Gravity and Sinking Objects in a Galaxy-Sized Water Planet

[yourboycal]

Say floating around in space there was a galaxy sized planet of nothing but water. Assuming this was enough mass to have gravity kick in, if we placed an object that is not buoyant in the planet's water, at what point would it stop sinking? Would it stop at the centre? Would it go through the planet completely?"

 

[Drakkith]

Absurd masses of your example aside, I think it would stop at the center. =)

Edit: Just FYI: That much mass all together would definitely collapse into a black hole. Also, gravity "kicks in" always, no matter what the mass of the object. Everything has gravity no matter the size.

 

[Nik_2213]

Uh, you know how big even a dwarf galaxy is ??
http://en.wikipedia.org/wiki/Dwarf_galaxy
"A dwarf galaxy is a small galaxy composed of up to several billion stars, a small number compared to our own Milky Way's 200-400 billion stars."

Assuming even slight initial rotation and turbulence, my best guess is that the centre of such a blob would promptly collapse to a massive black hole and accretion toroid. Smaller holes would form in a cloud around that, with many merging explosively. Massive stars would form further out, and much of the remaining material would be blown into interstellar space by vaporisation, ionisation then the blast of the stars' & holes' solar winds...

Uh, if you want it to stay liquid water all the way through, rather than supercritical or worse, you must limit your 'goldfish bowl' to a size that the self-gravity will not cause pressure and temperature to exceed those bounds. Don't forget to allow for spin, if required.

And, d'uh, IIRC, the apparent gravity at the centre will be zero...

 

[yourboycal]

Lets imagine this "giant " water body in space the size of jupitor ...

lets pretend that the mass is not enough to collapse and cause a black hole


just a giant body of water shaped like a planet its stable ...

now if you put an object at the top of the water planet would it sink all the way through or stop in middle?


we know the Earth if you were to dig a hole from the top all the way to bottoem and you dropped something it would even out in the middle ...there would be no force but ther still would be pressure .


but the giant body of water does not have a core ... if the mass is not concentraed in the middle without a core ...


would the object not fall through?

 

[Nik_2213]

Compressibility of water...
http://en.wikipedia.org/wiki/Properties_of_water#Compressibility
Note the phase diagram and the critical point...
http://en.wikipedia.org/wiki/Critical_point_(thermodynamics )
quote: this is the point at which the phase boundary between liquid and gas terminates. In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa (3200 PSIA or 218 atm)[1].
/

Sadly, my math is no longer good enough to work out how big a blob you can have before the heating due to compression due to self-gravity pushes the core beyond water's critical point...

 

[IsometricPion]

now if you put an object at the top of the water planet would it sink all the way through or stop in middle?

Whether an object sinks or floats is determined by the forces acting on it. Ideally the only forces acting on the object are gravity and the force due to the absence of water (or any fluid) in the space occupied by the object. An object that sinks must weigh more than the volume of water it displaces. Realistically, the rate at which an object sinks is determined by the viscosity of the water (the water will slow the object, so it will lose energy and eventually come to rest at the center of the planet). If one assumes that the water exerts no other forces on the object besides that due to buoyancy, then conservation of energy requires that an object released at the surface would oscillate between that point and the point on the opposite side of the planet forever (buoyancy only increases the period of the oscillation/decreases the average velocity).

... if the mass is not concentraed in the middle without a core ...


would the object not fall through?

Since the acceleration of the object (sinking) is due to the gravity of the water, the vector will be of the same magnitude and point in opposite directions on opposite sides of the center (assuming nothing acting on the object except the buoyancy force). No matter where on the planet the object is, the force due to gravity will be in the direction of the center of the planet.

Sadly, my math is no longer good enough to work out how big a blob you can have before the heating due to compression due to self-gravity pushes the core beyond water's critical point...

I did some calculations and found that for a (non-rotating) sphere of water in isothermal equilibrium near 273.16 K, the radius must be around 1700 Km or so before the water undergoes a phase transition to ice VI (P~500 MPa) in the center. (I assumed it would be liquid from surface to center. In fact, the it would require the equivalent of about 1.2 meters of water (~611.7 Pa) to ensure the surface was liquid.)

 

[Synetos]

If the water blob was stable then the object that would be tossed in (assuming that its density is larger then that of water) would sink to the center and stay there, as if it sank further, you would be able to turn the planet around and envision it as sinking upwards, which ofc is impossible.

It probably would oscillate a bit, but it would eventually stop at the center.