1331. You sure?

The radius of Jupiter is 11 times the radius of the earth. Then, how many earths can we fit inside Jupiter? Obviously, none of the "earths" is to be powdered or melted.

#Geometry

Easy Math Editor

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Comments

Perhaps you can find a range for it. First consider a cube concentric with Jupiter, whose body diagonal equals the diameter of Jupiter. Fit Earths in this cube using Kepler's conjecture. Then consider another concentric cube whose edge length equals the diameter of Jupiter. Now fit Earths in this cube using Kepler's conjecture again. This will give you a range of values the number of Earths in Jupiter can assume.

Saurabh Chaturvedi - 5 years, 4 months ago

Sphere packing

Vishnu Bhagyanath - 5 years, 3 months ago

Technically speaking, there is no fit pattern to solving it for larger numbers.

Vishnu Bhagyanath - 5 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$