The force that keeps planets in orbit around the Sun is gravitational force. Gravity is a fundamental force that attracts objects with mass toward each other. In our solar system, the Sun’s massive gravitational pull keeps planets in their elliptical orbits. The balance between the gravitational force and the inertia of a planet moving forward keeps it in a stable orbit. This relationship was famously described by Isaac Newton in his law of universal gravitation and further explained by Albert Einstein's theory of general relativity, contributing to our understanding of celestial mechanics.