Could an Earth-sized planet be cold?

Question

This question poses the question of why the Earth is still hot after 4.5 billion years, and the primary reasons were:

(1) heat from when the planet formed and accreted, which has not yet been lost; (2) frictional heating, caused by denser core material sinking to the center of the planet; and (3) heat from the decay of radioactive elements.

With that in mind, would it be possible for a planet of Earth's size and age to have a cold core, mantle, and crust?

The entire planet, or just the surface? https://en.wikipedia.org/wiki/Snowball_Earth — Phil N DeBlanc, Jul 24 '18 at 17:27
The actual planet. The temperature of the surface isn’t very interesting to me, since it would largely depend on the local solar conditions — Daniel B, Jul 24 '18 at 17:37
relatively speaking, without a major moon, it's relatively possible. The Earth is 6000'C core and Mars is 1300'C core, It's possible that a similar Earth has 5 times as much crust width as earth if it doesn't have a major moon to place force on the mantle and core, perhaps 30 times, but it seems unlikely that a planet the size of earth is as cold as 3000 degrees at the center and has >100x times more crust, say 250km of crust on a Earth type planet, the radius is 6300, so, 500km of crust after 4 billion years is perhaps possible withouta moon, It takes a lot of maths to state a figure — bandybabboon, Jul 25 '18 at 01:58
It's absolutely possible, the question is, how long would it take. Probably longer than the current age of the Universe I would think at least for rocky worlds. Earth size (a baby neptune or large Ganymede or Titan which aren't planets), those might cool more quickly but 350 K is very cold for this situation. Might take 100 billion years or so if I was to make a bad guess. — userLTK, Jul 25 '18 at 03:25
This problem was analyzed back in the 19th century, when radioactivity was not yet discovered (let alone the radioactive levels of the core), and the scientists at the time understood that, based on cooling rate calculations, the Earth could not be close to as old as other geology methods suggested. Scientists left this as a question to be studied; certain religious groups jumped on this as proof of a 'young Earth' . — Carl Witthoft, Jul 25 '18 at 15:25

score 1 · Answer 1 · edited Jul 25 '18 at 17:50

If you peruse Google for Earth cooling rates, you might find what you're looking for. Here's one of many sources. I strongly recommend reading the entire page,as it discusses some of the geology-based estimates as well.

Kelvin's primary attack on geologic dating was that measurements of the rates of geologic processes were highly uncertain, if it was possible to measure them at all (Hallam, 110). Accordingly, Kelvin sought to apply the knowledge of physics to the problem. Given that temperature increases the further one descends below Earth's surface, Kelvin concluded that Earth was slowly cooling. He set out to calculate the time required for the Earth to cool, and thereby solidify, from an initially molten state. The idea that Earth had begun as an incredibly hot sphere of liquid dates back to Descartes and Leibnitz. This assumed initial condition was the linchpin for Kelvin's entire method (Hallam, 110). Bits of material at the surface would sink before solidifying, creating convection currents that kept the Earth at a uniform temperature until solidification began at the core (Hallam, 110; Knopf, 445). Kelvin needed to know: (1) the temperature at Earth's core, (2) the temperature gradient with regard to depth below the surface, and (3) the thermal conductivity of rocks. The gradient was established to be around one degree Fahrenheit for every fifty feet. Kelvin made his own measurements of conductivity. The problem was determining the temperature at the core. This is where Kelvin's theory of solidification enters the picture. Because the core was thought to be solid rock, its temperature could not exceed the melting point of rocks (Hallam, 110). He constructed the following equation:

dθ / dx = S / h √(π t)

The temperature gradient is expressed by dθ / dx; h is the thermal conductivity; x is the distance below the surface, and θ is the temperature (Holmes, 445). In 1862, Kelvin arrived at a likely age of 100 million years. Because of uncertainties in the data, the lower and upper limits were 20 million and 400 million years (Dalyrmple, 26; Hallam, 111).

That said, there are plenty of more recent papers which estimate the cooling rates (with and without the help of the radioactive elements) based on the kinds of data now available as to the current and historical makeup of the core, mantle, and outer layer(s), heat transfer cycles, etc.

Could an Earth-sized planet be cold?

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