How does gravity provide the centripetal force that keeps Earth in orbit around the Sun?

In the context of celestial mechanics, Earth’s orbit is maintained by a continuous balance between inertia and gravity.12

According to the law of inertia, an object in motion tends to travel in a straight line at a constant speed. Without the influence of gravity, Earth would move away from the Sun along a straight, tangential path. However, the Sun exerts a gravitational force on Earth that acts as an inward, centripetal force.12

This gravitational pull constantly redirects Earth’s velocity vector toward the Sun, producing the centripetal acceleration necessary to keep the planet in a curved orbit. Essentially, Earth is in a state of constant "free fall" toward the Sun, but its forward velocity is sufficient to ensure that it continuously "misses" the Sun, resulting in a stable orbital path. This interaction demonstrates that an orbiting planet is a freely falling body, with the gravitational force serving to overcome the planet's inertial tendency to fly off into space.12