Is geothermal energy ultimately derived from solar energy?
It is not a correct statement:
Geothermal energy comes from the heat within the earth. The word "geothermal" comes from the Greek words geo, meaning earth," and therme, meaning "heat." People around the world use geothermal energy to produce electricity, to heat buildings and greenhouses, and for other purposes.
The earth's core lies almost 4,000 miles beneath the earth's surface. The double-layered core is made up of very hot molten iron surrounding a solid iron center. Estimates of the temperature of the core range from 5,000 to 11,000 degrees Fahrenheit (F). Heat is continuously produced within the earth by the slow decay of radioactive particles that is natural in all rock
italics mine.
Geothermal energy comes from the original energy of the matter solidifying into the sun-planetary system, ultimately from the Big Bang, and from continuous nuclear decays and reactions .
No , the geothermal Energy is not derived from Sun's Energy or Has any relation to Sun's heat energy under normal circumstances. It comes/transforms/translates from within the Earth's Crust through several Chemical and Physical Events inside.
The Answer given is Nuclear Energy , because Of the RadioActive Decay of Matter inside the crust but this is one of the factors that may result in Thermal Energy
An excerpt from Wikipedia says this.
Geothermal energy is thermal energy generated and stored in the Earth. Thermal energy is the energy that determines the temperature of matter. The geothermal energy of the Earth's crust originates from the original formation of the planet and from radioactive decay of materials (in currently uncertain but possibly roughly equal proportions).
Wikipedia Article Here About Geothermal Energy
To the extent that Geothermal Energy arises from the Primordial Energy from the accretion of the planets during the formation of the Solar System, you could correctly argue that Geothermal Energy is also ultimately attributable to the sun, albeit via the suns gravitational attraction rather than it's radiation. More precisely, however, Geothermal energy is comes not only this 'Primordial Heat, but also from 'Radiogenic Heat' from the decay of radioactive isotopes, in roughly similar proportions. According to this Wikipedia article the ranges of these sources are estimated at 15–41 TW and 12–30 TW for radiogenic heat and primordial heat, respectively. https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget