Orbital Velocity

This formula gives the speed an object must have to stay in a circular orbit around a much larger body, such as a satellite around a planet or a planet around a star. It comes from setting gravitational force equal to the centripetal force needed to keep the object turning in a circle: gravity provides exactly the inward pull required for the motion. The result shows that orbital speed depends only on the central mass and orbital radius, not on the orbiting object's mass (ignoring effects like atmosphere or engine thrust).

Use this when analyzing ideal circular orbits in astronomy, satellite engineering, or introductory celestial mechanics. It is especially useful for finding the speed of a spacecraft, moon, or planet at a given orbital radius around a dominant central body.

• Using the orbiting object's mass in the formula; it cancels out for ideal circular orbits
• Forgetting that r is measured from the center of the central body, not from its surface
• Mixing units, such as using kilometers for r while G and M are in SI units