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.