How To Derive The Orbital Velocity For A Circular Orbit
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Welcome, my name is Phil, and in this video I show you how to derive the orbital velocity for a circular orbit.
The orbital velocity of an object in a circular orbit around a central body can be derived using the principles of centripetal force and gravitational force.
Centripetal Force: In circular motion, the centripetal force required to keep an object moving in a circle is provided by the gravitational force between the object and the central body.
Gravitational Force: Newton's law of universal gravitation states that any two masses in the universe are drawn toward each other with a force that increases in direct proportion to the product of their masses and decreases in inverse proportion to the square of the distance between them.
Equating Forces: In an orbit, the centripetal force is provided by the gravitational force. So, we can equate the centripetal force with the gravitational force to derive the orbital velocity.
Hence, the velocity (v) required for an object to maintain a circular orbit around a central body with mass M, positioned at a distance r from the central body's center, is determined by taking the square root of the product of the gravitational constant G and the central body's mass M, divided by the radius r of the orbit.
It's important to note that this formula applies specifically to circular orbits involving only two bodies: the orbiting object and the central body. For orbits with elliptical trajectories or more intricate scenarios, the derivation process becomes more complex.