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Planetary Hill Sphere Gravitational Dominance Radius Calculator

Easily calculate and compute planetary hill sphere gravitational dominance radius calculator with accurate equations, live formulas, and expert guidance.

Planet distance from host star (1 AU for Earth).

Mass of the orbiting planet.

Primary star mass (1.0 = Sun = 1.989e30 kg).

Orbital eccentricity of planet around host star.

Calculated Result
1,471,537 km

Hill Sphere Radius

Hill Sphere Radius

1,471,537 km

Hill Sphere Radius Km

1471537

Hill Sphere Radius A U

0.009837

Stable Prograde Orbit Limit Km

490512

Stable Retrograde Orbit Limit Km

735769

1,471,537 — km

Calculation Breakdown

  1. Applied FormulaSizes the gravitational sphere of influence within which a planet can retain permanent natural or artificial satellites despite stellar tides.r_{stable,prograde} \approx \frac{1}{3} r_H, \quad r_{stable,retrograde} \approx \frac{1}{2} r_H

Hill Sphere Radius Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.0367.9k735.8k1103.7k1471.5kHill Sphere Radius

What Is the Planetary Hill Sphere Gravitational Dominance Radius Calculator?

This tool computes planetary hill sphere gravitational dominance radius calculator with high precision arithmetic.

How Does the Planetary Hill Sphere Gravitational Dominance Radius Calculator Work?

Sizes the gravitational sphere of influence within which a planet can retain permanent natural or artificial satellites despite stellar tides.

Planetary Hill Sphere Gravitational Dominance Radius Calculator Formula & Variables

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

rstable,prograde≈13rH,rstable,retrograde≈12rHr_{stable,prograde} \approx \frac{1}{3} r_H, \quad r_{stable,retrograde} \approx \frac{1}{2} r_H

Sizes the gravitational sphere of influence within which a planet can retain permanent natural or artificial satellites despite stellar tides.

How to Use the Planetary Hill Sphere Gravitational Dominance Radius Calculator

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

Step-by-Step Example Calculation

Planetary Hill Sphere Gravitational Dominance Radius Calculator Example

Input Values:

semiMajorAxisAU:1.0
planetMassKg:5.972e24
starMassSolarMasses:1.0
orbitalEccentricityE:0.0167
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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