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physics

Orbital Velocity Calculator

Calculate the orbital velocity required for a circular orbit around a massive body using v = √(GM/r). Determine satellite speeds, orbital periods, and understand Keplerian orbital mechanics.

Reviewed by Christopher FloiedPublished Updated

This free online orbital velocity calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

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Results

Orbital Velocity

7672 m/s

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Orbital Velocity Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Orbital Velocity Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Orbital Velocity Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About Orbital Velocity Calculator

The Orbital Velocity Calculator determines the speed needed for a stable circular orbit around a massive body. Derived by equating gravitational force with centripetal force, v = √(GM/r) reveals that orbital speed depends only on the central body's mass and the orbital radius — not on the orbiting object's mass. The International Space Station orbits at about 7,700 m/s (27,600 km/h) at 400 km altitude. Closer orbits require higher speeds; more distant orbits are slower. This fundamental relationship governs satellite placement, planetary motion, and spacecraft trajectory design.

The Math Behind It

Orbital velocity comes from balancing gravity and centripetal acceleration: GMm/r² = mv²/r, giving v = √(GM/r). The orbiting mass cancels — a feather and a spacecraft orbit at the same speed at the same radius. **Key relationships**: - v ∝ 1/√r (higher orbits are slower) - Orbital period: T = 2πr/v = 2π√(r³/GM) - Orbital energy: E = −GMm/(2r) (bound orbits have negative total energy) **Earth orbit velocities**: - LEO (400 km): 7,672 m/s, T = 92 min - MEO (20,200 km): 3,874 m/s, T = 12 h (GPS) - GEO (35,786 km): 3,075 m/s, T = 24 h (geostationary) - Moon (384,400 km): 1,022 m/s, T = 27.3 days **Escape velocity**: v_esc = √(2GM/r) = √2 × v_orbital. To leave orbit completely, you need √2 times the circular orbital speed. **Hohmann transfer**: To move between orbits, spacecraft use elliptical transfer orbits. They burn to speed up (raise orbit) at one point and burn again at the new altitude to circularize. This is the most fuel-efficient two-impulse transfer. **Geostationary orbit**: At exactly 35,786 km altitude, orbital period matches Earth's rotation (24 hours). The satellite appears stationary from the ground — used for communication and weather satellites. **Lagrange points**: Locations where orbital velocity around one body matches the angular velocity needed to maintain position relative to both bodies. The James Webb Space Telescope orbits at L2, 1.5 million km from Earth.

Formula Reference

Orbital Velocity

v = √(GM/r)

Variables: G = 6.674×10⁻¹¹ N·m²/kg², M = central body mass, r = orbital radius

Worked Examples

Example 1: ISS Orbit

M = 5.972×10²⁴ kg (Earth), r = 6,771,000 m (400 km altitude)

Step 1:v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 6,771,000)
Step 2:= √(3.986×10¹⁴ / 6,771,000)
Step 3:= √(58,867,000) = 7,672 m/s

ISS orbits at 7,672 m/s (27,620 km/h) — completing one orbit in 92 minutes.

Example 2: Geostationary Orbit

r = 42,164,000 m (35,786 km altitude)

Step 1:v = √(3.986×10¹⁴ / 42,164,000)
Step 2:= √(9,453,000) = 3,075 m/s

3,075 m/s — orbital period exactly 24 hours.

Example 3: Moon Around Earth

r = 384,400,000 m

Step 1:v = √(3.986×10¹⁴ / 384,400,000)
Step 2:= √(1,037,000) = 1,018 m/s

Moon orbits at about 1,018 m/s (3,665 km/h).

Common Mistakes & Tips

  • !Using altitude above surface instead of orbital radius — r = R_planet + altitude.
  • !Forgetting that the orbiting mass does not affect orbital velocity.
  • !Confusing orbital velocity with escape velocity — escape velocity is √2 times larger.
  • !Using wrong mass — the central (more massive) body, not the orbiting object.

Related Concepts

Escape Velocity

Minimum speed to leave a gravitational field entirely.

Gravitational Force

The force that provides centripetal acceleration for orbits.

Kepler's Third Law

Relates orbital period to orbital radius.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Centripetal Force Calculator

Escape Velocity Calculator

Kepler's Third Law Calculator

Frequently Asked Questions

Why do astronauts float in the ISS?

The ISS and astronauts are in continuous free fall — they orbit at the same speed and fall toward Earth at the same rate. They do not escape gravity (gravity at ISS altitude is still 89% of surface value). They experience weightlessness because everything falls together.

Why are higher orbits slower?

v = √(GM/r) decreases with r. Physically, gravity is weaker at greater distances, so less centripetal force is available, supporting only a slower orbit. This is why the Moon (1 km/s) orbits much slower than the ISS (7.7 km/s).

What is a geostationary orbit?

An equatorial circular orbit at 35,786 km altitude where the orbital period is exactly 24 hours. The satellite remains above the same point on Earth. Used for communication satellites, weather monitoring, and TV broadcasting.