• Pixel-art sticker of Hillock, personifying Hill Sphere, with the caption “My Moons Stay Close.”

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Hillock

Hill Sphere Physics

\[r_H \approx a\sqrt[3]{\frac{m}{3M}}\]
$4.99 USD
$4.99 USD
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Meet Hillock, a planet who keeps her moons close so the Sun cannot steal them. The Hill sphere is the region where a planet's gravity beats the Sun's pull. For Earth its radius is about 1.5 million km, and our Moon orbits comfortably inside at about 384 000 km. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Hillock, a planet who keeps her moons close so that the Sun cannot steal them.

A planet's gravity holds a moon, but the Sun is pulling on that moon too. Close to the planet, the planet wins. Far away, the Sun's pull takes over and a would-be moon drifts off into its own orbit around the Sun. The boundary region where the planet's grip is strong enough is called the Hill sphere.

Its radius is roughly r_H ≈ a∛(m/3M), where a is the planet's distance from the Sun and m/M is the ratio of the planet's mass to the Sun's. For the Earth, m/M is about 3 × 10⁻⁶, giving a Hill radius of about 1.5 million km.

Our Moon orbits at about 384 000 km, comfortably inside. In practice, stable moons stay well within about a third to a half of the Hill radius.

Giant planets far from the Sun, such as Jupiter and Neptune, have enormous Hill spheres, which helps them hold on to large families of moons.

Equations

\[r_H \approx a\sqrt[3]{\frac{m}{3M}}\]
SymbolMeaningUnit
\(r_H\) radius of the Hill sphere \(\mathrm{m}\)
\(a\) distance between the planet and the star \(\mathrm{m}\)
\(m\) mass of the planet \(\mathrm{kg}\)
\(M\) mass of the star \(\mathrm{kg}\)

Sources

  1. Wikipedia — Hill sphere
  2. NASA — Moon Facts

Field notes

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