Hill Sphere Radius Calculator

Hill Sphere Radius Calculator helps you determine the gravitational sphere of influence of a celestial body, where it dominates the attraction of satellites over the primary body it orbits.

Hill Sphere Radius Calculator

This tool computes the gravitational influence zone of a body, like Earth’s Moon or Jupiter’s moons, for stable satellite orbits.

How It Works

Input primary and satellite masses and orbital distance to calculate the radius defining stable orbits, like Earth-Moon dynamics.

Benefits of Use

It helps study Earth’s satellite orbits, Jupiter’s moon stability, or exoplanet systems, aiding astronomers and students in orbital research.

Applications in Astronomy

The Hill Sphere Radius Calculator enables analysis of stable orbits for satellites, moons, or exoplanets, enhancing celestial mechanics studies.

Hill Sphere Radius Calculator

This tool computes the gravitational influence zone of a body, like Earth’s Moon or Jupiter’s moons, for stable satellite orbits.

How It Works

Input primary and satellite masses and orbital distance to calculate the radius defining stable orbits, like Earth-Moon dynamics.

Benefits of Use

It helps study Earth’s satellite orbits, Jupiter’s moon stability, or exoplanet systems, aiding astronomers and students in orbital research.

Applications in Astronomy

The Hill Sphere Radius Calculator enables analysis of stable orbits for satellites, moons, or exoplanets, enhancing celestial mechanics studies.

How to Use:

1. Enter the mass of the primary body (e.g., star) and secondary body (e.g., planet).
2. Specify the semi-major axis of the orbit and its eccentricity.
3. Select a predefined celestial system or enter custom values.
4. Click “Calculate Hill Sphere Radius” to see the gravitational sphere of influence.

Formulas Used:

Hill Sphere Radius Formula:

\( r_H \approx a (1 – e) \sqrt[3]{\frac{m}{3M}} \)

Where:
\( r_H \) = Hill sphere radius
\( a \) = semi-major axis of the orbit
\( e \) = orbital eccentricity
\( m \) = mass of the secondary body (e.g., planet)
\( m \) = mass of the primary body (e.g., star)

Stability Factor:
\( S = \frac{r_H}{R} \times 100\% \)
Where \( R \) is the radius of the secondary body.