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This is the answer. You can get corundum (sapphire/ruby) in pretty much any colour you want in a lab for fairly cheap, and it is among the most durable gemstones so is great for bands.

It would likely be pretty impractical to get a solid band of crystal with a good looking gradient, though it could be done. The main issue would be the durability of a solid band without it being incredibly thick. The nicest option would likely be an eternity band made out of individual stones that are each a slightly different colour, which will give a gradient effect.

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Sounds like how a lot of computer counters work. -1? Nah that’s just 2 billion

what about growing single crystal of quartz with one dopant, and then grafting quartz with another dopant on it

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The question about amethyst and sapphire has been answered. They won't melt together the way you want.

For a practical alternative, a few gemstones sometimes do have two or more colors within the same crystal. An example is tourmaline, which can form bi-color crystals, typically red on one end and green on the other. The color change can also be concentric, called watermelon tourmaline.

You could certainly engineer it to make it work but keep in mind you'd need many many galaxies worth of material. Something like a Dyson sphere would need a few planets worth of material so they become less probable on those grounds alone.

Yes, hundreds of them. Mankind dates back maybe 200,000 years, if you limit it to Homo sapiens, and there are many species far younger than that:

>Haplochromine cichlid fishes of Africa’s Lake Victoria region encompass >700 diverse species that all evolved in the last 150,000 years.

--Ancient hybridization fuels rapid cichlid fish adaptive radiations

So there's hundreds of new species far younger than humans, in a single lake.

Glaciation (including the most recent Ice Age, which is of course more recent than humans) has also led to lots of speciation, as populations became isolated and diverged. For example:

>Pleistocene glacial cycles resulted in a burst of species diversification... By sampling across the geographic range of the five kiwi species, we discovered many cryptic lineages, bringing the total number of kiwi taxa that currently exist to 11 and the number that existed just before human arrival to 16 or 17. We found that 80% of kiwi diversification events date to the major glacial advances of the Middle and Late Pleistocene.

--Explosive ice age diversification of kiwi

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That's not a conventional definition of temperature. A particle gaining energy but losing entropy is strange, but it's not what people think when you say 'negative temperature' since these particles are indeed, quite hot.

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It is totally possible. As you correctly noticed, at different stages of the star's evolution its spectral energy distribution changes, meaning that at some stages most energy is emitted in the infrared range, and at other stages - in visible, ultraviolet, etc. Depending on the planet's atmosphere composition, it will absorb/reflect/transmit different wavelengths with different efficiency. Atmosphere composition, in turn, depends on many factors, such as geological age of the planet, its initial composition, amount of water, presence of life, etc. In other words, the surface temperature on the planet depends on many factors that can and do change as the central star and the planet itself evolve. Consequently, the Goldilocks zone can move.

Would it have to be a ring though? I was thinking something like a galaxy sized 'metropolis' or like a solar system sized ship. Is that theoritically possible?

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How much time do you have? The only loss of energy (loss of heat) will be by radiation. There is no conduction and of course no convection. Energy emission by radiation will be from black-body radiation (the emission of "light" energy that depends on the temperature of the body itself).

As temps decrease, the energy being emitted decreases, so the temperature of the body would approach but never really reach the limit of 0 contained thermal energy, although after a huge amount of time, it would be close enough that you couldn't measure the difference. The death of the universe condition (everything at absolute zero or, actually, slightly above because absolute zero is not possible for other reasons) is trillions of years in the future according to estimates I have seen (never tried to calculate it myself; not exactly certain how to).

There is a minor problem with your question, because the black body emissions can be absorbed too, so even in the absence of big energy sources like stars, all matter is being bathed in a low amount of energy, which would counter the loss by emissions, through absorption of radiation coming from other objects. Not much energy, certainly, but still energy. Also, there is a lot of energy zooming around which was emitted ages ago and has yet to interact with matter, and all matter will encounter some of that energy and heat up slightly by absorbing it.

The role of collisions and conversion of energy of motion (kinetic energy) to heat (or kinetic energy at the atomic level, which is pretty much what temperature is truly measuring) would lengthen that cooling process as well. Cannot have true absolute zero if things are moving.

Simple answer is that isolated matter in space does not cool to absolute zero (or as close to that state as can be attained by matter). Stuff in space is a bit warmer, a few degrees warmer in the sparser regions of space and considerably warmer if there is a decent source of emitted energy nearby. Still usually extremely cold by our human standards though, just not absolute zero.

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Yes, different stars are different sizes and output different amounts of radiation, light, heat, and gravitational pull. All of these things affect the planets and celestial bodies around them. And stars in their final days balloon outwards as they expend the last hydrogen inside of them. This also shifts the Goldilocks zone outward.

So yes.