Two-hemisphere global composites of Moderate Resolution Imaging Spectroradiometer (MODIS) data, taken in 2001 and 2002. Observations show that Earth is nearly perfectly round, but must all planets be? Image credit: NASA.

We know that the Earth isn’t flat, and have known this for hundreds of years. There are many ways to demonstrate this, from ships’ masts disappearing as they sail out over the horizon, to your ability to see farther at higher altitudes, to the longer shadows cast by the Sun at higher latitudes, to measuring the shape of the Moon’s shadow on the Earth during a solar eclipse, to actually going to space and seeing the shape of the Earth for yourself.

But just because the Earth isn’t flat doesn’t necessarily mean a planet couldn’t be. In fact, there are many observations that we make that would be consistent with a flat, circular Earth.

The two ways Earth could cast a circular shadow on the Moon: by being a spherical object (bottom) or a disk-like object (top). Lunar eclipse observations cannot determine the Earth’s sphericity on theirown. Image credit: Windows to the Universe Original (Randy Russell), under a c.c.a.-s.a.-3.0 unported license.

So how close could we actually get to a flat planet? One strategy would be to take a solid slab of material — stone, steel, or something even harder like diamond or graphene — and build the largest flat disk you could. If you used conventional materials like this, you could create a thin, flat disk many hundreds of kilometers in radius that was stable. In other words, you could make a flat world that was larger than any object in our asteroid belt, and possibly even nearly the size of our Moon.

The line for a planet vs. a non-planet is mass-dependent, and making a thin, rigid body fails on that account. You can have a flat “thing” in space, but it wouldn’t be a planet if you did. Image credit: Margot (2015), via http://arxiv.org/abs/1507.06300.

But it wouldn’t be a planet if you did it that way. Back in 2006, we famously set forth the three criteria for defining a planet. (That definition has since been extended to exoplanets, too!) In order to be a planet, a world:

1. must be in orbit around the Sun (and not any other body like another planet),
2. must have sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium shape (round, or oblate/prolate in the case of a rapid rotation), and
3. must clear the neighborhood around its orbit (so that there are no other comparably large bodies also in/near its orbit).

That second part of the definition is what fails for our specially-created flat, thin world. If it isn’t massive enough to pull itself into hydrostatic equilibrium, it can’t be classified as a planet.

The rotations of the planets (and Pluto) in our solar system. Image credit: NASA / Calvin J. Hamilton (1999).

But there is a way to create a relatively flat planet: have it spin. Here on Earth, our planet is a relatively slow spinner: it takes 24 hours for us to rotate a full 360°. This means that a person living on the equator, the maximal distance from the Earth’s axis of rotation, experiences an extra speed of 464 meters per second (about 1,000 miles per hour) compared to someone at the poles. This extra speed affects the entire shape of the Earth, and causes it to elongate into a shape known as an oblate spheroid: a near-perfect sphere that’s flattened at the poles and elongated at the equator.

An oblate spheroid is compressed at the poles and elongated around the equatorial axis. Image credit: Sam Derbyshire of Wikimedia Commons.

The diameter of the Earth at the equator is 12,756 km, while at the poles its only 12,714 km. You are 21 kilometers closer to the center of the Earth standing at the North Pole than you are at the equator. This doesn’t seem like much, but there are worlds out there that rotate far faster. The gas giants all rotate quite quickly, with Saturn’s poles compressed by 10% relative to its equator.

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