🛰️ Orbital Velocity Calculator

Calculate orbital velocity for circular orbits around Earth

Semi-Major Axis, a (meters)

Distance from Earth's center. For circular orbits, this equals the orbital radius.

Example: 6,871,000 m = 500 km altitude (6,371 km Earth radius + 500 km)

How to Use This Calculator

Enter Semi-Major Axis

Input the semi-major axis of the orbit in meters. For circular orbits, this is the distance from Earth's center to the satellite. Remember to add Earth's radius (6,371 km) to the altitude if you're working with altitude values.

Calculate Orbital Velocity

Click "Calculate" to get the orbital velocity, period, and altitude. The calculator uses Newtonian gravity to compute these values accurately for circular orbits.

Interpret Results

Review the orbital velocity (speed needed to maintain orbit), orbital period (time for one orbit), and altitude above Earth's surface. These values are essential for satellite mission planning.

Formula

v = √(GM/a)

Circular Orbital Velocity

Where:

v = Orbital velocity (m/s)
G = Gravitational constant = 6.67430 × 10⁻¹¹ m³kg⁻¹s⁻²
M = Earth mass = 5.972 × 10²⁴ kg
a = Semi-major axis (meters)

Example Calculation: Low Earth Orbit

For a satellite at 500 km altitude:

Earth radius: R = 6,371,000 m
Altitude: h = 500,000 m
Semi-major axis: a = R + h = 6,871,000 m

Calculation:

v = √(GM/a)

v = √((6.67430×10⁻¹¹ × 5.972×10²⁴) / 6,871,000)

v = √(5.802×10⁷)

v ≈ 7,616 m/s ≈ 7.62 km/s

This is approximately 27,400 km/h - very fast!

Common Orbital Velocities:

LEO (500 km): ~7.62 km/s (~27,400 km/h)
ISS (400 km): ~7.66 km/s (~27,600 km/h)
GPS (20,200 km): ~3.87 km/s (~13,900 km/h)
Geostationary (35,786 km): ~3.07 km/s (~11,000 km/h)
Escape Velocity (for comparison): ~11.2 km/s from Earth's surface

About the Orbital Velocity Calculator

The Orbital Velocity Calculator determines the speed required for a satellite or spacecraft to maintain a circular orbit around Earth. This velocity balances gravitational pull with the centripetal force needed for circular motion. Understanding orbital velocity is fundamental to satellite design, space mission planning, and orbital mechanics.

When to Use This Calculator

Satellite Design: Determine required orbital velocity for different altitudes
Mission Planning: Calculate velocity requirements for orbital insertion
Educational Purposes: Learn about orbital mechanics and gravitational physics
Space Station Operations: Understand ISS orbital velocity characteristics
Orbital Maneuvers: Calculate velocity changes needed for orbital transfers

Why Use Our Calculator?

✅ Accurate Formula: Uses standard orbital velocity equation from physics
✅ Complete Results: Calculates velocity, period, and altitude simultaneously
✅ Educational Tool: Understand the relationship between altitude and velocity
✅ Real-World Values: Matches actual satellite orbital velocities
✅ Free to Use: No registration required
✅ Mobile Friendly: Works on all devices

Understanding Orbital Velocity

Orbital velocity is the speed needed to maintain a stable circular orbit:

Balance of Forces: Gravitational force provides the centripetal force needed for circular motion
Inverse Square Root Relationship: v = √(GM/a) means velocity decreases as altitude increases
Lower Orbits = Higher Velocity: Satellites closer to Earth must move faster to avoid falling
Higher Orbits = Lower Velocity: Satellites farther from Earth can move slower
Mass Independent: Orbital velocity is the same for all objects at the same altitude, regardless of mass

Physical Derivation

The orbital velocity formula comes from balancing forces:

Gravitational Force: F_g = GMm/a² (Newton's law of universal gravitation)
Centripetal Force: F_c = mv²/a (required for circular motion)
Balance: F_g = F_c → GMm/a² = mv²/a
Solving: v² = GM/a → v = √(GM/a)

Comparison to Escape Velocity

Orbital velocity and escape velocity are related:

Orbital Velocity: v_orb = √(GM/a) - maintains circular orbit
Escape Velocity: v_esc = √(2GM/a) - leaves orbit entirely
Relationship: v_esc = √2 × v_orb ≈ 1.414 × v_orb
Example: At Earth's surface, orbital velocity would be ~7.9 km/s, escape velocity is 11.2 km/s

Real-World Applications

Satellite Deployment: Rockets must reach orbital velocity to deploy satellites
Space Station: ISS maintains ~7.66 km/s velocity at 400 km altitude
Geostationary Satellites: Move at ~3.07 km/s to maintain 24-hour orbit
GPS Satellites: Orbit at ~3.87 km/s at 20,200 km altitude
Orbital Rendezvous: Spacecraft must match orbital velocity to dock with space stations

Tips for Using This Calculator

For circular orbits, the semi-major axis equals the orbital radius
Remember to add Earth's radius (6,371 km) when calculating from altitude
Lower orbits require higher velocities - LEO satellites move much faster than geostationary
Orbital velocity is independent of the object's mass - a small satellite and large space station have the same velocity at the same altitude
For elliptical orbits, velocity varies throughout the orbit (faster at perigee, slower at apogee)

Frequently Asked Questions

What is orbital velocity?

Orbital velocity is the speed required for an object to maintain a stable circular orbit around a celestial body. It's the speed at which gravitational force exactly provides the centripetal force needed for circular motion. For Earth, orbital velocities range from ~7.6 km/s for low orbits to ~3.1 km/s for geostationary orbit.

Why do lower orbits have higher velocities?

Lower orbits have higher velocities because gravity is stronger closer to Earth. The stronger gravitational pull requires a higher centripetal force to maintain orbit, which means higher velocity. The relationship is v = √(GM/a), so as distance (a) decreases, velocity must increase.

How fast is the International Space Station moving?

The ISS orbits at approximately 400 km altitude and moves at about 7.66 km/s (27,600 km/h or 17,100 mph). At this speed, it completes one orbit around Earth in about 92.6 minutes, experiencing 15-16 sunrises and sunsets per day.

Does orbital velocity depend on the object's mass?

No, orbital velocity is independent of mass. Both a small satellite and a large space station have the same orbital velocity at the same altitude. This is because gravitational force is proportional to mass (F = GMm/a²), and centripetal force is also proportional to mass (F = mv²/a), so mass cancels out in the equation.

What's the difference between orbital velocity and escape velocity?

Orbital velocity (v = √(GM/a)) maintains a circular orbit. Escape velocity (v = √(2GM/a)) is the speed needed to leave the orbit entirely. Escape velocity is √2 (about 1.414) times the orbital velocity. At Earth's surface, orbital velocity would be ~7.9 km/s, while escape velocity is 11.2 km/s.

Can I use this for elliptical orbits?

This calculator gives the velocity for circular orbits. For elliptical orbits, velocity varies throughout the orbit - faster at perigee (closest point) and slower at apogee (farthest point). The average velocity is close to the circular orbital velocity for the semi-major axis.