4 ms·

Most objects in space have some amount of spin to them. That is particles throughout a body, each with a velocity that may be changing, but the change in veloci

Most objects in space have some amount of spin to them. That is particles throughout a body, each with a velocity that may be changing, but the change in velocity with position is smooth, or the object would be ripping itself apart. This means the object has flow. A noticeably misshapen object will not have relatively constant speed and angular direction as a function of latitude and radius. However, objects that gravity rounds out do have this feature (to within an approximation, there is still weather). Thus the term hydrostatic equilibrium. The reason we don't just say "circular" is that this does not include oblate objects, which result from higher spin.

schindlabua 8y ago
It took some additional help from IRC but I think I got it now. Thanks for your answer! In general, while total angular momentum is conserved, rigid bodies tend to rotate in an unstable fashion, because rigid-body forces apply different amounts of torque to different parts of the object. Which I kind of knew about but I didn't connect the dots. Hence no constant speed and angular direction, and no hydrostatic equilibrium. That was the missing link for me!
- pas 8y ago
  Now I think I don't understand it! :o) So, flow velocity is simply the fluid mechanical velocity vector field/mapping. And it has to be constant, otherwise the object would not be in equilibrium, but it'd be still flowing (as in it would have parts that are going somewhere). Now I think this definition you have found is not directly applicable to rotating celestial bodies, as the point velocity is a vector, and it constantly changes due to the rotation. So probably a higher order derivative is zero, and that's the condition that we should use. Or of course we can transform to a non rotating frame. But what the parent poster said confuses me: "a velocity that may be changing, but the change in velocity with position is smooth, or the object would be ripping itself apart. This means the object has flow." You can have smooth and constant rotation but with many axes (tumbling), so I don't really see how this gets us to roundisness. As I understand the concept, the point is that "the object doesn't have parts that want to fall toward its center of gravity, but can't because rigid forces", because it's big enough that gravity creates enough pressure and heat that everything becomes plastic over thousands of years, and thus flows. (But this doesn't make much sense, because cold enough rock is pretty stable - as far as I know - so the material will only allow gravity to overcome it if it undergoes enough crystal structure faults [due to radioactive decay or exogenous damage, such as micrometeorites] - so the flow rate is constant, zero, even if there are stresses and forces that would increase the flow.)
  - grigjd3 8y ago
    You have a few misconceptions and you are waaaaay overthinking this. The primary measure for this equilibrium is the time derivative of the mass-density-velocity, or momentum-density if you like. Now imagine a cube spinning on a primary axis. Since a cube is not constant radius, there are times where matter exists at a given point and other times where the matter does not exist at that point. Clearly, the time derivative of the momentum-density is not zero. This is not the case for a sphere as any point that has mass under the spinning sphere will have mass at all later points in time. The reason we don't just say sphere, though, is this kind of equilibrium accounts for oblate objects as well, and many planets are oblate.

schindlabua 8y ago

It took some additional help from IRC but I think I got it now. Thanks for your answer! In general, while total angular momentum is conserved, rigid bodies tend to rotate in an unstable fashion, because rigid-body forces apply different amounts of torque to different parts of the object. Which I kind of knew about but I didn't connect the dots. Hence no constant speed and angular direction, and no hydrostatic equilibrium. That was the missing link for me!

pas 8y ago
Now I think I don't understand it! :o) So, flow velocity is simply the fluid mechanical velocity vector field/mapping. And it has to be constant, otherwise the object would not be in equilibrium, but it'd be still flowing (as in it would have parts that are going somewhere). Now I think this definition you have found is not directly applicable to rotating celestial bodies, as the point velocity is a vector, and it constantly changes due to the rotation. So probably a higher order derivative is zero, and that's the condition that we should use. Or of course we can transform to a non rotating frame. But what the parent poster said confuses me: "a velocity that may be changing, but the change in velocity with position is smooth, or the object would be ripping itself apart. This means the object has flow." You can have smooth and constant rotation but with many axes (tumbling), so I don't really see how this gets us to roundisness. As I understand the concept, the point is that "the object doesn't have parts that want to fall toward its center of gravity, but can't because rigid forces", because it's big enough that gravity creates enough pressure and heat that everything becomes plastic over thousands of years, and thus flows. (But this doesn't make much sense, because cold enough rock is pretty stable - as far as I know - so the material will only allow gravity to overcome it if it undergoes enough crystal structure faults [due to radioactive decay or exogenous damage, such as micrometeorites] - so the flow rate is constant, zero, even if there are stresses and forces that would increase the flow.)
- grigjd3 8y ago
  You have a few misconceptions and you are waaaaay overthinking this. The primary measure for this equilibrium is the time derivative of the mass-density-velocity, or momentum-density if you like. Now imagine a cube spinning on a primary axis. Since a cube is not constant radius, there are times where matter exists at a given point and other times where the matter does not exist at that point. Clearly, the time derivative of the momentum-density is not zero. This is not the case for a sphere as any point that has mass under the spinning sphere will have mass at all later points in time. The reason we don't just say sphere, though, is this kind of equilibrium accounts for oblate objects as well, and many planets are oblate.