Question

What would happen to the earth if both the sun and the moon were to disappear instantly?

Answer 1

Earth would become colder and fly off into space in a (mostly) straight line. It would also spin much faster due to the loss of tides (source).

Explanation:

Since the sun and the moon provide almost all the gravitational pull on earth, the earth would fly off into space at its tangential velocity. The loss of tides (which are caused by the Moon's and Sun's gravity) could decrease Earth's rotational inertia and increase its angular velocity, but more importantly, Earth would lose its main source of heat and light. Since wind is caused by temperature differentials, it would gradually slow down and stop.