Cubic Planet Earth

[Leovinus]

Imagine if the Earth were the same mass but in the shape of a cube. I would like to consider two orientations: one where the north and south poles are in the center of opposite faces and the other where the north and south poles are on opposite corners. Aside from that, the orbit around the Sun is the same and the length of the day is the same.<br /><br />I would expect that on either type of world, the atmosphere would pool into the centers of each face with the corners being like high mountains sticking up out of the atmosphere. I also expect that gravity would only point straight down into the flat face at the center of that face and that everywhere else you'd get the sensation that you were on a slope. Also, gravity would be stronger in the center of the face than at the edges, but I'm not 100% sure about that. <br /><br />I think that if you had one side with a big ocean, it would tend to pile up in the center in an inverted bowl shape and also I think the atmosphere would have to do the same thing. <br /><br />My first thought was that there would be no hurricanes or spiral storms because the Earth was not round. But if the atmosphere is bowl-shaped anyway, then you might get a Coriolis effect anyway.<br /><br />I wonder if you could cancel out the Coriolis effect and the bowl-shaped atmosphere by having each side of the cube be a regular bowl-shaped depression such that the top of the atmosphere was flat... <div class="Discussion_UserSignature"> </div>

 

[ve7rkt]

If you made bowl-shape depressions in the faces, I think the atmosphere-puddles would be lens shaped.

 

[centsworth_II]

<font color="yellow">"Also, gravity would be stronger in the center of the face than at the edges, but I'm not 100% sure about that."</font><br /><br />Wouldn't the edges be like really huge mountain ranges on a spherical planet, with the corners being the highest mountains on the planet? And isn't gravity strongest over a mountain? Maybe the atmosphere would hug the corners and thin out toward the center of the faces. <div class="Discussion_UserSignature"> </div>

 

[Leovinus]

You may be right about the corners having higher gravity since there's more mass below. But you're also farther from the center of gravity so maybe that cancels out. <div class="Discussion_UserSignature"> </div>

 

[centsworth_II]

A test example would be: Is a person's weight increased while standing on the top of Mt. Everest because of the mass below them, or is it decreased because they are farther from the Earth's center of gravity? <br /><br />googling "mount everest mass effect on weight" brings up a lot. The answer at http://www.physlink.com/Education/AskExperts/ae111.cfm <br />agrees with your thoughts. But others aknowlege the weight increasing effect of the mass of the mountain. However, Mt. Everest's mass in relation to the mass of the Earth is tiny so the increase in distance from the Earth's center of gravity wins out. But the mountains at the corners of your square planet would have a much more significant mass in relation to the overall mass of the planet. They would also be much higher.<br /><br />I'm sure the necessary calculations to find the answer are easy, for some, not for me.<img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> </div>

 

[Leovinus]

That's why I post such questions here -- so that people who enjoy solving these kinds of problems can work out the answer for me. <div class="Discussion_UserSignature"> </div>

 

[nexium]

Since gravity decreases as the square of the distance, my guess is the mountains would have slightly less gravity unless the corners had higher density than the centers of the faces. The corners would likely have less than one milibar of atmosphere. The corners need to have very high cohession and adhession or they would sink into the planet until it was approximately a sphere. I agree six lens shape oceans and atmospheres if the centers of the are depressed into a bowel shape. An eqilateral tetrahedron would have 4 faces. Neil

 

[vogon13]

Perhaps for more fun, we could consider orbiting such a world.<br /><br />From far enough away, orbits would approach circularity, but as altitude decreased, the orbits would be more and more strongly perturbed by the 'lumpy' (cornery?) gravitational field. Even if an orbit cleared an obstruction, it may not be stable for very long.<br /><br />Interesting to see an orbit sim of various paths.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>