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When a rocky planet like the Earth or Mars forms the gravitational potential energy is converted to heat energy within the planet.

Planets lose heat energy over time by emitting radiation.

But is there a limit to how much heat energy a body can lose? The moon is still hot at its core.

I find it hard to imagine a core still under tremendous pressure yet frozen.

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    $\begingroup$ A lot of the heat in earth's core is due to radioactive decay. $\endgroup$ – David White Dec 5 '19 at 1:15
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    $\begingroup$ The current state of the inner core is crystallized, so that is pretty frozen. High pressure and low temperatures don't exclude each other. Have a look at the physics of degenerate plasmas for example... $\endgroup$ – AtmosphericPrisonEscape Dec 5 '19 at 5:19
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Planets loose heat energy over time by emitting radiation.

Correct. And planets also gain heat energy from radioactive decay (mostly by potassium, uranium, thorium; see Earth's internal heat budget - Radiogenic heat) and by absorbing light from the sun.

But is there a limit to how much heat energy a body can loose ? The moon is still hot at the core.

The planet's core and mantle (several 1000 km of iron and rock) is quite a good heat isolation. Therefore cooling takes a long time (several billion years). See also Earth's internal heat budget - Primordial heat. Neglecting the above mentioned radioactive decay, cooling of the core will continue until the temperature of the core is the same as the temperature of the surface (currently somewhere between 0 °C and 40 °C).

I find it hard to imagine a core still under tremendous pressure yet frozen.

There is no contradiction between high pressure and low temperature. So a cold core will be possible.

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  • $\begingroup$ Also, heat is liberated when liquid metal in the outer core crystallizes onto the inner core. $\endgroup$ – PM 2Ring Dec 5 '19 at 6:45

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