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Simulation · Space

How small can you squeeze it?

Shrink Earth, the Sun or a stellar core and see density, gravity and escape speed rise until it turns into a black hole.

Ordinary matter
Earth · 1 M⊕Schwarzschild radius 8.87 mm
Dashed ring ↔ Drag to squeeze
Radius6,371 kmtrue size
Ordinary matter

Density5.5×10³kg/m³
Gravity9.82m/s²
Escape3.7×10⁻⁵of c

Thought experiment: real objects reach these states by collapse, not by being squeezed.

More numbers and limits
rs8.87 mm
rs ÷ R1.4×10⁻⁹
Escape11.2 km/s

White dwarfs cannot exceed about 1.4 M☉ (Chandrasekhar limit). Neutron stars top out near 2 to 3 M☉ (TOV limit). Past that, collapse to a black hole.

Density

Mass divided by volume. Halve the radius and the volume drops by eight, so density rises eight times. White dwarfs reach about a billion kg/m³ and neutron stars about 4 × 10¹⁷.

ρ = 3M4πR³

Gravity and escape

Surface gravity grows as 1 ÷ R². Escape speed is how fast you must travel to leave for good. It is shown as a fraction of the speed of light.

v = √2GM ÷ R

The black hole radius

Set the escape speed equal to c and solve for R. Squeeze all the mass inside this radius and light cannot get out. The cyan ring marks it.

rs = 2GMc²

How small can you squeeze Earth or the Sun before it becomes a black hole?

Any object becomes a black hole if all its mass fits inside its Schwarzschild radius, r_s = 2GM/c². For Earth that is 8.87 mm, about the size of a grape. For the Sun it is 2.95 km. Shrink the object below that and the escape speed passes the speed of light, so nothing can leave, not even light.

The simulation above lets you do that squeeze on a log scale. Pick Earth, the Sun or a 1.4 solar mass core, slide the radius down, and the page recalculates mean density, surface gravity and escape speed. On the way you cross three landmarks: white dwarf density (around 10⁹ kg/m³), neutron star density (around 4 × 10¹⁷ kg/m³) and the black hole threshold.

One honesty point first. You cannot actually squeeze a planet into a black hole with any tool. Real stars reach these states by collapsing under their own gravity after their fuel runs out. The slider is a way to see what each state means in numbers. For the real story of the objects, read The mystery of neutron stars.

Key results from the simulation

  • Schwarzschild radius: r_s = 2GM/c² grows in step with mass. Earth: 8.87 mm. Sun: 2.95 km. A 1.4 solar mass core: 4.13 km.
  • Density: it climbs as 1/R³, so halving the radius multiplies it by 8. Earth starts at 5.5 × 10³ kg/m³ and reaches white dwarf density at a radius of 113 km.
  • A neutron star is not a black hole. A real 1.4 solar mass neutron star has a radius near 12 km, nearly three times its 4.13 km Schwarzschild radius. Its escape speed is about 59% of light speed.
  • Two limits decide the outcome: about 1.4 solar masses for white dwarfs (Chandrasekhar) and roughly 2 to 3 solar masses for neutron stars (Tolman–Oppenheimer–Volkoff, or TOV). Above them, nothing known stops the collapse.

Six squeezes, step by step

Each section gives the numbers the simulation shows, says what they mean, and has a button that loads it above. The button also switches to the right object. Radius is shown on a log scale: each tick on the slider is a factor of 100 smaller.

Earth as it is

Starting point

At true size Earth has a mean density of 5.5 × 10³ kg/m³, surface gravity of 9.82 m/s² and an escape speed of 11.2 km/s, which is 3.7 × 10⁻⁵ of the speed of light. Nothing here is extreme.

Earth's Schwarzschild radius is 8.87 mm. That is the size you would have to reach, with every kilogram of the planet inside, for light to stop escaping. Compared with Earth's real radius it is a factor of 7.2 × 10⁸ smaller.

Related reading: How much energy it takes to blow up Earth

Radius 6,370 km Density 5.5 × 10³ kg/m³ Gravity 9.8 × 10⁰ m/s² Escape speed 3.7 × 10⁻⁵ c

Earth as wide as the Eiffel Tower is tall

Squeeze to a nucleus

Shrink Earth to a radius of 160 m and its density becomes 3.5 × 10¹⁷ kg/m³, the density of an atomic nucleus. This is neutron star matter: a teaspoon would weigh a couple of billion tonnes.

Surface gravity would be 1.6 × 10¹⁰ m/s², about 1.6 × 10⁹ times what you feel today. Escape speed would reach 0.74% of the speed of light. Yet this is still not a black hole, because 160 m is far larger than 8.87 mm.

Reality check: a real neutron star lighter than about 0.1 solar masses cannot exist, so an Earth-mass one is only a thought experiment.

Related reading: The mystery of neutron stars

Radius 160 m Density 3.5 × 10¹⁷ kg/m³ Gravity 1.6 × 10¹⁰ m/s² Escape speed 7.4 × 10⁻³ c

Earth as a black hole

Past the horizon

At a radius of 8.87 mm (a ball under 2 cm across) the escape speed hits the speed of light. The simulation then draws the event horizon and reports the horizon values: a density of 2 × 10³⁰ kg/m³ and a Newtonian g of 5.1 × 10¹⁸ m/s².

Far away, nothing changes. An Earth-mass black hole pulls on the Moon exactly as Earth does, so the Moon would keep orbiting. Only objects that dare to come within a few centimetres notice the difference.

No process we know makes a black hole this light. The smallest ones that form from dying stars are a few times the Sun's mass.

Related reading: Why the name "black hole" was chosen

Radius 8.87 mm Density 2 × 10³⁰ kg/m³ Gravity 5.1 × 10¹⁸ m/s² Escape speed c (light trapped)

The Sun squeezed to Earth size

Squeeze to a white dwarf

Squeeze the whole Sun into a ball of radius 6,340 km and its density is 1.9 × 10⁹ kg/m³, close to the 10⁹ kg/m³ of a white dwarf. Surface gravity reaches 3.3 × 10⁶ m/s², about 3.4 × 10⁵ times Earth's, and escape speed is 2.2% of light speed.

This matches what the Sun will actually do, with one difference. In about five billion years it will puff off its outer layers and leave a white dwarf of roughly 0.5 to 0.6 solar masses, about Earth-sized. The rest of its mass drifts away, and electron pressure holds the core up.

Related reading: What if we replace the Sun?

Radius 6,340 km Density 1.9 × 10⁹ kg/m³ Gravity 3.3 × 10⁶ m/s² Escape speed 0.022 c

The Sun as a black hole

Past the horizon

To trap light the Sun would have to fit inside a radius of 2.95 km, about three kilometres, shorter than most city bridges. That is 2.4 × 10⁵ times smaller than its real radius.

Again, the planets would not care. Earth would circle a one-solar-mass black hole at the same speed and distance as it does now, just in the dark. The Sun cannot do this on its own: it does not have enough mass to collapse.

Related reading: What if we replace the Sun?

Radius 2.95 km Density 1.8 × 10¹⁹ kg/m³ Gravity 1.5 × 10¹³ m/s² Escape speed c (light trapped)

A 1.4 solar mass core becomes a neutron star

How it really happens

This is the one squeeze nature performs. When a massive star runs out of fuel, its iron core, about 1.4 solar masses and roughly 2,000 km wide in this model, collapses in about a second. It stops at a radius near 12 km, where its density is 3.8 × 10¹⁷ kg/m³ and escape speed is 0.59 c.

Surface gravity there is 1.3 × 10¹² m/s², roughly 1.3 × 10¹¹ times Earth's. The slider stops this core short of a black hole because its 4.13 km horizon is much smaller than 12 km. Add more mass, above about 2 to 3 solar masses, and neutron pressure loses the fight. See Bizarre object orbiting a distant star at high speed for what extreme compact objects can do to their neighbours.

Related reading: 10 cosmic objects that will amaze you

Radius 12.1 km Density 3.8 × 10¹⁷ kg/m³ Gravity 1.3 × 10¹² m/s² Escape speed 0.59 c

Ten squeezes side by side

CaseRadiusDensity (kg/m³)Gravity (m/s²)Escape / cState
Earth, true size6,370 km5.5 × 10³9.823.7 × 10⁻⁵Ordinary matter
Earth at 10⁹ kg/m³113 km1 × 10⁹31,5002.8 × 10⁻⁴Electron-degenerate
Earth at 4 × 10¹⁷ kg/m³153 m4 × 10¹⁷1.7 × 10¹⁰7.6 × 10⁻³Neutron-star matter
Earth at r_s8.87 mm2 × 10³⁰5.1 × 10¹⁸1 (horizon)Black hole
Sun, true size696,000 km1.4 × 10³2742.1 × 10⁻³Ordinary matter
Sun at Earth’s radius6,370 km1.8 × 10⁹3.3 × 10⁶0.022Electron-degenerate
Sun at 12 km12 km2.7 × 10¹⁷9.2 × 10¹¹0.5Neutron-star matter
Sun at r_s2.95 km1.8 × 10¹⁹1.5 × 10¹³1 (horizon)Black hole
1.4 M☉ core, 2,000 km2,000 km8.3 × 10¹⁰4.6 × 10⁷0.045Electron-degenerate
1.4 M☉ core at 12 km12 km3.8 × 10¹⁷1.3 × 10¹²0.59Neutron-star matter

Same formulas as the simulation: density ρ = 3M/(4πR³), gravity g = GM/R², escape speed v = √(2GM/R). The black hole rows use the horizon. The core row uses a rough 2,000 km starting radius. A state label is a density band, not proof that the object would be stable there.

How the simulation works

You choose an object (its mass and true radius are fixed) and a squeeze factor f on a log scale, so the radius is R = f × R_true. From R the page computes mean density ρ = 3M/(4πR³), surface gravity g = GM/R², escape speed v = √(2GM/R) and the Schwarzschild radius r_s = 2GM/c². The escape speed is shown as a fraction of c.

The state of matter comes from the density: below 10⁶ kg/m³ it reads ordinary matter, up to 10¹¹ electron-degenerate (the pressure inside a white dwarf), up to 2.3 × 10¹⁷ neutron-rich, above that neutron star matter, and a black hole once R falls to r_s. The slider track is coloured with those same bands. The dashed ring on the stage is a familiar size picked from a ladder (a hair, a person, Manhattan, the Moon) to match the object, and the cyan ring marks r_s when it is large enough to see.

The stage mixes scales, so the drawing always zooms so that the larger of the object and the ring fits. Read the label at the bottom for the real size of the ring.

What the model leaves out

  • Real stars are not uniform. The Sun is about 100 times denser at its centre than its mean of 1,410 kg/m³. The model uses the mean.
  • Newtonian formulas near a horizon. Near r_s, g and v from Newton are only rough guides. General relativity is needed, though it gives the same r_s.
  • No equation of state. Real white dwarfs and neutron stars sit at a radius set by quantum pressure, and that radius shrinks as mass grows. The slider ignores this and lets you go anywhere.
  • No heat. Compressing matter heats it, and a star born from collapse is millions of degrees. State labels use density alone.
  • No spin or charge. The Schwarzschild radius applies to a non-rotating, uncharged object. Real black holes spin.

Common misconceptions

“Black holes suck everything in.” Outside r_s the gravity is the same as before the squeeze. Shrinking Earth to a marble does not change the Moon’s orbit.

“A neutron star is almost a black hole.” It is dense, but a 1.4 solar mass neutron star is nearly three times wider than its Schwarzschild radius, and its light still escapes.

Frequently asked questions

Could Earth ever become a black hole?

No, not by any natural process. Earth would have to be squeezed to 8.87 mm, and nothing in nature does that to a planet. Stellar black holes come from dead stars of many solar masses.

Why is a neutron star about 12 km wide if its Schwarzschild radius is only about 4 km?

Because neutron degeneracy pressure and the nuclear force push back. A 1.4 solar mass neutron star has r_s of 4.13 km but a radius near 12 km, a ratio of about 3. General relativity says no stable star can be smaller than 9/8 of r_s, and real ones stay well outside it.

What are the Chandrasekhar limit and the TOV limit?

The Chandrasekhar limit, about 1.4 solar masses, is the heaviest a white dwarf can be before electron pressure fails. The Tolman–Oppenheimer–Volkoff limit is the same idea for neutron stars. Its value is uncertain because it depends on how matter behaves at extreme density, but it sits roughly between 2 and 3 solar masses. The heaviest known neutron stars are about 2.1 to 2.3 solar masses.

Is escape speed above the speed of light really why black holes are black?

It is a handy picture and it gives the right r_s, but the real explanation comes from general relativity, where inside the horizon every path leads inward. The Newtonian formula happens to agree on the radius.

Would the Sun ever become a black hole?

No. It is too light. It will end as a white dwarf. Very roughly, stars that start with more than 20 or so solar masses can leave black holes behind.

Does gravity far away change when the object shrinks?

No. For a spherical object, the pull outside its surface depends only on mass and distance. Only the gravity at the surface grows as the radius falls.

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