Given perfect conduction (uniform surface temperature, bright side and dark side have the same temperature at all times), https://en.wikipedia.org/wiki/Black-body_radiation#Temperature_relation_between_a_planet_and_its_star applies : temperature does not depend on rotation speed. Then T = T_sun sqrt(R_sun/(2D)) ; it is the temperature T that balance incoming radiation P_inc = pi (R_planet^2) (R_sun^2) (T_sun^4)/(D^2) and emitted radiation P_em = 4 pi (R_planet^2) * T^4
Let’s suppose no conduction at all. The bright side and the dark side does not exchange heat at all. Let’s take two limiting cases : tide-locked planet, and an “infinitely fast” fliping planet.
In the first case, the dark side of the planet is at absolute 0. The bright side of the planet receives the same incoming radiation but emit half its radiation (halved surface) -- change 4 pi to 2 pi in P_em. Its temperature is T_bright = 2^(1/4) T. Average temperature of the planet is (0+T_bright)/2=2^(-3/4) T
In the second case, each side gets half the incoming power from the sun and radiates half the energy (surface halved). Average surface temperature of the planet is the same that the average surface temperature of any side, which is the same temperature that the perfectly conducting planet, T (the .5 from halved incoming power and .5 from halved outgoing radiation cancel each other).
So : rotation raises temperature of a non-perfectly-heat-conducing planet, bringing its surface temperature closer to the perfectly-heat-conducting planet surface temperature.
You’re right, the 2^(-3/4) (and the 2^1/4) is probably quantitatively wrong (unless each side is perfectly heat-conducing but both are isolated from each other. Or if the planet is a coin facing the sun. You know, spherical cows in a vacuum…). But I don’t think that changes the qualitative conclusion, which hold as long as the bright side is hotter but not twice as hotter than the perfectly-heat-conducing planet.
Given perfect conduction (uniform surface temperature, bright side and dark side have the same temperature at all times), https://en.wikipedia.org/wiki/Black-body_radiation#Temperature_relation_between_a_planet_and_its_star applies : temperature does not depend on rotation speed. Then T = T_sun sqrt(R_sun/(2D)) ; it is the temperature T that balance incoming radiation P_inc = pi (R_planet^2) (R_sun^2) (T_sun^4)/(D^2) and emitted radiation P_em = 4 pi (R_planet^2) * T^4
Let’s suppose no conduction at all. The bright side and the dark side does not exchange heat at all. Let’s take two limiting cases : tide-locked planet, and an “infinitely fast” fliping planet.
In the first case, the dark side of the planet is at absolute 0. The bright side of the planet receives the same incoming radiation but emit half its radiation (halved surface) -- change 4 pi to 2 pi in P_em. Its temperature is T_bright = 2^(1/4) T. Average temperature of the planet is (0+T_bright)/2=2^(-3/4) T
In the second case, each side gets half the incoming power from the sun and radiates half the energy (surface halved). Average surface temperature of the planet is the same that the average surface temperature of any side, which is the same temperature that the perfectly conducting planet, T (the .5 from halved incoming power and .5 from halved outgoing radiation cancel each other).
So : rotation raises temperature of a non-perfectly-heat-conducing planet, bringing its surface temperature closer to the perfectly-heat-conducting planet surface temperature.
This is clearly wrong. The bright side hasn’t an uniform temperature T.
You’re right, the 2^(-3/4) (and the 2^1/4) is probably quantitatively wrong (unless each side is perfectly heat-conducing but both are isolated from each other. Or if the planet is a coin facing the sun. You know, spherical cows in a vacuum…). But I don’t think that changes the qualitative conclusion, which hold as long as the bright side is hotter but not twice as hotter than the perfectly-heat-conducing planet.
Oh, yes, it does change, of course.
The result, that a faster rotating planet is warmer, is against the Al Gore’s theology about Climate Change, formerly known as the Global Warming.
As Scott Alexander said—the scientific community consensus was wrong, I was right.
I am not sure about him, I know I am right here and the “science community” as it is self-proclaimed—is wrong.
A faster rotating planet is warmer.