Rocky Planet Surface Temperature: Internal Heating

[BDanielMayfield]

The internal temperature of a rocky planetary body is generated by formational collisions and compression under the force of gravity as well as by radioactive decay if any radioisotopes are present. Heat will flow from the hot compressed core outward to the surface. If the body has no atmosphere the heat would then be radiated out into space, but the surface temp should come to an equilibrium at the point where the rate of heat flows are equal (heat reaching surface from below = heat lost to space). The point is that this body's surface temp will be warmer than it would otherwise be as long as there is still remaining internal thermal energy to provide heat flow. If the body has an atmosphere then it too should be heated at least somewhat at it's base by the heat from the planetary body before this heat is also lost to space.

The above was given to set up my questions re the estimated surface temperatures of planets and exoplanets. Such estimates seem to be solely based on stellar flux and leave out any possible contribution from internal heating. Is my thinking sound or am I missing something important here?

Bruce

[Ann]

Me, the Dunce of all Math, thinks you are right, Bruce.

I think we are lucky here on Earth to live on a planet with such a large core, and the ability to store so much heat in its interior.

Ann

[BDanielMayfield]

Only very very slightly right on this, I now understand. I've learned that the internal heat of the Earth is minuscule compared to what it receives from the Sun. I had wondered if this may have been a partial answer to the Faint Young Sun Problem, (since there would have been more internal heat in the deep past), but 2 and 4 times a small number is still a small number.

Bruce

[neufer]

I think we are lucky here on Earth to live on a planet with such a large core, and the ability to store so much heat in its interior.

• Luck has nothing to do with it:

By the Skinner of our teeth!

---

<<The phrase "anthropic principle" first appeared in Brandon Carter's contribution to a 1973 Kraków symposium honouring Copernicus's 500th birthday. Carter, a theoretical astrophysicist, articulated the Anthropic Principle in reaction to the Copernican Principle, which states that humans do not occupy a privileged position in the Universe. As Carter said: "Although our situation is not necessarily central, it is inevitably privileged to some extent." Specifically, Carter disagreed with using the Copernican principle to justify the Perfect Cosmological Principle, which states that all large regions and times in the universe must be statistically identical.

Carter defined two forms of the anthropic principle, a "weak" one which referred only to anthropic selection of privileged spacetime locations in the universe, and a more controversial "strong" form which addressed the values of the fundamental constants of physics.

[In The Emperor's New Mind, Chapter 10] Roger Penrose explained the weak form as follows:

The argument can be used to explain why the conditions happen to be just right for the existence of (intelligent) life on the Earth at the present time. For if they were not just right, then we should not have found ourselves to be here now, but somewhere else, at some other appropriate time. This principle was used very effectively by Brandon Carter and Robert Dicke to resolve an issue that had puzzled physicists for a good many years. The issue concerned various striking numerical relations that are observed to hold between the physical constants (the gravitational constant, the mass of the proton, the age of the universe, etc.). A puzzling aspect of this was that some of the relations hold only at the present epoch in the Earth's history, so we appear, coincidentally, to be living at a very special time (give or take a few million years!). This was later explained, by Carter and Dicke, by the fact that this epoch coincided with the lifetime of what are called main-sequence stars, such as the Sun. At any other epoch, the argument ran, there would be no intelligent life around to measure the physical constants in question—so the coincidence had to hold, simply because there would be intelligent life around only at the particular time that the coincidence did hold!>>

[BDanielMayfield]

I think we are lucky here on Earth to live on a planet with such a large core, and the ability to store so much heat in its interior.

• Luck has nothing to do with it:

I agree with Art, but for different reasons.

Bruce

[Chris Peterson]

The internal temperature of a rocky planetary body is generated by formational collisions and compression under the force of gravity as well as by radioactive decay if any radioisotopes are present. Heat will flow from the hot compressed core outward to the surface. If the body has no atmosphere the heat would then be radiated out into space, but the surface temp should come to an equilibrium at the point where the rate of heat flows are equal (heat reaching surface from below = heat lost to space). The point is that this body's surface temp will be warmer than it would otherwise be as long as there is still remaining internal thermal energy to provide heat flow. If the body has an atmosphere then it too should be heated at least somewhat at it's base by the heat from the planetary body before this heat is also lost to space.

The above was given to set up my questions re the estimated surface temperatures of planets and exoplanets. Such estimates seem to be solely based on stellar flux and leave out any possible contribution from internal heating. Is my thinking sound or am I missing something important here?

Bruce

I don't think that any planet that is near enough its sun to have liquid water, and which has an atmosphere, will have a detectable component of its temperature come from its internal temperature. In general, all of the inner system bodies (say, inside of five or ten AU) of any significant size (say, 1000 km or larger) will have surface temperatures overwhelmingly determined by their sun, assuming they are not tidally locked.