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Sphere of Influence (Laplace & Hill Radius) Calculator

Easily calculate and compute sphere of influence (laplace & hill radius) calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
924,540 km

Laplace Gravitational SOI Radius (r_soi)

Laplace Gravitational SOI Radius (r_soi)

924,540 km

Hill Sphere Radius Km

1496418

Laplace Soi Earth Radii

145.1

Hill Sphere Earth Radii

234.9

Mass Ratio Mu

0.000003003

924,540 — km

Calculation Breakdown

  1. Applied FormulaCalculates the Laplace Sphere of Influence (SOI) and Hill sphere boundary radius for patched-conic orbital transfers between planets, moons, and primary stars.r_{\text{soi}} = a \left( \frac{m}{M} \right)^{2/5}, \quad r_{\text{Hill}} = a \left( \frac{m}{3 M} \right)^{1/3}

SOI & Hill Sphere Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.0231.1k462.3k693.4k924.5kLaplace Gravitational SOI Radius (r_soi)

What Is the Sphere of Influence (Laplace & Hill Radius) Calculator?

This tool computes sphere of influence (laplace & hill radius) calculator with high precision arithmetic.

How Does the Sphere of Influence (Laplace & Hill Radius) Calculator Work?

Calculates the Laplace Sphere of Influence (SOI) and Hill sphere boundary radius for patched-conic orbital transfers between planets, moons, and primary stars.

Sphere of Influence (Laplace & Hill Radius) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

rsoi=a(mM)2/5,rHill=a(m3M)1/3r_{\text{soi}} = a \left( \frac{m}{M} \right)^{2/5}, \quad r_{\text{Hill}} = a \left( \frac{m}{3 M} \right)^{1/3}

Calculates the Laplace Sphere of Influence (SOI) and Hill sphere boundary radius for patched-conic orbital transfers between planets, moons, and primary stars.

How to Use the Sphere of Influence (Laplace & Hill Radius) Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Sphere of Influence (Laplace & Hill Radius) Calculator Example

Input Values:

semiMajorAxisAKm:149600000
secondaryMassKg:5.972e+24
primaryMassKg:1.989e+30
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required km.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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