I was on Yahoo! Answers and I asked: "Flat-earthers: If the earth was really flat or cubical or rectangularly prismatic, how could the moon rotate around it?", and I was told, "The diameter of the earth is about 1/30 of the moon's distance from it. So if the earth were a cube of that size, it would make very little difference to the moon's orbit. That's how a flat-earther who knows his Newtonian physics would answer."

I responded with "The diameter of the earth is about 7,917.5 mi. so when you say "if the earth were a cube of that size", do you mean a cube with the length of one side being 7,917.5 mi.? A 7,917.5 mi. * 7,917.5 mi. * 7,917.5 mi. cube, or a cube with a volume of (7,917.5)^3 mi.^3?"

Am I right or am I missing something? What does "if the earth were a cube of that size" mean?

Someone there responded with, "As a simple geometry question? The volume of a sphere is V = (4/3) pi r^3. The volume of a cube is V = R^3. The volume of the (spherical) Earth is 2.59876×10^11 cubic miles. So a cube with the same volume would have sides of length 6381.49 miles. 6381.49^3 = 2.59876×10^11 The moon's average distance is nearly 29.01 times the Earth's average diameter."

Okay, but IS this a volume question? How do we know this is a about volume and not surface area?

• We can't know what was in the mind of the person who wrote it. More to the point, I seriously doubt that flat-earthers imagine that the world is a cube instead of a sphere. – lulu Apr 19 '18 at 10:44
• I seriously doubt flat-earthers even believe these formulas to be true :) – Matti P. Apr 19 '18 at 10:45
• I'm voting to close this question as off-topic because interpreting an ambiguous statement made by a random commenter on the internet is not a mathematical question. – Rahul Apr 19 '18 at 12:02
• I just wanted to know if the MATH is correct or not, Rahul. – Jason Shalom Goldman Apr 19 '18 at 13:20

Many modern members of the Flat Earth Society do not actually believe in a flat earth; they just produce arguments that true 19th and 20th century flat-earthers either used to use or which they think they might now use. They certainly do not believe the Earth is a cube, though they may be prepared to consider what the hypothetical consequences might be

Here they have picked up your use of "cube" and they have suggested that the orbit of the Moon around a hypothetical cubical Earth would be close to the orbit of the Moon around a hypothetical spherical Earth of the same mass, because the Moon is sufficiently far away from the Earth's surface for the Newtonian point mass calculation to be a good approximation in either case

The next step would be to say that mass is related to volume (assuming densities do not change significantly between the cube and the sphere). So this would be a volume issue rather than a surface area issue

• Henry, so the math in the second part is correct then? – Jason Shalom Goldman Apr 19 '18 at 13:21
• @JasonShalomGoldman A sphere with diameter $d$ has the same volume as a cube with side $\sqrt[3]{\dfrac {\pi}{6}} \, d \approx 0.806\, d$. The numbers $7917.5$ and $6381.49$ are consistent with this ratio – Henry Apr 19 '18 at 14:31
• Okay, cool. Thank you Henry. – Jason Shalom Goldman Apr 20 '18 at 6:05

There are several problems claiming that the earth is a cube - here are a few of them.

(1) The strength of the rocks (mostly granite type materials) are not strong enough to resist the pull of gravity to make the earth spherical. That is why the earth is spherical

(2) If the earth were a cube then as people ventured away from the centre of one side the earth would feel as though one were climbing a large rising slope and one would eventually find the edge where gravity and the earth surface were at 45 degrees