Cube planet scaled one in sixty million

This is a simulation of how would the water and other fluids distribute on a cube of the same volume and density as Earth. The simulation and modelling was made using MATLAB R2016a.
The file's names explained: name_1_x_10_y.stl is 1 : x * 10y. So _1_6_10_7 is 1:600000000 or one in 60 million.

Cube planets

There are several cube shaped planet in fictional literature. Most of them are present in a satirical way, as opposite of the classical spherical planet. In this model of planet the contour of continents and oceans are drawn all across every face of the cube, edge to edge. Some example of this are Aocicinori, and Htrae, a parody of an opposite Earth in DC universe. These cubic planets have a simple fault, that is the water and gases would "fall" to the center of mass, that is not necessary normal to the face surface. If you were near the edge of a face of the cube, you would feel the attraction of gravity toward the center of the face, not normal to the ground, like if you were in the side of a mountain. Walking to the edge would be like climbing the mountain. This leds us to the other model, that is one of the possible planets you can find randomly on the game Spore. In those planets the water form a sphere around the center of mass, like a sphere overlapping the cube. This model is not entirely true, because the gravity force in any place of the cube surface is not homogeneous. To get the right model I decided to simulate the gravity attraction around a cube of the same volume and density as Earth. To simulate the sea level I assume that the sea level only depends on the air pressure, and therefore, only dependant on the gravity vector value. Once you go far from the floor, the gravity force became weaker. The algorithm calculate for every spherical coordinate the height off the floor when it reaches a reference value of gravity acceleration. If the gravity is too low at the surface it means that is too high to be the ocean surface. The result is something between the two models, with a nearly spherical surface, but flattened compared with the Spore model. Of course this results are assuming a homogeneous density, and a non deformable cube, if the mass were concentrated in the nucleus, the results would be closer to the last model.

imageimage
Bizarro worldCube planet from Spore

Environment

Lets assume that this kind of planet exists, its shape is nearly rigid, and it orbits a Sun like star at the right distance to have Earth like conditions, the environment would be quiet different from ours. Near the coastline, where the air pressure and gravity are similar to those of Earth, the climate would be pleasant, but moving toward the "edge" of a "face" of the cube, the air pressure drops drastically. A few kilometres more in that direction and the climate would be top mountain like, with snow covering the floor wherever the latitude. If there were rivers, they would ran radially straight to the ocean. If you keep going to the edge the atmosphere would became so tenuous that no snow could reach there. In the edge regions there would only be crude rock exposed to the vacuum, leaving the surface vulnerable to the impact of any small asteroid. Impact craters in this regions could not be eroded by the atmosphere. The giant oceans would also be hostile to life. Again, near the coastline everything would be fine, but leaving it the oceans became kilometres deep. At the bottom the pressure would be so high that water cannot be liquid. This would form an ice layer that would prevents the interchange of nutrients and minerals with the rocky crust. Offshore, the oceans would be sterile aside for the influence of the coasts.

References



I spend part of my time making these models, letting them available and free for everyone. If you want to support my work, you can contribute with me here:

Other astronomical objects

Object

Scale [1:x]

K = 103 (thousand)
M = 106 (million)
G = 109 (billion)

Image

Inner Solar System

Mercury 20M, 60M, 120M image
Venus 60M, 120M, 250M image
Earth 60M, 120M, 250M image
Luna 10M, 20M, 60M image
Mars 20M, 60M, 120M image
Phobos and Deimos 200K, 500K image

Man-made

Salyut 7 40, 48, 80, 160 image

Near Earth Asteroids

Moshup and Squannit 8K, 20K, 40K image
Ra-Shalom 20K, 40K image
Castalia 8K, 20K, 40K image
Bacchus 8K, 20K image
Bennu 3K, 8K image
Ryugu 3K, 8K, 20K image
Geographos 40K, 80K image
Phaethon 40K, 80K image
Itokawa 3K, 8K image
Eros 80K, 200K, 500K image
Nereus 3K, 8K image
Didymos and Dimorphos 8K, 20K image
Mithra 20K, 40K image
Golevka 8K image
Toutatis 40K, 80K image

Main Asteroid Belt

Gaspra 200K image
Annefrank 40K, 80K image
Braille 20K, 40K image
Vesta 2M, 4M, 10M image
Šteins 40K, 80K, 200K image
Iris 2M, 4M image
Hebe 1M, 2M, 4M image
Lutetia 500K, 1M, 2M image
Julia 1M, 2M, 4M image
Mathilde 500K, 1M image
Juno 2M, 4M image
Ceres 4M, 10M image
Pallas 4M, 10M image
Kleopatra 2M, 4M image
Ida 500K, 1M image
Psyche 2M, 4M image
Interamnia 2M, 4M image
Elektra 1M, 2M, 4M image
Hygiea 2M, 4M, 10M image
Antiope 1M, 2M image

Jovian System

Jupiter 500M, 1G image
Amalthea 2M, 4M image
Thebe 1M, 2M image
Io 20M, 60M image
Europa 20M, 60M image
Ganymede 60M, 120M image
Callisto 60M, 120M image

Saturn System

Saturn 500M, 1G image
Pan, Daphnis and Atlas 80K, 200K, 500K, 1M image
Prometheus and Pandora 1M, 2M image
Janus and Epimetheus 2M, 4M image
Mimas 2M, 4M, 10M image
Methone, Anthe and Pallene 40K, 80K image
Enceladus 4M, 10M image
Tethys 4M, 10M, 20M image
Telesto and Calypso 200K, 500K image
Dione 4M, 10M, 20M image
Helene 500K, 1M image
Rhea 10M, 20M image
Titan 60M, 120M image
Hyperion 2M, 4M image
Iapetus 10M, 20M image
Phoebe 1M, 2M, 4M image

Uranian System

Uranus 250M, 500M, 1G image
Puck 1M, 2M, 4M image
Miranda 4M, 10M image
Ariel 10M, 20M image
Umbriel 10M, 20M image
Titania 10M, 20M image
Oberon 10M, 20M image

Neptunian System

Neptune 250M, 500M, 1G image
Larissa 2M, 4M image
Proteus 2M, 4M, 10M image
Triton 20M image

Comets

Tempel 1 40K, 80K, 200K image
Wild 2 40K, 80K image
Churyumov-Gerasimenko 20K, 40K, 80K image
Hartley 2 20K, 40K, 80K image
Borrelly 40K, 80K, 200K image
Halley 80K, 200K image

Centaurs and TNOs

Hidalgo 500K, 1M image
Chariklo 2M, 4M image
Pluto and Charon 10M, 20M image
Styx, Nix, Kerberos and Hydra 500K, 1M image
Haumea, Namaka and Hiʻiaka 10M, 20M image
Arrokoth 200K, 500K, 1M image
Largest TNOs and their moons 10M, 20M image

Extrasolar

Exoplanets 120M, 250M, 500M image
Nearest white dwarfs 120M, 250M image
HD 189733 b 1G image
Pulsars 200K, 500K image
Cygnus X-1 accretion disk 10M, 20M image
M87* photon ring 1.5*1014 image

Sky maps

Heliosphere 7.5*1013, 1.5*1014 image
Constellations - image
CMBR 2*1028 image

Ancient

Earth (540 Mya to 20 Mya) 60M, 120M, 250M image
Luna (4 Gya) 20M, 60M image

Speculative

Planet Nine 250M, 500M image
Cube planet 60M, 120M, 250M image

Science Fiction

Ghroth 4M, 10M image
Arda 60M, 120M image
Life Foundation rocket 160, 200, 350, 500 image
B612 10, 20, 32, 40 image
Mesklin 500M, 1G image
Arrakis 60M, 120M image
Borg cube 8K, 20K, 40K image
Pern 60M, 120M image
Europa Monolith 200K, 500K image
Leonora Christine 500, 600, 1K, 3K image
Rama 80K, 200K, 500K image
Death Star 500K, 1M, 2M image
Starkiller Base 2M, 4M, 10M image
Z-95 40, 80, 160, 200 image
Eternia 60M, 120M image
Visitors mothership 20K, 40K image
Wheel of Time Earth 60M, 120M, 250M image
Nirn, Secunda and Masser 20M, 60M, 120M image
ID mothership 2M, 4M, 10M image
ID troop transporter 200, 350, 500, 600, 1K image
Heptapod spaceship 1K, 3K, 8K image
Gaijin flowership 3K image
Red Moon 60M, 120M image
Halo Array 4M, 10M, 20M, 60M image
Gem Homeworld 120M, 250M, 500M image
Citadel of Ricks 200K image
The Skeld 40, 80, 160, 200, 350, 500 image

Misc

Mars (1962 reconstruction) 60M, 120M image
Flat Earth 250M image
Expanding Earth 60M, 120M image
Spaceship of Ezekiel 80, 160 image