{"uid":"cap_Li6n9dQUID56_abFmXhVN","slug":"nasa-exoplanets-hill-radius-calculator-a66b4794","name":"NASA Exoplanets Hill Radius Calculator","description":"Hill radius of a planet in AU and km from its mass, orbit, eccentricity and star mass, with the stable-moon region.","url":"https://exoplanets-nasa.x402tookit.com/hill-radius?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":["planetMass","orbitAu"],"properties":{"orbitAu":{"type":"number","description":"Semi-major axis in AU, 0.001 to 10000"},"massUnit":{"type":"string","description":"earth (default) or jupiter"},"planetMass":{"type":"number","description":"Planet mass value, 0.001 to 100000"},"eccentricity":{"type":"number","description":"Orbital eccentricity 0 to 0.99 (default 0)"},"starMassSolar":{"type":"number","description":"Star mass in solar masses, 0.05 to 100 (default 1)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"hillRadiusAu":{"type":["null","number"]},"hillRadiusKm":{"type":["null","number"]},"planetMassSolar":{"type":["null","number"]},"stableProgradeAu":{"type":["null","number"]},"stableProgradeKm":{"type":["null","number"]},"stableRetrogradeAu":{"type":["null","number"]},"stableRetrogradeKm":{"type":["null","number"]},"hillRadiusInEarthRadii":{"type":["null","number"]},"hillRadiusInJupiterRadii":{"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_wjV3R9yriMCwGt9_G7fZF","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 a planet's Hill radius in AU and km from its mass, orbital parameters, and star mass, including stable prograde and retrograde moon regions.","exampleAgentPrompt":"What is the Hill radius for a planet with 5 Earth masses orbiting at 1.5 AU from a Sun-like star with eccentricity 0.1? Give me the stable moon regions too.","exampleUseCases":[{"title":"Moon stability check for super-Earth","prompt":"I'm studying a super-Earth with 8 Earth masses at 2 AU around a star that's 0.9 solar masses — what's its Hill radius and how far out could a moon stably orbit it?"},{"title":"Jupiter analog Hill sphere","prompt":"Calculate the Hill radius for a Jupiter-mass planet (1 Jupiter mass) at 5.2 AU from a 1 solar mass star with eccentricity 0.05, and tell me the stable prograde and retrograde moon distances."},{"title":"Habitable-zone planet moon feasibility","prompt":"Could a planet with 3 Earth masses at 0.8 AU from a 0.6 solar mass star realistically host a stable moon? What's its Hill sphere size?"}],"resultDescription":"Returns the Hill radius in AU, km, Earth radii, and Jupiter radii; the stable prograde moon region boundary (roughly 1/3 of the Hill radius) in AU and km; and the stable retrograde moon region boundary in AU and km; plus the planet mass expressed in solar masses.","failureModes":["Missing required parameters (planetMass or orbitAu) returns a validation error","Planet mass outside the range 0.001–100000 triggers an out-of-bounds error","Semi-major axis outside 0.001–10000 AU triggers a range error","Eccentricity of 1.0 or higher (parabolic/hyperbolic orbit) is rejected","Star mass below 0.05 or above 100 solar masses returns an error","Payment failure (insufficient USDC balance) returns a 402 response"],"whenToPreferThis":"Use this endpoint when you need precise gravitational sphere-of-influence calculations for exoplanets or solar system bodies — especially to determine whether a moon could exist or remain stable around a given planet. It is the right choice over general orbital mechanics libraries when you want precomputed stable prograde/retrograde boundaries alongside the Hill radius in multiple unit systems, without writing your own physics code.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T07:02:36.410Z","isFirstParty":false,"canonicalSlug":"nasa-exoplanets-hill-radius-calculator-a66b4794"}