Orbital period (Kepler 3rd) API

Returns the orbital period from Kepler's third law T=2*pi*sqrt(a^3/mu) in seconds/minutes/hours/days/years plus mean motion, for any semi-major axis about a named body. Answers 'Orbital period at this altitude?', 'How long is one orbit?'.

Price$0.04per request

MethodPOST

Route/v1/space/orbital-period

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

spaceastronomykeplerorbital-periodorbital-mechanicsastrodynamicsmean-motionsatellite

API URLhttps://x402.hexl.dev/v1/space/orbital-period

Integration docs

Example request

{
  "body": "earth",
  "semiMajorAxisM": 6771000
}

Example response

{
  "body": "earth",
  "mu": 398600441800000,
  "semiMajorAxisM": 6771000,
  "periodS": 5544.8551,
  "periodMin": 92.41425,
  "periodHours": 1.540238,
  "periodDays": 0.064177,
  "periodYears": 0.000176,
  "meanMotionRadPerS": 0.001133155907,
  "interpretation": "Period for a=6771 km about earth is 92.41 min."
}

Input schema

{
  "type": "object",
  "required": [
    "semiMajorAxisM"
  ],
  "properties": {
    "body": {
      "type": "string",
      "examples": [
        "earth"
      ]
    },
    "mu": {
      "type": "number"
    },
    "centralMassKg": {
      "type": "number"
    },
    "semiMajorAxisM": {
      "type": "number",
      "examples": [
        6771000
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}