How long a lever would Archimedes need?

Archimedes once was quoted by Pappus as saying

Give me a place to stand, and I shall move the Earth.

In reference to the lever.

So how long a lever would Archimedes need to lift the Earth? The equation for lever force is F₁ * D₁ = F₂ * D₂ .

F₁ being the force exerted by object one (the Earth).

D₁ is the distance between F₁ and the fulcrum.

F₂ is the force Archimedes is exerting on the lever (lets say 500 newtons).

D₂ is the distance between F₂ and the fulcrum.

Let us say that this is occurring on an infinite plane with no mass. If the force pushing Earth “down” is one g (9.81 m/s) then the amount of newtons the Earth is exerting is ⊕ * g (or 5.97219*10²⁴ kg * 9.81 m/s). That is 5.8587*10²⁵ newtons. Our equation is now:

5.8587*10²⁵ * 1 = D₂ * 500

All we have to do now to get D₂ in meters is 5.8587*10²⁵/500.

The lever is 1.1717*10²³ meters long. That is 12.4 million light years (3.8 million parsecs).

Or roughly 100000000000000000000000 meters.