Semi-major axis from period API

Returns the semi-major axis a=(mu*T^2/4*pi^2)^(1/3) from a given orbital period (inverse Kepler 3rd), in meters/km/AU. Answers 'What altitude gives a 90-minute orbit?', 'Orbit size for this period?'.

Price$0.04per request

MethodPOST

Route/v1/space/semimajor-axis-from-period

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

spaceastronomykeplersemi-major-axisorbital-mechanicsinverse-keplerastrodynamicsorbit-design

API URLhttps://x402.hexl.dev/v1/space/semimajor-axis-from-period

Integration docs

Example request

{
  "body": "earth",
  "periodS": 86164.0905
}

Example response

{
  "body": "earth",
  "mu": 398600441800000,
  "periodS": 86164.0905,
  "semiMajorAxisM": 42164169.624,
  "semiMajorAxisKm": 42164.1696,
  "semiMajorAxisAU": 0.00028185,
  "interpretation": "A 0.997-day period about earth implies a=42164.2 km."
}

Input schema

{
  "type": "object",
  "required": [
    "periodS"
  ],
  "properties": {
    "body": {
      "type": "string",
      "examples": [
        "earth"
      ]
    },
    "mu": {
      "type": "number"
    },
    "centralMassKg": {
      "type": "number"
    },
    "periodS": {
      "type": "number",
      "examples": [
        86164.0905
      ]
    }
  }
}

Output schema

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