Orbital Velocity

This formula gives the speed needed for an object to stay in a stable circular orbit around a much larger body. It comes from setting the inward gravitational force equal to the centripetal force required to keep the object moving in a circle, then solving for speed. Because stronger gravity or a smaller orbit radius requires more inward acceleration, the orbital speed increases as the central mass grows and decreases as the orbit gets larger.

Use this when you need the speed of a circular orbit around a planet, star, or other gravitating body. It is especially useful for satellites, moons, and simplified orbital-motion problems where the orbit can be treated as nearly circular.

• Using the planet’s surface radius instead of the orbital radius measured from the center
• Forgetting that M must be the mass of the central body, not the orbiting object
• Dropping the square root or mixing up units so the result is not in m/s