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Hard ideas.
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MESSAGE_0042.TXT[–] [□] [×]

FROM editor@plaintext.click

TO curious-human@earth

SUBJ How small would Earth be as a black hole?

ISSUE 0042 / GRAVITY

Earth’s mass, squeezed into a marble.

START HERE

A black hole is a region where gravity is so strong that anything crossing its boundary cannot return, including light. That one-way boundary is called the event horizon.

Turning Earth into a black hole would not require more mass. It would require squeezing the mass already here inside a sphere only about 1.8 centimetres across.

THE FORMAL IDEA

The Schwarzschild radius, rₛ, gives the boundary’s radius in the simplest model. G sets gravity’s strength, M is mass, and c is the speed of light.

rₛ = 2GM / c²

Earth’s mass → rₛ ≈ 8.9 mm2 × Earth’s mass → rₛ ≈ 17.8 mmtwice the mass → twice the radius

LIMIT: This version assumes the black hole is not rotating and carries no electric charge. Real black holes usually rotate.

KEEP THIS: DOUBLE THE MASS, AND THIS SIMPLE MODEL DOUBLES THE HORIZON RADIUS.

Hard ideas.Plain text.

Hard ideas.
Plain text.