.0	3.1624e+20	237476.7	254.51	1.0003
Mars	0.0	0.0000e+00	110447.6	210.18	1.0000
Jupiter	5440.0	3.3439e+24	13563.3	124.42	1.6697
Saturn	2010.0	8.5815e+23	4391.4	93.85	1.8440
Uranus	42.0	3.3953e+21	683.0	58.94	1.0655
Neptune	433.0	3.3029e+22	697.0	59.24	2.6399
Titan	0.0	0.0000e+00	2927.3	84.80	1.0000