• Isaac Newton Gravity pixel-art physics sticker, 3" × 3" / White

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Isaac Newton Sticker

Gravity Hits Different | Physics

\[\vec F = \frac{d\vec p}{dt}\]
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$4.99 USD
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Same rule for an apple and an orbit. Newton’s Principia (1687) set out the laws of motion and universal gravitation: one law for falling apples and orbiting planets. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Returns & replacements21 days

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The physics

Newton's second law says force equals the rate of change of momentum. His law of gravitation says every two masses attract with a force proportional to their product and inversely proportional to the square of their distance, and together they explain falling apples and planetary orbits.

The sticker says Gravity Hits Different. The apple is a story Newton told in old age; whatever happened in the orchard, the physics took him about twenty years.

The first formula on this page is the second law in the form that has lasted: force is the rate of change of momentum. Newton's own wording ties force to the change of motion, which we now call momentum, mass times velocity. Written as a rate, dp/dt, the law survives even into special relativity, where momentum is no longer simply mass times velocity and F = ma fails. Newton needed new mathematics to say any of it. His method of fluxions, his name for calculus, is built around rates of change. Gottfried Leibniz developed calculus independently, and the two camps fought over priority for years.

The second formula is universal gravitation, one rule for the apple and the Moon. Set out together in the Principia in 1687, the two laws produced Kepler's ellipses as consequences rather than observations.

His experimental work holds up too. With prisms he showed that white light is a mixture of colours, which a second prism cannot split any further. Lenses of his day blurred images with coloured fringes, so he built a telescope that focused with a mirror instead.

His second career was at the Royal Mint, first as Warden, then as Master, where he oversaw a recoinage and pursued counterfeiters, who could be hanged.

Newton's mechanics is not the last word. Near the speed of light, special relativity takes over; in strong gravity, general relativity; at atomic scales, quantum mechanics. Each of them reduces to Newton under everyday conditions, which is the best compliment one theory can pay another.

Gravity hits different. It also hits everything the same.

Equations

\[\vec F = \frac{d\vec p}{dt}\]
\[F = \frac{G m_1 m_2}{r^{2}}\]
SymbolMeaningUnit
\(\vec F\) net force \(\mathrm{N}\)
\(\vec p\) momentum \(\mathrm{kg·m/s}\)
\(G\) gravitational constant \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(m_1, m_2\) masses \(\mathrm{kg}\)
\(r\) separation \(\mathrm{m}\)

Sources

  1. Encyclopaedia Britannica — Isaac Newton
  2. Encyclopaedia Britannica — Newton’s laws of motion
  3. NIST CODATA 2022 — Newtonian constant of gravitation G
  4. Feynman Lectures on Physics Vol. I Ch. 9: Newton’s Laws of Dynamics
  5. Royal Mint Museum — Isaac Newton, Warden and Master of the Royal Mint 1696–1727
  6. Newton Project (Oxford) — Newton and the Mint

Source Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica (Axioms, Law II; Book III, universal gravitation). London: Royal Society (J. Streater).

Field notes

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