What is the largest distance at which a Cube-world is distinguishable from a spherical world?

Question

A Cubeworld and Cubemoon with uniform surface gravity have been engineered using materials of arbitrary strength and density, the cubeworld made habitable, and placed into orbit around a star. The Cubeworld is similar in both surface area and mass to Earth, and the Cubemoon is similar in surface area and mass to Luna.

While not exactly like Earth, Cubeworld's orbital characteristics are similar. Cubeworld is in a low-eccentricity orbit around its star in the habitable zone, rotating relatively quickly (18-30 Earth-hour day) on an axis between two corners like a spinning d6. The Cubemoon is similar to Luna by the same metrics.

What is the largest distance this system could be from earth that still allowed us to detect (using current Earth technology) that it is a cube-planet? How about just being able to detect that there was something weird about the planet?

Answer 1

With current technology? Not much further than our solar system.

We rarely take direct images of exoplanets. The majority of exoplanet detection methods involve observing the star it orbits, then looking for anomalies its gravity or luminosity that could only be explained by the existence of a planet of a certain mass or size. Gravitational methods will not reveal anything about the shape of the planet. Luminosity methods might - see the edits below.

Direct imaging won’t be of much help. To date, the smallest exoplanet ever directly imaged is Candidate 1 in the Alpha Centauri system. It is approximately half the radius of Jupiter and just over 4 light years away. Here’s the image (the planet is labelled C1)

Image from Wikipedia. If this planet was a Cube, it would still be difficult to tell from this image alone. And this planet is several times larger than your Cube Earth. The Cubic nature of your planet cannot be confirmed until significantly better telescope technology is invented.

Edit: In light of other responses, I must admit that it’s not entirely impossible to detect a cube world with current technology. But as others have mentioned this will depend on a number of factors. It’s nevertheless an unlikely conclusion that would be very difficult to confirm with certainty, but not impossible.

Edit 2: So I decided to do a little more research. This post found that the projected surface area of a rotated cube can increase by up to a factor of √3 times the area of a single face. This means the apparent size of the Cube world can fluctuate by up to 73% in the best case, though this would require the cube to be tumbling in an unnatural way. This could certainly be noticed as unusual considering that the apparent size of a spherical planet doesn’t change significantly as it rotates. But you still run into issues with size - terrestrial planets are much harder to detect than gas giants. A luminosity based detection method like transit photometry works by measuring the star’s change in apparent brightness caused by an orbiting planet passing between the star and the Earth, obscuring some of its light. For an Earth sized planet in an Earthlike orbit around a Sun sized star, you’re usually looking at a change in apparent brightness of ~0.008%. Because the Cube world’s shadow will change in size as it rotates, the change in apparent brightness could fluctuate by as much as 0.008% to 0.013% on a period equal to the Cube world’s rotational period. Assuming that’s 24 hours, our current telescopes are definitely sensitive enough to notice something strange. Since your Cube Earth also has a Cube Moon they’d notice some anomalies from that as well. Still, a cube shape is not a likely conclusion to draw from these observations. There are other configurations of planets and moons in odd orbits that could produce a similar effect which would be deemed more likely than an artificial Cube world. Because of the planet’s relatively small size it would be impossible for our telescopes to truly confirm one way or the other. But the Cube world would be a valid theory that matches the data.

In summary: Your best case would be to have the Cube rotating on a short period like 24 hours, and to be in an orbit around a relatively small star which happens to transit between that star and the Earth. Ideally its axis of rotation should be perpendicular to our viewing angle to maximize the fluctuations in its apparent size. In this case the Cubic nature of the planet could theoretically be detected from several hundred light years away. In worse cases, like the planet not being in a transiting orbit, it might be impossible for current telescopes to notice anything strange at any distance. I maintain that the range at which we could confirm without a doubt that this planet is a Cube is not much further than the confines of our solar system.

Answer 2

How about just being able to detect that there was something weird about the planet?

Oh, that is easy. At almost any distance at all at which the planet is distinguishable (for an Earth-sized planet with current technology I'd guesstimate about 30-40 light-years). Its apparent luminosity would change following a cosine law, which would match neither a spherical planet with sea/land patterns nor any reasonable planetary structure or orbital debris distribution.

You can simulate something like this using a simple VRML model of a cube, having it rotate and revolve around its primary. Depending on the viewing angle, you can get significant luminosity variations.

Quite probably, someone would jump to the conclusion that this is a spherical planet, whose surface has been shaped into a gigantic Fresnel curved mirror for reasons unknown.

If the planet was near enough (but in this case I'd say much less than 30 light-years), it might be possible to verify that the lightness variations are exactly those expected of a rotating cube.

The cube hypothesis is wont to meet an enormous resistance, though, because an object the size of Earth (or the Moon) is expected to collapse into a sphere under its own gravity. I expect that an ingenious enough disposition of planes on a spherical surface might mimic closely enough the reflectivity of a cube to be deemed a preferable explanation.

To be able to say "Cube!" without a doubt, in the face of the pressures against such a weird hypothesis, you'd need to be able to actually image the planet -- not just measure its luminosity (or rather the difference in luminosity from its parent star it causes). Judging from the images of Pluto taken from space telescopes, I'd guesstimate a distance of no more than around 140 AU, or four times the current distance of Pluto from the Sun (assuming the planet's brightness is comparable to Earth's, not Pluto's, much less at four times the distance). That's just 0.002 light-years.

Answer 3

We are actually on the breakthrough to looking on planets from several light years away in high detail.

https://en.wikipedia.org/wiki/Solar_gravitational_lens https://en.wikipedia.org/wiki/FOCAL_(spacecraft)

You goto go through layers of perception of course - and it takes a generation of spacelaunches- but eventually you get high res pictures of another world.