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Imagine a world that spun just fast enough (and had a strange enough composition to hold itself together as a spinning sphere) to create an outward, centrifugal force which was as strong as its gravity, causing the effects of gravity to cancel out. In other words, the planets surface would be located at the same position as geosynchronous orbit.

If the description seems to implausible for you: On this planet, the gravity on the surface is zero. As you move away from the surface (upward or downward) the effects of gravity would increase, pulling things towards the planet's core.

What would life on this planet be like?

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    $\begingroup$ Umm , if its enough to negate gravity , would the planet tear apart? $\endgroup$ – user15036 May 23 '16 at 19:08
  • $\begingroup$ a little perhaps. but as soon as it did, the bits would slowly fall back down. The entire surface would be in a state of flux. $\endgroup$ – Hoytman May 23 '16 at 19:10
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    $\begingroup$ That's not how that works , when pieces separate , they'll be ejected from the planet , due to the decrease in the force of gravity the farther you get from the center of mass , along with the centrifugal force pushing mass away from the center $\endgroup$ – user15036 May 23 '16 at 19:21
  • $\begingroup$ as objects move away from the surface, they slow, which lowers the effect of centrifugal force. $\endgroup$ – Hoytman May 23 '16 at 19:26
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    $\begingroup$ How big did you say this planet was? $\endgroup$ – Schwern May 23 '16 at 20:54
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Unfortunately, if your planet spins fast enough to negate gravity, your planet won't have an atmosphere. The velocity required for a given orbit is inversely proportional to the square root of the radius of that orbit. In other words, the higher up you go the slower you need to go in order to have a circular orbit.

So here we have two possibilities. If the atmosphere is spinning as fast as the planet, instead of gravity counteracting air pressure to give the planet a nice, thick, breathable atmosphere, the atmosphere will spread out and the surface of the planet will be a near-vacuum. If the atmosphere isn't spinning as fast as the planet, it will act as a brake on the planet and slow the planet's spin over time (a shorter timescale than what it takes for life to evolve). Also, when the atmosphere isn't moving as fast as the planet you've got a devastating global windstorm - Randall Munroe explored the idea in the first chapter of his "What If" book.

So what does life on such a planet look like? Either it is something that lives easily in the vacuum of space, or there's an unobtainum bubble around the planet keeping its atmosphere in, in which case life looks like whatever the advanced civilization that put the bubble there wants it to look like.

How fast does the planet actually spin?

Note that this was the original intro to my answer. I realized that this isn't actually that important for the atmosphere problem, so I'm moving it below the actual answer.

The two biggest formulas to worry about are gravity $F=G\frac{m_1m_2}{r^2}$ and centripetal force $F=\frac{mv^2}{r}$. Another way to describe your planet is that the force of gravity provides exactly the centripetal force and no more. That means we can simplify the equation to get $Gm_2=rv^2$.

Now let's assume this planet is a rocky planet. Using the average density of the Earth (5510kg/m3) and the volume of a sphere ($\frac{4}{3}\pi r^3$) we get $m=23080r^3$. Using that in the above equation, we get $\frac{r}{v}\approx 800$. So for every 800 meters of radius, the required velocity increases by 1 meter per second. Because circumference is proportional to the radius, a planet of this density will have a day that is $2\pi*800=5026$ seconds long, regardless of how large the planet is.

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  • $\begingroup$ At the required velocity part, don't you mean 1 radian per second? $\endgroup$ – Simply Beautiful Art May 24 '16 at 22:04
  • $\begingroup$ @SimpleArt no, I do mean meters per second. But I did neglect to actually calculate how fast a Pluto-sized body would need to rotate and used an invalid shortcut. $\endgroup$ – Rob Watts May 24 '16 at 22:29
  • $\begingroup$ Yeah, I just thought your Pluto day was wrong. :) $\endgroup$ – Simply Beautiful Art May 24 '16 at 22:31
  • $\begingroup$ Would lowering the size of the planet assist with the atmosphere problem? $\endgroup$ – Gryphon Jan 25 at 18:26
  • $\begingroup$ @Gryphon no, the planet size doesn't matter. Now that I look at this again, the entire first part wasn't really relevant to the atmosphere problem - knowing how fast it would need to spin is interesting, but not necessary. $\endgroup$ – Rob Watts Jan 25 at 21:18
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Assuming this planet is made out of unobtanium that can hold itself together... it still cannot exist.

Rotational velocity on a rotating sphere is different depending where you are on the sphere. As you move towards the poles, you slow down. As you move towards the equator, you speed up. On the Earth, the rotational velocity at the equator is about 1675 km/h. At 45° latitude it's about 1185 km/h. At the poles it's 0. This is just geometry, the circle you're making as you rotate is smaller at higher latitudes, but you do it in the same time as everyone else, so you must move slower. If it wasn't this way, the planet would have to be liquid or something.

You can only have one latitude on your planet where the rotational velocity equals orbital velocity. If that's the equator, then the high latitudes will be a bit more normal. If that's not the equator, then everything below the equator is moving above orbital velocity and is constantly flung around and eventually shed into space.

Then there's the weather. Just as on Earth, the surface will drag the atmosphere with it. Just as on Earth, the differences in velocity between the various latitudes will produce cells of prevailing winds around the planet... except at this velocity they'll be crazy. Still assuming an Earth-sized planet, instead of going 1675 km/h at the equator, it's going 28500 km/h! That's about 24 times the speed of sound in air.

No material could accumulate on the surface. No soil could ever form. It will either be flung away by the rotational speed, or be blown away by the tremendous wind leaving just the unobtanium core. If the unobtanium is not smooth, it's possible there could be catchments in its ripples.

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As stated, this is simply not possible for the planet as a whole. In principle, you could get zero gs at the equator, but nowhere else.

Take the Earth as an example. The orbital period in LEO is about 90 minutes. So, if the Earth were to have a 90-minute day, the equator would be at zero gs. However, the poles have no centrifugal force associated with them, and surface gravity would be 1 g, dropping with latitude.

As a result, the other answers are correct about atmosphere loss, except that it would only occur in the vicinity of the equator, and therefore would take a bit longer than if the surface field were zero over the whole planet.

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If a planet spun so fast that "gravity" was negated and objects actually fly off the planet due to centrifugal force, you don't need to use science but simple logic to realize that if objects on the surface will be flung into space, then so will the ground of the planet as well, as everything in the planet was flung into space until there was nothing left.

You mentioned that in fact, the planet was made of a material that will not fling off due to centrifugal force. Well, then the planet must be solid rock.

Unfortunately, in our current science, gravity does not work like you said. Gravity is actually stronger the closer you get to the surface or the core, not the other way around. You are implying the opposite, which is a fantasy world, and even more fantastic (as in, scientifically null), that somehow gravity functioned normally below the surface and opposite above the surface? This makes no scientific sense, that much is for sure.

If you are claiming a fantasy world where what you say is what occurs, then we can no longer use science to determine an answer, since you are no longer actually relying on science as we know it. In fact, in this world, you made up your own science and your own physics, so in that case of course it will work, for you are the creator of this universe and this science and this physics and therefore you can do whatever you want - it is a fantasy world.

But since you said this is a science-based question, then your science is wrong and your planet cannot exist. There is no scientific answer to your question, you are totally free at this point to create any universe you want free from the bounds of science, as this is now a fantasy question.

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