The Formula
v = √(GM / r)
- G: Gravitational Constant
- M: Mass of Central Body
- r: Distance from center
Orbital Speed Calculator
Calculate circular orbital speed, orbital radius, or central mass with planetary presets.
Orbital Speed Calc
Calculate the velocity required to maintain a stable circular orbit around Planets or Stars.
v = √(GM / r)
Orbital Velocity Explained
Orbital velocity is the speed an object must travel to maintain a stable orbit around a massive body. It balances the object's inertia (which wants to fly off straight) with the gravitational pull (which pulls it inward).
Important Note
The orbital speed does not depend on the mass of the satellite (as long as the satellite is much smaller than the central body).
This is why a tiny satellite and the massive ISS orbit Earth at roughly the same speed at the same altitude!
orbital speed formulas and interpretation
Circular orbital speed balances inward gravitational acceleration with circular motion.
The legacy calculator preserves central-body presets and direct solutions for speed, radius, and mass.
How to use the orbital speed calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Circular orbital speed equals the square root of gravitational parameter divided by orbital radius.
v = √(GM/r)- v — Orbital speed
- Tangential circular-orbit speed (m/s)
- G — Gravitational constant
- Universal gravity constant (m³/kg·s²)
- M — Central mass
- Mass being orbited (kg)
- r — Orbital radius
- Distance from central-body centre (m)
Low Earth orbit example
Use Earth mass and an orbital radius near 6.771 × 10⁶ m.
- Earth mass
- 5.972 × 10²⁴ kg
- Orbital radius
- 6.771 × 10⁶ m
- v = √(GM/r)
- v ≈ 7.67 km/s
Result: Circular orbital speed is about 7.67 km/s.
The radius is measured from Earth’s centre, not its surface.
Understanding your results
Interpreting the result
At fixed central mass, orbital speed decreases as orbital radius increases.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.
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