Astrophysics

August 18, 2026 Lead Investigator: Simon Frye

What if Earth were as dense as a neutron star?

Earth would become impossibly small, but the consequences reach far beyond that. Explore how extreme density affects gravity, spacetime, and life on our planet.

Field explored: Physics, Astronomy, Mathematics

But before we explore

MAKE YOUR PREDICTION.

Will Earth…

A.) Become tiny?

B.) Become a black hole?

C.) Explode?

D.) Stay the same size?

E.) Do something else?

Our predictions

“The Earth would just turn into a black hole, right?”

THE RULES

1.) Earth’s mass will stay the same.

2.) Only the density will change, though matter can still be compressed.

3.) The change will happen instantly.

4.) The mechanism that could do this will be ignored.

WHAT WE NEED TO KNOW FIRST

Density

P = M/V

P is density, M is mass, and V is volume. This will help us understand how Earth’s volume will change with an increased density.

Force of Gravity

F = GM1M2/R²

F is force of gravity, G is Newton’s gravitational constant (6.67 × 10^-11), M1 is mass one, M2 is mass two, and R is radius of object. This will help explain how life on Earth and the moon will be affected.

Schwarzschild Radius

R = 2GM/C²

R is Schwarzschild Radius (Radius an object must be compressed to in order to become a black hole) G is Newton’s gravitational constant, C is the speed of light. This shows us if Earth will become a black hole.

Volume of a Sphere

V = 4/3πr³

V is volume and r is the radius of the sphere. This will help understand the density of the new earth.

THE PROCESS

For this question, we will use the known values of Earth’s mass and radius:

m = 5.97 × 10^24kg

r = 6.37 × 10^6m

The radius of Earth was found all the way back in 240 BCE by the Greek scholar Eratosthenes, while the mass wasn’t found until 1798 by British scientist Henry Cavendish.

We will assume the neutron star is one with an average density:

P = 4.5 × 10^17 kg/m^3

A single teaspoon of this material would weigh as much as a mountain here on Earth!

First, let’s find the volume of the Earth:

V = 4/3π x (6.37 × 10^6 m)³ = 1.08 × 10^21 kg/m³

That puts our density at 5,513 kg/m³, which is slightly denser than granite.

Now, let’s look at our current density equation:

P= (5.97 × 10^24 kg) x (1.08×10^21 m³)

The density equation was found by Archimedes in the 3rd century BCE.

And we plug in our new density:

4.5 × 10^17 kg/m³ = (5.97 × 10^24 kg) / v

Mass stays the same so we need to find the new volume

And let’s do that:

V = (5.97 × 10^24kg) / (4.5 × 10^17 kg x m³) = 1.32 × 10^7m³

This is about the same volume as the largest building in the world: The Boeing Everett Factory.

Finally, let’s find our new radius:

r = ∛((1.32 × 10^7m³) / (4/3 x π)) = 146.6m

That’s a sphere about 300 meters across, which is about how tall the Eiffel Tower is.

What about its new surface gravity?

F = ((5.97 × 10^24) x (6.67 × 10^-11)) / (146.6)² = 1.85 × 10^10 N

That’s 1.89 billion g. Not compatible with life.

Now the big question…will it turn into a black hole?

r = (2 x (6.67 × 10^-11) x (5.97 × 10^24)) / (3 × 10^8)² = .009m

Earth needs to be about the size of dime to be a black hole, and our neutron star Earth is a little over 16,000 times too big. No black hole today :(

So…What happens?

Earth would shrink down to the size of Ferris wheel, going from a planet it would take an entire day to fly around to a ball that would take about 3 minutes to walk around.

Regarding the moon, Earth’s mass is conserved so the moon’s orbit would not change considerably, but Earth’s shrinkage will cause the two bodies to be about 6.37 × 10^6 meters farther apart. This means the gravitational force between the moon and Earth will get about 3 percent weaker. Besides that, the moon will be relatively unaffected by this change, as gravity only starts becoming a problem as you get close.

All life on Earth would be unable to survive on our new planet. A surface gravitational force roughly 1.9 billion times stronger than our current one would ensure that. A human body would experience tidal differences (difference in gravitational strength across an object) of millions of g between its head and feet.

But my own prediction, Earth becoming a black hole, was wrong. Neutron stars rival black holes because they carry multiple solar masses, not Earth masses. Our planets mass makes a Schwarzschild radius of about the size of a grape or a dime, not a Ferris wheel. The important thing to note is that a black hole is never decided by density alone, mass and density have to work together.

And for the final prediction, Earth violently exploding. The answer is…yes! As soon as we stop squeezing our new Earth it would violently explode outwards, but why? Well there is an immense force expanding outwards called neutron degeneracy pressure. In a neutron star, matter is packed so tightly that protons and electrons melt into a dense field of neutrons. According to the Pauli exclusion principal, these neutrons cannot exist in the same space together. So like a compressed spring, these neutrons are waiting to explode. Tremendous gravitational pressure is required to contain this force, one that requires a mass of at least 1.4 suns. Our planet, despite its 1.9 billion g gravity, is no where near enough to contain this pressure, and would explode immediately with the force of a trillion nuclear bombs.

What surprised us?

I had originally assumed that Earth would turn into a black hole, but I was wrong. The Schwarzschild radius depends on mass, and poor Earth is simply not massive enough.