• Pixel-art sticker of Clinget, personifying Orbital Energy, with the caption “Bound To You, Less Than Zero.”

IndexRelativity & CosmosSticker

Clinget

Orbital Energy Physics

\[E = -\frac{G M m}{2 a}\]
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Meet Clinget, a satellite who stays near the Earth because his total energy is below zero. In a circular orbit kinetic energy is half the size of the negative potential energy, giving −GMm/(2a). The International Space Station sits near −29 MJ per kilogram. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
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Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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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.

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The physics

Meet Clinget, a satellite who stays close to the Earth because its total energy is less than zero.

An orbiting satellite has kinetic energy from its speed and gravitational potential energy from its height. By convention potential energy is zero very far away, so close to the Earth it is negative. For a circular orbit the kinetic energy is exactly half the size of the potential energy. That leaves a total that is negative, which means the satellite is bound.

The total orbital energy is E = −GMm/(2a). For the International Space Station, a ≈ 6,791 km and GM for the Earth is 3.986 × 10¹⁴ m³/s². That gives about −29 MJ for every kilogram of station.

To escape completely, the station would need about 29 MJ more per kilogram. A higher orbit has a total energy closer to zero, so it is less tightly bound, even though the satellite moves more slowly there.

Rocket engineers plan every manoeuvre from this budget.

Equations

\[E = -\frac{G M m}{2 a}\]
SymbolMeaningUnit
\(E\) total orbital energy \(\mathrm{J}\)
\(G\) gravitational constant \(\mathrm{N·m²/kg²}\)
\(M\) mass of the central body \(\mathrm{kg}\)
\(m\) mass of the satellite \(\mathrm{kg}\)
\(a\) semi-major axis of the orbit \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 1 — Satellite Orbits and Energy
  2. NIST CODATA — Newtonian constant of gravitation G

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