Explore the Hill sphere - the region where a body can keep satellites - with literacy r_H ~= a (m/3M)^(1/3). Earth's Hill sphere is ~1.5 million km; the Moon at ~384,400 km sits well inside it.
Published literacy: r_H ~= a (m/3M)^(1/3), Earth Hill ~1.5 million km, Moon distance ~384,400 km, Moon Hill ~60,000 km. On-screen sizes are compressed for teaching.
Drag to orbit and scroll or pinch to zoom. Switch Earth / Jupiter, or toggle the moon and the moon's own Hill shell.
Hill Sphere 3D Explorer
freetoolonline.com editorial team
This browser explorer shows the Hill sphere - the approximate region where a planet's gravity can keep satellites against the Sun - with literacy r_H ~= a (m/3M)^(1/3). Earth's Hill sphere reaches ~1.5 million km; the Moon at ~384,400 km stays well inside.
Roche Limit 3D owns tidal breakup distances. Lagrange Points 3D owns L1-L5 equilibrium spots. This page owns sphere-of-influence Hill radius literacy.
- Teal wire Hill shell around Earth or Jupiter
- Moon orbit cue inside Earth's Hill region
- Optional violet Moon Hill shell (~60,000 km literacy)
- Earth / Jupiter system presets
- Facts panel lists r_H formula, 1.5 million km, 384,400 km, 60,000 km
- Distinct from roche-limit and lagrange-points
- Runs fully in the browser with the vendored three.js engine - no account, no upload
Students see why the Moon is a stable Earth satellite; teachers contrast Hill spheres with Roche limits; curious readers connect the (m/3M)^(1/3) scaling to Jupiter's much larger shell.
| Figure | Value | Source note |
|---|---|---|
| Formula | r_H ~= a (m/3M)^(1/3) | Approximate circular Hill radius |
| Earth Hill radius | ~1.5 million km (~0.01 AU) | Published literacy |
| Moon distance | ~384,400 km | Mean Earth-Moon distance |
| Moon Hill radius | ~60,000 km | Published literacy |
| Jupiter Hill radius | ~53 million km (order of magnitude) | Teaching comparison |
Walking the controls, preset by preset
Five moves cover the whole scene. Run them in order and the shell size, the Moon cue, and the nested Moon shell each land on their own.
- Open the explorer and wait for the teal Hill shell to paint around the planet.
- Read the facts panel: r_H ~= a (m/3M)^(1/3), Earth ~1.5 million km, Moon ~384,400 km, Moon Hill ~60,000 km.
- Press Earth, then Jupiter, to see how much further the shell reaches for the heavier planet.
- Press Hide moon and Hide moon Hill to strip the scene back to the planet's shell alone, then bring them back.
- Drag to orbit, scroll or pinch to zoom, and press Fullscreen for a projector.
How this explorer compares with the sibling scenes
The Hill Sphere 3D Explorer teaches sphere-of-influence radius. Roche Limit 3D teaches tidal breakup; Lagrange Points 3D teaches the L1-L5 spots.
| Option | Strength | Access | Trade-off |
|---|---|---|---|
| Hill Sphere 3D (this page) | r_H literacy plus the Moon-inside cue | Free, in browser, USD 0, 0 MB to install | Compressed teaching scale |
| Roche Limit 3D sibling | Tidal breakup distance | Free web | Not sphere-of-influence focus |
| Lagrange Points 3D sibling | L1-L5 equilibrium | Free web | Not Hill radius focus |
Where the schematic stops
Everything renders on your device with WebGL. The 3D engine loads once (about 0.7 MB) and is cached; no scene data is sent to a server.
This is an educational schematic with compressed scales - not an N-body stability integrator.
When you need session fit and limits, see when to use Hill Sphere 3D Explorer. The Space 3D collection also includes Roche Limit 3D and Lagrange Points 3D.
Frequently Asked Questions
What does the Hill Sphere 3D Explorer show?
A teaching Hill shell around Earth or Jupiter, with the Moon orbiting inside Earth's ~1.5 million km sphere of influence. Literacy includes r_H ~= a (m/3M)^(1/3) and the Moon's own ~60,000 km Hill radius.
How is this different from Roche Limit 3D?
Roche Limit 3D teaches the tidal breakup distance. This page teaches where a body can keep satellites against the primary.
How is this different from Lagrange Points 3D?
Lagrange Points 3D teaches L1-L5 equilibrium spots. This page teaches the approximate spherical region of dominance (Hill radius).
Is the Moon inside Earth's Hill sphere?
Yes. The Moon averages about 384,400 km from Earth, while Earth's Hill sphere reaches about 1.5 million km.
Is this an N-body stability simulator?
No. It is an educational schematic with compressed scales - not a full gravitational N-body integrator.
What is the Moon's Hill sphere?
About 60,000 km - much smaller than the Earth-Moon distance, which is why stable "moons of the Moon" are hard.