orbital mechanics formulas and interpretation
Orbital mechanics connects gravity with satellite speed and period.
This calculator preserves planetary presets and reports both velocity and orbital period.
How to use the orbital mechanics 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 period follows Kepler’s third-law form using orbital radius from the central body’s centre.
T = 2π√(r³/GM)- T — Orbital period
- Time for one orbit (s)
- r — Orbital radius
- Body radius plus altitude (m)
- M — Central mass
- Mass being orbited (kg)
- G — Gravitational constant
- Universal gravity constant (m³/kg·s²)
Satellite period example
A satellite orbits Earth at a 400 km altitude.
- Earth radius
- 6,371 km
- Altitude
- 400 km
- r = 6,771 km
- T = 2π√(r³/GM)
Result: The ideal circular period is about 92.4 minutes.
Perturbations and atmospheric drag are excluded.
Understanding your results
Interpreting the result
Period grows rapidly with orbital radius because it depends on r to the three-halves power.
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.