Water World physics help

[mikoto]

I'm making a system of worlds for my new campaign and one of the worlds is made completely out of water. I always like my worlds to be as close to real world physics as possible. I want the world to have the same surface temperature and gravity as Earth.

How large would the planet have to be. What effect would the gravity and pressure be on the core. How large would the polar ice caps be during the season, depth as well as length and width.

[Cryopyre]

those are some damn big numbers you're working with.

[Zeta Kai]

Well, for starters, the mass of the planet Earth is 5.9736×10^24 kg, with a mean density of 5,515.3 kg/m³. So, for a celestial object composed entirely of water (density @ 0 degrees Centigrade = 999.8425 kg/m³), you'd have to, uh...

...hold on a second. Let me ponder this one a moment. Hmm...

[jindra34]

Well, for starters, the mass of the planet Earth is 5.9736×10^24 kg, with a mean density of 5,515.3 kg/m³. So, for a celestial object composed entirely of water (density @ 0 degrees Centigrade = 999.8425 kg/m³), you'd have to, uh...

...hold on a second. Let me ponder this one a moment. Hmm...

Plus gravitity... plus temperature uniformity... i think it aint possible....

[Zeta Kai]

Plus gravitity...

Isn't that what causes breasts to sag?

Sorry, I just couldn't resist.

[SITB]

The question is, could the water accrete into a dense enough shape that their gravity would pull them togther instead of having the water disappear into space?

My suggestion is to hand wave most of it with some help of science, and SCIENCE!.

For example, to have more gravity the water needs either to be more dense, or the world to have a bigger radius.

[jindra34]

let me put it this way: the physics will not work... thus find another explanation.

[mikoto]

I don't need it to be the same size as earth so more volume is probablyy neccesary

[Vuzzmop]

Are your players really that nitpicky? If I were you, I wouldn't bother with physics that heavy going just to play a realistic game. Just get the basics, but estimate the rest.

[Rob Knotts]

let me put it this way: the physics will not work... thus find another explanation.

Well, he can at least aim for plausability, if not physics.

How large would the polar ice caps be during the season, depth as well as length and width.

I don't think you're really talking about polar ice caps so much as a global ice shell defining the shape and most of the surface of the world. Things get hotter as the pressure builds toward the center, and cooler as you approach the surface. The icy terrain is liveable because of weather patterns and sunlight. You can even have earthquakes and steam volcanos in the icy shell, with the volcanos creating islands of fertile and temperate land built up from minerals that travel to the surface through the steam.

I don't remember the name, but I know that Jupiter (?) has an ice-moon (frozen shell with a liquid interior) that's been cited as a possible source of life, and the object of a lot of ice-tectonic theories.

[Citizen Joe]

I gotta ask if this is sci-fi or fantasy world.

If its sci-fi, there may not be an atmosphere. If that's so, then water will pass directly from a solid to a gaseous state. That's why that one moon is icy crust and liquid center. Liquid water can't exist without pressure.

In a fantasy world, I'd have to assume it has an atmosphere or there wouldn't be much point (you can't explore it). I think what you're looking for is water surface world. So it can have a solid core but the whole surface is covered with water. Weather would be weird on an all water world, since most weather effects stem from the interaction between water and land.

[DracoDei]

Other than instability in the shape I see no reason you couldn't have a gaseous atmosphere with 1 G at the water's surface and no core (I could just be missing something)... then again, putting the core 100 miles down would make even less difference from the scenario Citizen Joe describes, and it isn't like the PCs are likely to be able to ever go that deep anyway so as far as they know it would BE water all the way down.

[Darkkwalker]

Do it like the Death's Gate Cycle books world of water (chelestra?). Outer ice shell. Inner sun that floats around in an elipse warming the waters and cooling others. water=breathable+neutralize certain magics+not salt water. floating balls of rock and coral that have atmosphere and can sustain plant and animal life. some follow the sun around.
just a suggestion.

As to physics.....I dunno.

[Zeta Kai]

I don't remember the name, but I know that Jupiter (?) has an ice-moon (frozen shell with a liquid interior) that's been cited as a possible source of life, and the object of a lot of ice-tectonic theories.

You're thinking of Europa, which (probably) has vast sub-surface oceans. It's definately not water, through & through, but its close enough.

In order to figure this out (hard science be damned), you need to figure out the amount of water needed to provide 1.0g of gravitational force, & then determine the necessary volume of that amount of water, were it a free-floating body in space. I can only assume that the most logical assumption would be that the surface would be entirely frozen, a la Chelestra (great series, BTW).

You could always call up Margaret Weis & Tracy Hickman. I'll they did the math when they wrote the Death Gate Cycle.

[DracoDei]

The problem is that gravitational force decreases with radius as well as increasing with mass.
I could figure it out, but don't feel like it... the most important point is that the gravity on the surface of a homogeneous sphere is the same as at the same distance from the center if all the mass were concentrated in the center.

[Kyace]

A sphere with radius 35,000,000 meters will have a volume of 1.796 × 10^23 meters cubed. If you fill that volume with liquid water (which weighs 1000 kg per cubic meter (ignoring the great forces within the core)), that should weigh about 1.796 × 10^26 kilograms. Now, if you Newton's law of universal gravitation plugging in the distance from the core of the sphere to the outside and the weight of the sphere, you end up with a ball of water that on the surface will have an acceleration due to gravity 9.78 meters per second square, close to earth's 9.8 m/s^2.

That close enough?

[Arakune]

make it like earth, but witout surface land. problem solved.

[CthulhuM]

I think explaining the temperature of such a planet would be the biggest problem. When the planet first accretes (if you're going to be really true to real world physics) the entire thing would be incredibly hot - as all matter ejected from a supernova/big bang must be. You wouldn't have a ball of water so much as a ball of steam (just as Earth was a ball of magma, rather than rock). Assuming such a ball could stay together without being the size and mass of a gas giant (a big assumption, I think), it would eventually cool and contract into a globe of water... except that there just isn't a very big temperature range at which water can exist.

Above 100 degrees C everything would be vapor (except at the very high pressure core) and below 0 degrees C the planet would turn to ice. Since the planet would be starting out at many thousands of degrees C, the time it would spend as liquid water would be very limited. Since water conducts heat so well, the planet as a whole would rapidly move from the 100+ degree range to the 0- degree range, with the core only slightly hotter (relative to the Earth, anyway) than the surface.

The only way I could think of explaining it would be to have some sort of heat source in the middle of the planet (similar to the world from the Death Gate Cycle described above) that kept the overall temperature within that tiny equilibrium in which the surface was liquid water.

Even then, you'd have some problems - for one, the planet would have incredibly violent weather. Hurricanes would form and then just never stop, without land to break them (think Jupiter's Great Red Spot). For another, I have a suspicion that heat rising from the planet's center wouldn't do so consistently due to random variations in density/temperature/everything, so you'd often have massive bursts of heated water rising apocalyptically to various parts of the surface (much as convection bubbles carry energy from the fusing core of the sun to it's surface).

But, hey,this is fantasy, so you could always just ignore those sorts of things. Making a few permanent hurricanes racing around the planet's surface might be interesting though.

[Pronounceable]

I'd say don't bother with physics of a water planet (or any other kind of planet) unless you're going to write books or publish a setting. Players (probably) won't really care, and trying to get to a certain result (water planet) by RL physics is too much work and time spent better on more important fluff like world history.

Death Gate's Chelestra has been mentioned, which is a good one. As physics heavy as one would hopefully want to get.

[mikoto]

I was thinking that the only surface ice would be at the poles, so no planet covered entirely in ice. It's about the same difference fron the sun as earth is. How much of the world would be covered by that ice. It is a fantasy setting so the way it came to be was that 1.796 × 10^26 kilograms (thank you Kyace) of water was teleported there.