{"uid":"cap_Q4Ky4dY73rYxqzrt6InpY","slug":"cr3bp-five-libration-points-and-linear-spectrum-calculator-d8f56fef","name":"CR3BP Five Libration Points and Linear Spectrum Calculator","description":"Compute all five equilibria and local mathematical spectra of a supplied CR3BP model.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/circular-restricted-three-body-five-libration-points-linear-spectrum?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["cr3bp"],"properties":{"cr3bp":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["mass_ratio"],"properties":{"mass_ratio":{"type":"number","maximum":0.5,"minimum":0.00001}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","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":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_EV2e_hOcai-lnp6VbrRA0","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes all five Lagrange/libration equilibrium points and their local linear stability spectra for a Circular Restricted Three-Body Problem (CR3BP) model defined by a mass ratio.","exampleAgentPrompt":"Compute all five libration points and their local linear stability spectra for a CR3BP system with a mass ratio of 0.01215 (Earth-Moon system).","exampleUseCases":[{"title":"Earth-Moon Halo Orbit Mission Planning","prompt":"I'm designing a mission to a halo orbit around L2 in the Earth-Moon system — can you compute all five libration point positions and their linear stability eigenvalues using a mass ratio of 0.01215?"},{"title":"Sun-Jupiter System Trojan Analysis","prompt":"Analyze the five Lagrange equilibrium points and local linear spectra for the Sun-Jupiter CR3BP system, which has a mass ratio of approximately 0.000954."},{"title":"Custom Binary System Stability Check","prompt":"For a hypothetical binary star system with a mass ratio of 0.3, calculate all five CR3BP libration points and tell me the linear stability spectrum at each one."}],"resultDescription":"Returns all five libration point positions (L1 through L5) in the rotating frame, along with the local linear stability spectra (eigenvalues of the linearized equations of motion) at each equilibrium point, characterizing whether each point is stable, unstable, or center-type.","failureModes":["mass_ratio out of range (must be between 0.00001 and 0.5) causes validation error","missing or malformed 'cr3bp' artifact object returns schema error","non-numeric mass_ratio value causes parsing failure","server-side numerical instability for extreme mass ratio edge cases"],"whenToPreferThis":"Use this endpoint when you need a complete, simultaneous computation of all five CR3BP libration points and their linear spectra in a single call, rather than computing individual points separately. Preferred for astrodynamics mission design tasks, stability analysis of binary systems, or when both positional and spectral data are needed together for a given mass parameter.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:40:12.651Z","isFirstParty":false,"canonicalSlug":"cr3bp-five-libration-points-and-linear-spectrum-calculator-d8f56fef"}