The heat of the earth – geothermal energy – comes from the original heat from the earth’s formation, supplemented by heat derived from radioactive decay. Except to the extent that the formation of the earth itself depended on the existence of the sun, that does not come from the sun. Disassociation of atoms (nuclear power, hydrogen power) also do not depend on the sun, again except to the extent that the distibution of elements in the early earth was controlled to some extent by the sun – its presence, its gravity, its solar flux, etc.
Flowing water, wind, solar, wave, biological energy (oil, gas, coal, ethanol, biomass, etc) all ultimately derive their energy from the sun – its heat, its light, etc.
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