Darby
Epochal Historian
It equally applies to solids, liquids and gasses. If you have a sphere of liquid (or gas - like a star or gas giant planet...Jupiter, Saturn, Neptune) and measure the surface gravity then compress the ball and re-measure the surface gravity you'll find that the change in surface gravity is proportional to the inverse square of the change in the radius of the sphere. Compress it by half and you have 4X surface gravity. Double the radius and you have 1/4th the surface gravity.
Just how strong the field is is dependent on the density of the mass. But the phase state of the matter (solid, liquid or gas) has no effect on the laws of gravitation.
Darby
Epochal Historian
jmpet,
GIve a look see at this Wiki on Surface Gravity. It will help you fill in the Neuron Gap.
Surface Gravity Wiki
GIve a look see at this Wiki on Surface Gravity. It will help you fill in the Neuron Gap.
Surface Gravity Wiki
Darby
Epochal Historian
jmpet,
I looked at the Wiki and at the bottom of the page and it discusses non-spheical objects. I guess that I should revise and extend my remarks.
It is true that you would see changes in the surface gravity if you had a real planet made of gas and compressed it. I was talking about idealized spheres. In the real world you rarely find idealized spheres. The actual shape of the planet or star defines the shape and local intensity of the gravitational field. The distribution of the various chemical elements that make up the body also affect the shape and local intensity of the gravitational field. For instance, Earth is a slightly oblate "sphereoid of rotation" with two tidal bulges located 180 apart. It is squished a bit at the poles due to the angular monentum of its spin and has an equatorial bulge. It also has two gravitational bulges that travel at ~1000 mph (the surface angular velocity of the earth) around the planet slightly behind the position of the moon. They are the tidal bulges caused by the moon's gravitational field.
Real planets have angular momentum - they spin. Angular momentum is conserved when you compress the radius. The surface angular velocity increases just like when skaters spin faster when they pull their arms in closer to their body. The gas planet, in that case, would become more oblate - in would pancake out. That would alter the shape of the gravitational field. Thus if, for example, you originally measured the surface gravity at one of the poles of rotation and measured the surface gravity at the same place after compression it would be less than what you would expect from the simple inverse square proportion because mass would have propogated out along the rotational equator (the bulge at the equator caused by centrifigual forces).
The same thing would occur to a lesser and more complex degree if it was a water ball or a rocky planet.
This is a good lesson to remember as we talk about physics and physical laws. We derive the laws from a study of idealized situations. The laws are generally correct. But when we get out into the real world, say a world where you might be designing an aircraft, you have to carefully consider how to apply the idealized laws to real world situations. The real world is a lot more complex than an idealized laboratory study.
Making too simplistic a statement while discussing the situation on a BBS at worst results in embarassment. At best it calls for a retraction, expanded explanation and a restatement in a more complete form, which is what I'm doing in this post. /ttiforum/images/graemlins/smile.gif Making the same mistakes while designing an aircraft usually results in tragedy: the loss of life and/or property. /ttiforum/images/graemlins/frown.gif
I looked at the Wiki and at the bottom of the page and it discusses non-spheical objects. I guess that I should revise and extend my remarks.
It is true that you would see changes in the surface gravity if you had a real planet made of gas and compressed it. I was talking about idealized spheres. In the real world you rarely find idealized spheres. The actual shape of the planet or star defines the shape and local intensity of the gravitational field. The distribution of the various chemical elements that make up the body also affect the shape and local intensity of the gravitational field. For instance, Earth is a slightly oblate "sphereoid of rotation" with two tidal bulges located 180 apart. It is squished a bit at the poles due to the angular monentum of its spin and has an equatorial bulge. It also has two gravitational bulges that travel at ~1000 mph (the surface angular velocity of the earth) around the planet slightly behind the position of the moon. They are the tidal bulges caused by the moon's gravitational field.
Real planets have angular momentum - they spin. Angular momentum is conserved when you compress the radius. The surface angular velocity increases just like when skaters spin faster when they pull their arms in closer to their body. The gas planet, in that case, would become more oblate - in would pancake out. That would alter the shape of the gravitational field. Thus if, for example, you originally measured the surface gravity at one of the poles of rotation and measured the surface gravity at the same place after compression it would be less than what you would expect from the simple inverse square proportion because mass would have propogated out along the rotational equator (the bulge at the equator caused by centrifigual forces).
The same thing would occur to a lesser and more complex degree if it was a water ball or a rocky planet.
This is a good lesson to remember as we talk about physics and physical laws. We derive the laws from a study of idealized situations. The laws are generally correct. But when we get out into the real world, say a world where you might be designing an aircraft, you have to carefully consider how to apply the idealized laws to real world situations. The real world is a lot more complex than an idealized laboratory study.
Making too simplistic a statement while discussing the situation on a BBS at worst results in embarassment. At best it calls for a retraction, expanded explanation and a restatement in a more complete form, which is what I'm doing in this post. /ttiforum/images/graemlins/smile.gif Making the same mistakes while designing an aircraft usually results in tragedy: the loss of life and/or property. /ttiforum/images/graemlins/frown.gif
>I looked at the Wiki and at the bottom of the page and it discusses non-spheical objects. I guess that I should revise and extend my remarks.<
Actually, I saw that too and glossed right over it, using the Hodge Conjecture as the solution- all objects are either spheres of globs of spheres.
Actually, I saw that too and glossed right over it, using the Hodge Conjecture as the solution- all objects are either spheres of globs of spheres.
>Thus if, for example, you originally measured the surface gravity at one of the poles of rotation and measured the surface gravity at the same place after compression it would be less than what you would expect from the simple inverse square proportion because mass would have propogated out along the rotational equator (the bulge at the equator caused by centrifigual forces).<
One counter-argument or observation I had re: surface gravity is the correlation between that and the dual wave properties of light. Case in point- you can compress a balloon quite a bit before it pops, but if you used far less energy in the form of a pinhead would also cause it to pop.
Why does it take so much more energy to "squeeze pop" a balloon? Because you are displacing your energy as you apply it. So the question becomes- how much energy does it really take to pop a balloon? I see a connection there.
Another comment, although I still cannot properly form the question:
>if your sphere of constant mass started with a radius of 1000 km and was compressed to a black hole and you are floating in space at a distance of 1000 km (where the original surface was located) the strength of the gravitational field is precisely the same at that point as it was before the sphere collapsed.<
Every part of me disagrees with this statement, yet I see it has to be true. The 24,000 mile round Earth was once a ball of hydrogen gas as large as the solar system- so shouldn't the influence of the Earth's gravity affect the solar system?
Is the answer "We do emit a gravity field the strength of a cloud of hydrogen, which is less than a degree above Cosmic Background Radiation, but the sun's gravity overpowers whatever gravity we may emit"?
One counter-argument or observation I had re: surface gravity is the correlation between that and the dual wave properties of light. Case in point- you can compress a balloon quite a bit before it pops, but if you used far less energy in the form of a pinhead would also cause it to pop.
Why does it take so much more energy to "squeeze pop" a balloon? Because you are displacing your energy as you apply it. So the question becomes- how much energy does it really take to pop a balloon? I see a connection there.
Another comment, although I still cannot properly form the question:
>if your sphere of constant mass started with a radius of 1000 km and was compressed to a black hole and you are floating in space at a distance of 1000 km (where the original surface was located) the strength of the gravitational field is precisely the same at that point as it was before the sphere collapsed.<
Every part of me disagrees with this statement, yet I see it has to be true. The 24,000 mile round Earth was once a ball of hydrogen gas as large as the solar system- so shouldn't the influence of the Earth's gravity affect the solar system?
Is the answer "We do emit a gravity field the strength of a cloud of hydrogen, which is less than a degree above Cosmic Background Radiation, but the sun's gravity overpowers whatever gravity we may emit"?
Darby-
What do you make of this:
http://www.expanding-earth.org/
It makes an awful lot of sense to me- it's very anthropic. It's also very profound.
What do you make of this:
http://www.expanding-earth.org/
It makes an awful lot of sense to me- it's very anthropic. It's also very profound.