The core of the earth provides half of the earths heat due to nuclear reactions.
Simply not true. It is true that nuclear reactions in the Earth provide more heat than tidal forces from the Sun/moon combo, but 99.5%+ of the heat is from the Sun. Uranium and thorium in the crust (not the core) provide most of the internal heat, keeping the core warm, and the pressure differential also adds to the heat (although not for the Moon or Mars, which both have cold cores).