{"uid":"cap_Te86h7vMJQ6Tiex7EmvpL","slug":"space-objects-orbital-period-calculator-kepler-s-third-law-14b1bd54","name":"Space Objects: Orbital Period Calculator (Kepler's Third Law)","description":"Orbital period from semi-major axis via Kepler's third law, with perihelion, aphelion and speeds when eccentricity is given.","url":"https://space-objects.x402tookit.com/orbital-period?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["semiMajorAxisAu"],"properties":{"eccentricity":{"type":"number","description":"Eccentricity 0 to 0.99, to also get perihelion, aphelion and speeds"},"semiMajorAxisAu":{"type":"number","description":"Semi-major axis in AU, 0.01 to 10000"},"centralMassSolar":{"type":"number","description":"Central mass in solar masses, 0.01 to 100 (default 1, the Sun)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"source":{"type":["null","string"]},"formula":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"aphelionAu":{"type":["null","number"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"periodDays":{"type":["null","number"]},"periodYears":{"type":["null","number"]},"eccentricity":{"type":["null","number"]},"perihelionAu":{"type":["null","number"]},"semiMajorAxisAu":{"type":["null","number"]},"centralMassSolar":{"type":["null","number"]},"meanDistanceNote":{"type":["null","string"]},"speedAtAphelionKmS":{"type":["null","number"]},"meanMotionDegPerDay":{"type":["null","number"]},"speedAtPerihelionKmS":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_lVc2R-UkSTZoMHAtNHM_0","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Calculates orbital period from semi-major axis using Kepler's third law, and optionally returns perihelion, aphelion, and orbital speeds given eccentricity.","exampleAgentPrompt":"What's the orbital period of an object with a semi-major axis of 3.2 AU and eccentricity of 0.15 orbiting the Sun? Also give me the perihelion and aphelion distances and orbital speeds.","exampleUseCases":[{"title":"Asteroid orbit period estimation","prompt":"I'm looking at an asteroid with a semi-major axis of 2.77 AU and eccentricity of 0.08 — can you calculate its orbital period around the Sun, plus its closest and farthest distances and speeds at those points?"},{"title":"Exoplanet orbital mechanics","prompt":"I have an exoplanet orbiting a star with 1.5 solar masses at a semi-major axis of 0.8 AU and eccentricity of 0.2. What's its orbital period in years and days, and how fast does it move at perihelion and aphelion?"},{"title":"Hypothetical outer solar system body","prompt":"If there were a planet-sized body in the outer solar system at 400 AU from the Sun with an eccentricity of 0.6, what would its orbital period be and how extreme would the difference be between its nearest and farthest distances?"}],"resultDescription":"Returns orbital period in both days and years, mean motion in degrees per day, and (when eccentricity is provided) perihelion distance, aphelion distance, speed at perihelion, and speed at aphelion — all based on Kepler's third law. Also includes the formula used, the input parameters echoed back, and optional notes or disclaimers.","failureModes":["Missing required semiMajorAxisAu parameter returns an error","Semi-major axis out of range (below 0.01 or above 10000 AU) may return an error or degraded result","Eccentricity out of range (must be 0 to 0.99) causes failure","centralMassSolar out of range (0.01 to 100) causes failure","Payment failure due to insufficient USDC balance returns 402 error"],"whenToPreferThis":"Use this endpoint when you need a fast, authoritative Kepler's-law-based orbital period calculation with optional full orbital parameter set (perihelion, aphelion, speeds). Ideal for astrodynamics calculations around the Sun or other stars with configurable central mass, without needing a full ephemeris lookup. Prefer this over NASA/JPL ephemeris endpoints when you have the orbital elements and need pure physics computation rather than a historical or observational data query.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-21T07:19:49.154Z","isFirstParty":false,"canonicalSlug":"space-objects-orbital-period-calculator-kepler-s-third-law-14b1bd54"}