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== PREM Chart for acceleration is incorrect due to Newton ==
My subject here is gravity wells and their composition.
Gravity is a fascinating subject for me. The fact that we don’t quite understand one of the 4 fundamental forces is tantalizing. Some of this is due to antiquated assumptions which have garnered attention here. I think the best place to look for and understand gravity is right here on Earth. We have gravity AND the internet.
It should be a great clue to the error in thinking here that we can measure a higher acceleration at the poles where there is less physical matter underfoot than at the top of an equatorial mountain where there's considerably more mass underfoot.▼
• ''Gravity can be explained by Newton’s law of universal gravitation, which states that the force of gravity is proportional to the product of the masses and inversely proportional to the square of the distance between them [/r²]. Gravity can also be understood by Einstein’s theory of general relativity, which states that gravity is a result of curvature in space-time caused by the mass of an object -www.uu.edu.''
It adds to the current state of confusion to primarily explain gravity with a 300-year-old formula that has nothing to do with time and which was completely supplanted by Einstein’s theory of general relativity and his explanation of 4-dimensional space-time. GR isn’t ‘another way’ that gravity can be understood, it’s THE way. Newtonian gravitational models can get you to Mars, but they don’t work when explaining gravity wells and their composition.
''The gravity depends only on the mass inside the sphere of radius r''▼
Here’s some basic scientific observations on gravity taken at known locations and altitudes on Earth.
It's a Newtonian notion of mass attracting mass that has you arriving at an acceleration of zero at the core. That's incorrect.▼
''• Sea-level gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles.''
''• Gravity on the Earth's surface varies by around 0.7%, from 9.7639 m/s2 on the Nevado Huascarán mountain in Peru to 9.8337 m/s2 at the surface of the Arctic Ocean'''
The oblate flattening of the earth results in an equatorial bulge that sees the equator on average 21 kilometers further away from the center of this gravity well than the poles. So, there is more mass underfoot at the equator, but less acceleration.
▲It should be a great clue to the
''from phys.org "A trio of researchers in Denmark has calculated the relative ages of the surface of the Earth versus its core and has found that the core is 2.5 years younger than the crust. [it's likely considerably younger than even this] During one of his famous lectures at Caltech in the 1960's, Richard Feynman remarked that due to time dilation, the Earth's core is actually younger than its crust. General relativity suggests that really big objects, like planets and stars, actually warp the fabric of spacetime, which results in a gravitational pull capable of slowing down time. Thus, an object closer to Earth's center would feel a stronger pull—a clock set near the core would run slower than one placed at the surface, which means that the material that makes up the core is actually younger than the material that makes up the crust. In this new effort, the research trio ran the math to discover the actual number involved. They found that over the course of our planet's 4.5-billion-year history, the pull of gravity causes the core to be approximately 2.5 years younger than the crust—ignoring geological processes, of course." -phys.org▼
You cannot develop a theory of what gravitational acceleration looks like at the center of a gravity well without approaching it from the standpoint of time.
Time cannot be slower at the core and simultaneously be at zero acceleration. That's not how relativity works.▼
''• Researchers have built an atomic clock that is more precise and accurate than any previous clock. For the first time, the clock can detect the effects of gravity predicted by the theory of general relativity at the microscopic scale. Hence, as we envision clocks like these being used around the country or world, their relative performance would be, for the first time, limited by Earth's gravitational effects.-nist.gov''
As a thought experiment, consider the Earth, as it is with its stratified layers - a dense core with progressively less dense layers on top until you get to the crust and out into the atmosphere. Now take the moon and shrink it down to the size of a softball. Retain the mass of the moon, but now it’s close to a neutron star in density. Hold this ultra-dense object directly over the surface of the Earth and let it fall. The deepest portion of Earth’s core and the center of the softball-sized moon will quickly displace the less dense materials between them and merge, with the little moon traveling the most distance and the core moving slightly for the merging. There will be some oscillation, but the dropped "softball moon" will quickly occupy the center of the center, driving the gravity well ever deeper with its added mass. And due to its ultra-density, it will reside at the point of greatest acceleration - the center.▼
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-Thanks, Joe <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2605:59C8:41D:2010:707E:6379:1269:FB26|2605:59C8:41D:2010:707E:6379:1269:FB26]] ([[User talk:2605:59C8:41D:2010:707E:6379:1269:FB26#top|talk]]) 16:22, 25 August 2024 (UTC)</small> <!--Autosigned by SineBot-->▼
▲Time cannot be slower at the core and simultaneously be at zero acceleration. That's not how relativity works. Acceleration slows time. They are interlinked.
▲In this PREM chart there is no consideration for relative time, and it therefore falls victim to antiquated thinking. It's a Newtonian notion of mass attracting mass that has
Acceleration would continue to increase the closer an observer got to the center. This is because the entire mass present is contributing to the depth of the well (in 4 dimensional spacetime) a well which is deepest at its center.
Acceleration (gravity) depends on the total mass in the gravity well and the radial distance from the center of the gravity well. Acceleration will increase the closer an observer gets to the center. This would be detectable by atomic clocks at differing radial distances.
All the mass present is driving the depth of the well, not just the mass under the point of measurement.
''• 9.7639 m/s2 on the Nevado Huascarán mountain in Peru (Larger radius, more mass)''
''• 9.8337 m/s2 at the surface of the Arctic Ocean (smaller radius, less mass)''
It’s not about weightlessness, it’s about time, what do identical clocks say at increasing depths? They will say that time is predictably slowing all the way to the core and acceleration is therfore increasing.
As a thought experiment, consider the Earth, as it is with its stratified layers - a dense core with progressively less dense layers on top until you get to the crust and out into the stratified atmosphere. Now take the moon and shrink it down to the size of a softball. Retain the mass of the moon, but now it’s close to a neutron star in density. Hit pause and hold this ultra-dense object directly over the surface of the Earth
Being motionles, the Moon’s curved spacetime line will be straight to the center of the core.
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So, for essentially the same volume, Earth’s surface acceleration is now over 10 m/s² due to being in a deeper gravity well without gaining any significant volume.
An acceleration tapering to zero at the core is a physics recipe for a hollow Earth rather than the home for the densest matter in the well.
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