# NASA Exoplanets Hill Radius Calculator

> NASA Exoplanets Hill Radius Calculator is a paid API for AI agents from exoplanets-nasa.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

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.

## Facts

- Endpoint: GET https://exoplanets-nasa.x402tookit.com/hill-radius?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/nasa-exoplanets-hill-radius-calculator-a66b4794
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Li6n9dQUID56_abFmXhVN

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability nasa-exoplanets-hill-radius-calculator-a66b4794
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Hill radius of a planet in AU and km from its mass, orbit, eccentricity and star mass, with the stable-moon region.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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",
        "numb
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/nasa-exoplanets-hill-radius-calculator-a66b4794/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from exoplanets-nasa.x402tookit.com](https://www.zero.xyz/host/exoplanets-nasa.x402tookit.com/llms.txt)