How many earth size spheres would fit inside a sun size sphere?

Question

I am not asking about volumes. I am not asking how many times in volume is the sun larger than the earth. My question is analogous to asking how many marbles can fit inside an average fish ball. I am sure there is mathematical formula out there on how many spheres with a certain radius could fit inside a sphere with a much larger radius. I am just curious.

Thank you in advanced.

Answer 1

The best packing density of spheres is about 74%. The Sun is large enough relative to the Earth that edge errors will be negligible since we're also ignoring the Sun nor Earth actually being spheres.



How many Earths could one make out of 74% of the Sun's volume?

0.74V⊚/V♁= 0.74 • 1.412[18] km³/1.083[12] km³ = 9.65[5].



Wiki give the volume of the Sun as 1.3[6] Earths. 0.74 • 1.3[6] = 9.62[5].



Sounds good to me.



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Answer 2

There probably is a formula, but I don't know it. However, the ratio of V sphere to V cube (the diameter of the sphere being the same as the side of the cube) is just under 2:1. In other words, if a sphere were inside a cube, just under half of the cube woud be empty



So given that about 1,250,000 volumes of Earth would fit into the sun, then roughly 600,000 spheres would do the same.



Someone correct me if my reasoning's out.



EDIT: Zardoz has done that. My method assumed that the spheres would be stacked only along three axes,in other words, like your marbles placed in a 3-D lattice. They would, of course, stack closer together.

Answer 3

The answer is about a million, maybe 1.1 million pulverized Earths. Less as Earth's material would be hot plasma, but compressed by the stronger gravity.

Asking how many ping pong balls would fit in a basket ball size sphere has fewer complications. I'll guess 700. Neil

Answer 4

You would be wrong. As far as I know, there's no formula that says there's a certain amount of spheres that can fit into another. It's an estimation kind of thing.