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Spaghetta

Spaghettification Physics

\[\Delta a \approx \frac{2GML}{r^{3}}\]
$21.99 USD
$21.99 USD
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Meet Spaghetta. Gravity pulls your feet harder than your head. Near a small black hole that difference tears you apart before you reach the horizon; at the giant one in our galaxy's centre you would cross without feeling it. On the mug: Δa ≈ 2GML/r³. Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

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

Tidal stretch Δa ≈ 2GML/r³ is strongest near small black holes. At the horizon of a 10-solar-mass hole a 2 m person feels about 2×10⁷ g; at Sgr A* only about 10⁻⁴ g.

Spaghetta stretches anything that falls toward a black hole, feet first.

Gravity weakens with distance, so it pulls your feet, nearer the black hole, harder than your head. For a body of length L at distance r from a mass M, the difference is Δa ≈ 2GML/r³, the formula on this mug. It grows as 1/r³, far faster than gravity itself.

The horizon of a black hole sits at the Schwarzschild radius r_s = 2GM/c², found by Karl Schwarzschild in 1916. Put r = r_s and the stretch at the horizon becomes c⁶L/(4G²M²): the bigger the black hole, the gentler its horizon. Small black holes are worse.

A worked number, for a person 2 m tall: at the horizon of a 10-solar-mass black hole the stretch is about 2×10⁸ m/s², twenty million g, and you are torn apart long before you reach it. At Sagittarius A*, the 4.3-million-solar-mass black hole at our galaxy's centre, it is about 10⁻³ m/s², a ten-thousandth of g. You would cross without feeling it.

“Little black holes are rude,” says Spaghetta. “The big ones let you in before they say hello.”

Equations

\[\Delta a \approx \frac{2GML}{r^{3}}\]
\[r_s = \frac{2GM}{c^{2}} \;\Rightarrow\; \Delta a(r_s) = \frac{c^{6}L}{4G^{2}M^{2}}\]
SymbolMeaningUnit
\(\Delta a\) difference in gravitational acceleration between the two ends (tidal stretch) \(\mathrm{m/s²}\)
\(G\) Newtonian constant of gravitation \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M\) black hole mass \(\mathrm{kg}\)
\(L\) length of the falling body \(\mathrm{m}\)
\(r\) distance from the centre of the black hole \(\mathrm{m}\)
\(r_s\) Schwarzschild radius \(\mathrm{m}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)

Sources

  1. GRAVITY Collaboration (2020) Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole, A&A 636, L5
  2. NobelPrize.org — The Nobel Prize in Physics 2020 (Penrose, Genzel, Ghez)
  3. Schwarzschild (1916) On the gravitational field of a mass point according to Einstein's theory, English translation, arXiv:physics/9905030

Source Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 189–196. English translation:arxiv.org/abs/physics/9905030

Field notes

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