Circular Orbit Period and Speed Calculator
Calculate ideal circular-orbit speed, period, local gravity and escape speed from a central mass and center-to-center orbital radius.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use Newtonian point-mass gravity. Equate gravitational and centripetal acceleration for circular speed, then divide one circumference by that speed for period.
μ=GM; v=√(μ/r); T=2π√(r³/μ); g=μ/r²; vescape=√(2μ/r)
Worked example
Using mass 5.9722×10²⁴ kg and radius 6,771 km (400 km above a 6,371 km reference radius) gives a period near 92.4 minutes and circular speed near 7.67 km/s.
Assumptions and input details
Ideal two-body circular orbit. The entered body radius only converts center radius to altitude. Atmosphere, body rotation, oblateness, other bodies, relativistic effects and maneuver requirements are excluded. An orbit below or within a physical atmosphere may not persist even when the arithmetic is valid.
References: NASA: applying Kepler’s third law · NASA: orbits and Kepler’s laws
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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