• Pixel-art sticker of Escapa, personifying Escape Velocity, with the caption "Fast Enough To Never Fall."

IndexForces & FieldsSticker

Escapa

Escape Velocity Physics

\[v_{\mathrm{esc}} = \sqrt{\frac{2GM}{r}}\]
$4.99 USD
$4.99 USD
Sale Sold out

Meet Escapa, moving at escape velocity, where kinetic energy equals the gravitational binding energy, so an unpowered object never falls back, ignoring drag. Her speed is v = √(2GM/r), which from Earth's surface comes to about 11.19 km/s. 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 Escapa, who leaves Earth for good if she's fast enough, and falls back if she isn't.

Throw something up and gravity slows it. Throw it faster and it rises higher before falling back. There is a special launch speed at which its kinetic energy exactly equals the energy needed to climb out of the gravitational well to infinite distance. That is the escape speed, √(2GM/r). It depends on the planet's mass and on your distance from its centre, not on the mass of the object being launched.

From Earth's surface, using Earth's mass and radius, the escape speed comes out at about 11.19 kilometres per second, roughly 40,000 km/h.

Rockets bound for the Moon and planets must reach near this speed. Escape speed also explains why small bodies like the Moon have kept almost no atmosphere: fast gas molecules can leak away.

The formula assumes an unpowered object and ignores air drag and the pull of other bodies such as the Sun. A rocket that keeps firing its engines can leave at any speed.

Equations

\[v_{\mathrm{esc}} = \sqrt{\frac{2GM}{r}}\]
SymbolMeaningUnit
\(v_{\mathrm{esc}}\) escape speed \(\mathrm{m/s}\)
\(G\) Newtonian constant of gravitation \(\mathrm{N·m²/kg²}\)
\(M\) mass of the planet \(\mathrm{kg}\)
\(r\) distance from the planet's centre \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 1 — Gravitational Potential Energy and Total Energy
  2. NIST CODATA — Newtonian constant of gravitation G
  3. Wikipedia — Escape velocity

Field notes

View all
  • Pixel-art illustration for this Pixelated Physics post: two pixel crowds: fermion characters each standing alone in their own boxes, and boson characters happily piling together into one box

    What Is the Spin–Statistics Theorem?

    The spin–statistics theorem ties a particle’s spin to the symmetry of its quantum state. Integer spin → bosons (symmetric); half-integer spin → fermions (antisymmetric). Fierz (1939) and Pauli (1940) made...

    What Is the Spin–Statistics Theorem?

    The spin–statistics theorem ties a particle’s spin to the symmetry of its quantum state. Integer spin → bosons (symmetric); half-integer spin → fermions (antisymmetric). Fierz (1939) and Pauli (1940) made...

  • Pixel-art illustration for this Pixelated Physics post: a pixel pendulum bob character swinging over a circular floor marked with pixel pegs, a few pegs knocked over showing the swing plane slowly turning, a pixel Earth spinning in the window

    How Does a Foucault Pendulum Prove Earth Rotates?

    A long pendulum’s swing plane slowly turns relative to the floor. Foucault showed in 1851 that the turn is Earth’s rotation made visible. The rate is 360° times the sine...

    How Does a Foucault Pendulum Prove Earth Rotates?

    A long pendulum’s swing plane slowly turns relative to the floor. Foucault showed in 1851 that the turn is Earth’s rotation made visible. The rate is 360° times the sine...

  • Pixel-art Einstein ring: a foreground galaxy bends the light of a galaxy directly behind it into a circular ring of arcs centered on it

    How Does Gravity Bend Light? Einstein Rings and...

    Gravity bends light because spacetime is curved. The 1919 eclipse measured the Sun’s deflection; Einstein’s 1936 note foresaw stellar lenses; modern telescopes image Einstein rings. Here is the physics without...

    How Does Gravity Bend Light? Einstein Rings and...

    Gravity bends light because spacetime is curved. The 1919 eclipse measured the Sun’s deflection; Einstein’s 1936 note foresaw stellar lenses; modern telescopes image Einstein rings. Here is the physics without...

1 3
View all