Possibility of a Spindle Shaped World

Question

We live on this lovely, assumed naturally shaped almost sphere (accepted as an oblate spheriod) that makes everything really nice and easy when it comes to things like constant gravity and horizon lines rather commonplace. But say back when Earth was just forming, some jerk-headed aliens decided to break the alien non-interference clause and make some trouble. So using their crazy elder race tech, reformatted the world into a spindle shape, with the same axial tilt, same orbit, etc., but the world was only 10,000 km wide at the equator but 16,000 km between poles.

Would this planetary structure be capable of retaining its shape without collapsing back into a sphere, or would it need something crazy (such as an internal adimantium system) to structurally support it? Warning: the following spoiler alert features a plot point from Avengers 2. You have been warned.

Like Avengers 2, Ultron's floating meteor/city thing which uses a "web" of vibranium to hold itself together.

This is part of a (hopefully) multi-question series.

Answer 1

Serious shenanigans required. Earth is mostly a very dense, hot liquid, and even a cooled-off, solid body with Earth's mass will end up as a spheroid due to gravity's effects.

(This is due to the Inverse-Square Law--the force exerted by gravity is inversely proportional to the square of the distance from the center of the mass exerting the gravitational force. So matter experiences equal amounts of gravity at all points on a sphere a given distance from the center of the mass. Therefore matter with sufficient mass for a nontrivial gravitational field which is then shaped into spindle isn't going to remain spindle-shaped because a spindle doesn't distribute the mass evenly across the sphere-shaped field. It's not at at an equilibrium, gravitationally. The mass at the pointy ends, or any other matter caught in the gravitational field, will fall toward the middle until the force of gravity is equalized across the surface, which is to say, when it's a spheroid.)

A spindle-shaped planet of earth's mass at equilibrium would require continually operating gravity manipulation. The shape of the gravitational field would have to be altered into and maintained as a spindle.

Moreover, the spinning, liquid, spherical core of earth (mostly iron and nickel) is also important for life's existence. It creates our planetary magnetic field, which in turn prevents us all from having our DNA constantly rearranged and destroyed by solar radiation. That deadly radiation instead gets trapped by earth's magnetic field in the van Allen radiation belts. None of which is compatible with a spindle-shaped planet. (Magnetism also follows the Inverse-Square Law, as does every flux- or field-based force.)

So in order to make a spindle-shaped planet workable, the aliens have got to either alter the Inverse-Square Law, either locally or across all of physical reality, either of which seems like it would be hard to do, and would have a ton of repercussions--all planets, stars, and orbits would be spindle-shaped, for one--or they've got to locally manipulate gravity and magnetism (or just gravity, and then provide some other means of shielding the planet from hard ionizing solar radiation) indefinitely.

Which leads me to the question: what do the aliens have against sphere-shaped planets that they're willing to go to all this trouble?

Answer 2

I didn't watch the movie you reference; but, eventually the forces of gravity will pull not only itself back into a sphere, but also pull nearby material in as well.

Exceptions

1. It can be exceptionally small - it wouldn't be hard to imagine an old asteroid maintaining a bumpy, but similar shape to a spindle. It won't be Earth-like, but you get to have your own satellite! You can shrink it, but it doesn't sound like you want it to.
2. You can have it artificially maintain the shape & size: the Aliens waved their gray, little hands, and now you have protection against the forces of gravity, artificial gravity distribution, protection against unusual forces of nature and geology, and protection from other rocks that might join you and make you more spherical.

In the end, it needs to be artificially maintained in order to be Earth-like for more than a few minutes.

Answer 3

Shenanigans are required. An object 1/10000th the mass of Earth or larger will naturally be pulled into a spherical shape by gravity (source). In fact, one of the many definitions for a planet is the fact that it has enough mass to have gravity overcome the electrostatic forces pushing it apart, which always results in a roughly spherical shape over time.