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Spaghetta

Black Hole Physics / Spaghettification Stretch Physics

\[\Delta a \approx \frac{2GM\,L}{r^{3}}\]
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A black hole doesn’t just pull you in. It pulls your feet harder than your head. Tidal stretch grows as one over distance cubed. At the horizon of a 10-solar-mass black hole it is about twenty million times Earth’s gravity; at the Milky Way’s four-million-solar-mass black hole it is far gentler, and you would cross unharmed. Spaghetta on a pixel-art unisex tee; equation, symbols and sources in the panel below.

Color
Size

Size guide S–5XL · inches

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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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

Spaghetta does not pull you in. She pulls your feet harder than your head, and that is worse.

Gravity weakens with distance, so near a heavy object the near end of anything is pulled more strongly than the far end. The difference is the tidal acceleration, the first formula on this page: it grows with the mass, with the length of the body, and very steeply, as one over the cube of the distance. Ordinary tides on Earth's oceans are the same effect, from the Moon. Near a black hole, it becomes the stretching astronomers call spaghettification: pulled long along the line toward the hole, squeezed in from the sides.

The second formula, the Schwarzschild radius, sets the size of the event horizon: about 3 kilometres for each solar mass. Now the surprise. Take a black hole of ten solar masses, with a horizon radius of about 30 kilometres. At the horizon, the difference in pull between the head and feet of a two-metre person is about twenty million times Earth's gravity. You would be torn apart long before reaching it.

Take instead the black hole at the centre of our galaxy, about four million solar masses. Its horizon is so large that the tidal stretch there is around a ten-thousandth of Earth's gravity. You would cross the horizon without feeling a thing. Spaghettification would still come, but later, deeper in. The bigger the black hole, the gentler its edge.

Astronomers watch this happen to whole stars. When a star wanders too close to a supermassive black hole, tides tear it apart and part of its gas falls in, flaring for months. Such tidal disruption events are now routinely observed.

Spaghetta is not cruel. She is just steeper than you.

Equations

\[\Delta a \approx \frac{2GM\,L}{r^{3}}\]
\[r_s = \frac{2GM}{c^{2}}\]
Symbols
SymbolMeaningUnit
\(\Delta a\) difference in gravitational acceleration across the body \(\mathrm{m/s²}\)
\(M\) black-hole mass \(\mathrm{kg}\)
\(L\) length of the body along the radial direction \(\mathrm{m}\)
\(r\) distance from the centre \(\mathrm{m}\)
\(r_s\) Schwarzschild radius \(\mathrm{m}\)