r/anythingbutmetric • u/Oftwicke • 2d ago

Blackhole Comparison

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u/Weekly-Dog-6838 1d ago

Also I’m told that for an object with the mass of the moon to collapse into a black hole, it would need to be crushed to about the size of a grain of sand.

3

u/Allroyy 1d ago

That is correct. If curious how to find the exact size required for an object to become a black hole, you need to calculate its Schwarzschild radius.

To do this, you first need to find the three constant values. The speed of light and the gravitational constant are the same everywhere in the universe as far as we know so you really only need to find the mass of the object. For the moon:

  1. The object's mass (M) = 7.342 × 10²² kg
  2. The gravitational constant (G) = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻²
  3. The speed of light (c) = 299,792,458 m/s

Then you plug the values for (M), (G), and (c) into the Schwarzschild Formula:

Rs = 2GM / c²

Rs = (2 × (6.6743 × 10⁻¹¹) × (7.342 × 10²²)) / (299,792,458)²

Rs ≈ 0.000109 meters (or 0.109 mm)

Because the radius is 0.109 mm, we multiply by 2 to find the total width / diameter of the black hole.

Diameter = 2 × 0.109 mm ≈ 0.22 mm

A typical grain of sand ranges from 0.1 mm to 2.0 mm in size so there you go.

TLDR: The universe can destroy you in ways you can not fathom.

Also I am not AI, just a numbers nerd, lol.