What is orbital velocity?

Orbital velocity is the speed a satellite must maintain in a circular orbit so that the gravitational pull from the central body exactly provides the centripetal force needed to keep it on that circular path. The formula is v = √(GM/r), where G is the gravitational constant, M is the central body mass, and r is the orbital radius measured from the center of the central body.

What is the orbital velocity of the ISS?

The International Space Station orbits at roughly 408 km altitude above Earth's surface, giving an orbital radius of about 6,779 km from Earth's center. Its orbital velocity is approximately 7.66 km/s (about 27,580 km/h).

How does orbital velocity relate to escape velocity?

Escape velocity is exactly √2 times the circular orbital velocity at the same radius. So if orbital velocity is v_orb = √(GM/r), then escape velocity is v_esc = √(2GM/r) = v_orb × √2 ≈ 1.414 × v_orb. You need about 41% more speed to escape than to orbit.

What happens if a satellite moves faster or slower than orbital velocity?

If a satellite moves faster than orbital velocity at a given radius, it will move into a higher orbit (or escape entirely if it reaches escape velocity). If it moves slower, gravity pulls it into a lower orbit or back toward the surface.

Does orbital velocity depend on the mass of the satellite?

No. Orbital velocity depends only on the mass of the central body (M) and the orbital radius (r), not the satellite's own mass. A feather and a space station at the same orbital radius travel at the same speed.

What units does this calculator use?

Mass is entered in kilograms (kg), radius in meters (m), and the result is given in km/s. The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² is used internally.

Orbital Velocity Calculator

Name: Orbital Velocity Calculator
Availability: InStock
Author: Nham Vu

Calculate the orbital velocity of a satellite given its orbital radius and the mass of the central body using v = √(GM/r).

Inputs

Select what to solve for, then fill in the required values.

Solve for

Central body preset (optional)

Central Body Mass (M)

Orbital Radius (r) — from center of body

G = 6.674 × 10⁻¹¹ N·m²/kg² (universal gravitational constant)

Result

Enter values and click Calculate.

Formula Reference

Find Velocity

v = √(GM / r)

Find Mass

M = v² · r / G

Find Radius

r = GM / v²

Summary

Calculate the orbital velocity of a satellite given its orbital radius and the mass of the central body using v = √(GM/r).

How it works

Select what you want to solve for: Orbital Velocity, Central Mass, or Orbital Radius.
Choose a preset celestial body to auto-fill common values, or enter custom inputs.
Click Calculate to apply the formula v = √(GM/r).
The result is displayed alongside a step-by-step mathematical breakdown.
Use the Reset button to clear all fields and start a new calculation.

Use cases

Calculating the orbital speed of the International Space Station or GPS satellites.
Astrophysics and orbital mechanics coursework and exam preparation.
Mission planning for satellite launches and orbital insertion burns.
Comparing orbital velocities at different altitudes around Earth or other planets.
Understanding the relationship between orbital radius and velocity (Kepler's third law).
Teaching Newtonian gravity and circular orbit mechanics.
Verifying known orbital speeds for Moon, ISS, and geostationary satellites.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu