If the Sun were to vanish, what would ultimately happen to the atmospheric engine that drives weather?

Answer

Winds would eventually cease as the atmosphere cooled toward equilibrium.

Solar radiation is the irreplaceable primary source of heat energy. Without this continuous input, the temperature gradients that generate pressure differences and wind would dissipate as the atmosphere cools, causing the weather engine to stop.

If the Sun were to vanish, what would ultimately happen to the atmospheric engine that drives weather?
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