Suppose the sun were to suddenly disappear. what would happen to the orbital path of earth? it would stay the same, but the earth would speed up. it would stay the same, but the earth would slow down. it would follow a path perpendicular to the radius of its current orbit. it would spiral outward in an ever-increasing orbit.

it would follow a path perpendicular to the radius of its current orbit

Explanation:

Currently, the Sun provides (with its gravitational attraction) the centripetal force that keeps the Earth in circular orbit around the Sun. The velocity of the Earth is always tangential to this orbit, while the centripetal force is directed towards the centre of the trajectory, therefore it is parallel to the radius of the orbit (which is perpendicular to the velocity of the Earth).

If the Sun suddenly disappears, then the centripetal force disappears. As a result, due to the law of the inertia, the Earth will continue its motion in a straight path, keeping its constant velocity (because there are no more forces that keep it along the circular trajectory): and since the velocity of the Earth was perpendicular to the radius of its previous orbit, the correct answer is

it would follow a path perpendicular to the radius of its current orbit

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