Which force keeps the planets in orbit around the Sun?

Gravity holds the solar system together. Every mass attracts every other mass, and the strength of the pull grows with the masses involved but falls off with the square of the distance between them, so doubling the separation quarters the force. A planet in orbit is not being held still; it is falling continuously toward the Sun while also moving sideways fast enough that it keeps missing. The two effects combine into a curved path that closes into an ellipse. That is why an orbit needs no fuel and no ongoing push. Newton's insight was that the force pulling an apple down and the force curving the Moon's path are the same thing, obeying one law. Einstein later reframed gravity not as a pull but as the curvature of space and time around a mass, with planets simply following the straightest available path through curved spacetime, a description that matches observation even more precisely.

Gravity is by far the weakest of the four fundamental forces, but it has unlimited range and never cancels out.