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It's hard to imagine how it could come into existence in the first place. Our solar system developed from coalescing masses of rock, dust and other junk. To get there I'll assume the Earth started as a chunk of ice from some other system that got caught by our sun.
"Would the center freeze? Would there be icecaps?" "Water all the way to the core with the same mass as the present earth"
I'd say ice caps at the poles, but liquid between on the surface due to solar radiation. What the core is like it tough. Our core is hot partially due to residual heat from the planets formation, partially (it is thought) due to radiactive decay, and partially due to compression and internal frictions.
Does water compress enough to rise in temperature? I don't know. I'm guessing, at the extremes created by an Earth sized mass, that it would. On the other hand, solar radiation would only penetrate so far. I'm guessing that there would be an icy core, surrounded by an ocean many miles deep. Lots of vertical currents, as iceberg sized chunks break from the core and rise, cool currents from the poles sink, and day and night sides of the planets rotate about. It would be like a big slushy machine, churning away.
"and no other minerals or elements?"
I'd think that would inhibit the initial formation of life, as many needed elements, when they eventually fell to Earth, would sink and become imbedded in the icy core. Eventually there would be a small, rocky, metallic core surrounded by a layer of ice, still insulating such elements form creating life.
We're finding there are lots of basic organic elements in space. Do any of these have a density lighter than water? If so, they could be deposited and form a layer on the surface, which could eventually give rise to life? I'm guessing so, but that it would take longer than the conditions that existing on our real Earth.
"Also, assume it would be the same distance from the sun and disregard the moon."
The moon has actually stripped away a lot of our atmosphere. Without it we'd be much more like venus. I'm guessing sunlight and vacuum acting on ice would cause it to sublimate, and split some water into little H's and O's. Many H's, being light, would escape, or join with trace elements falling to earth, and eventually we'd have an extremely oxygen rich, deeply clouded atmosphere.
Hmmm, that would be highly reflective. I just changed by guess from a big slushy to a big iceball. That keeps falling chunks of debris closer to the surface, but in colder temps. Yet, we're close enough to get a LOT of solar radiation.
So, I'm guessing we'd have a very deep, dense, completely clouded, oxygen rich atmosphere around a dirty iceball, perhaps with a thin coating of slime life forms here and there.
"I've always wondered if there is a model for determining these sorts of things and what would change if one started with a spehere of any particular element or compound. Does anyone know? Does it take a computer simulator to figure it out?"
Somewhere someone likely has such things, and they likely disprove all my guesses.
But it's fun to try!
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