The orbital velocity of an object around another body can be calculated using the following formula:
v = √(G * M / r)
where:
- v is the orbital velocity,
- G is the gravitational constant (approximately 6.674 × 10^-11 m^3/(kg s^2)),
- M is the mass of the central body (the body being orbited), and
- r is the distance between the centers of the two bodies.
This formula is derived from the principles of gravitational force and centripetal force. It assumes a circular orbit, where the gravitational force provides the necessary centripetal force to keep the object in orbit.
It's important to note that this formula provides the orbital velocity in the absence of other forces or factors such as atmospheric drag, other gravitational influences, or the eccentricity of the orbit. In reality, orbital mechanics can be more complex and require more precise calculations, especially for non-circular or highly elliptical orbits.