Orbital Velocity Explained

Orbital velocity ($v$) is the speed at which one body must orbit another to maintain a stable, circular path. This velocity is critical because it represents the balance between two opposing forces: the inward gravitational pull of the central body and the outward centrifugal effect of the orbiting object’s momentum.

The calculation uses Newton’s Law of Universal Gravitation and centripetal force, resulting in the clean, fundamental formula: $$ v = \sqrt{\frac{GM}{R}} $$

Significance and Real-World Applications: The concept of orbital velocity is foundational to modern space flight.

• Satellites: Every satellite, from communication relays to GPS units, must achieve a precise orbital velocity for its designated altitude.
• ISS Orbit: The International Space Station (ISS) orbits Earth at approximately 7.66 km/s to maintain its 400 km altitude.
• Space Missions: Calculating the exact velocity required to transfer from one orbit to another (orbital maneuvers) is key for missions like traveling to the Moon or Mars.

How to Use the Calculator

1. Enter the Mass of the Central Body ($M$): Input the mass of the body being orbited (e.g., Earth, Sun, Mars) in kilograms (kg). Use scientific notation (e.g., 5.972e24 for Earth) for very large numbers.
2. Enter the Orbital Radius ($R$): Input the distance from the center of the central body to the orbiting object in meters (m). This is the sum of the central body’s radius and the orbital altitude.
3. Click “Calculate Orbital Velocity”: Press the button to run the calculation and see the step-by-step formula substitution and the final orbital velocity ($v$) in meters per second (m/s).