Hill Radius

{
  "asOf": "2026-10-11T08:48:42.237Z",
  "degraded": false,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "hillRadiusAu": 0.0098368,
  "hillRadiusInEarthRadii": 230.7,
  "hillRadiusInJupiterRadii": 20.58,
  "hillRadiusKm": 1471600,
  "notChecked": [
    "the real stability of a moon: tides, the planet's spin and other bodies matter, and close-in planets lose moons to tidal decay",
    "other planets in the system",
    "…1 more"
  ],
  "planetMassSolar": 0.0000030035,
  "reasons": [
    "Hill radius = a (1 - e) (m / 3M)^(1/3).",
    "Stable satellite orbits extend to about 0.49 of the Hill radius for prograde moons and about 0.93 for retrograde moons (Domingos et al. 2006)."
  ],
  "source": "computed locally",
  "stableProgradeAu": 0.004815,
  "stableProgradeKm": 720300,
  "stableRetrogradeAu": 0.009157,
  "stableRetrogradeKm": 1370000,
  "summary": "Hill radius 0.009837 au (1472000 km) for a 1 earth-mass planet at 1 au around a 1 solar-mass star (eccentricity 0.0167). Prograde moons are stable out to roughly 720000 km.",
  "verdict": "COMPUTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://exoplanets-nasa.x402tookit.com/hill-radius?eccentricity=0.0167&massUnit=earth&orbitAu=1&planetMass=1&starMassSolar=1'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://exoplanets-nasa.x402tookit.com/hill-radius?eccentricity=0.0167&massUnit=earth&orbitAu=1&planetMass=1&starMassSolar=1' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fexoplanets-nasa.x402tookit.com%2Fhill-radius
const res = await pay("https://exoplanets-nasa.x402tookit.com/hill-radius?eccentricity=0.0167&massUnit=earth&orbitAu=1&planetMass=1&starMassSolar=1");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://exoplanets-nasa.x402tookit.com/hill-radius?eccentricity=0.0167&massUnit=earth&orbitAu=1&planetMass=1&starMassSolar=1")
    print(res.status_code, res.text)