Talk:Gravity of Earth

Propose to remove 2 too-long tables

I propose that two too-long tables in this article be removed because they obstruct the reading of the article and don't add much to the discussion. The table for "Comparative gravities in various cities around the world" was apparently generated by using a widget from Wolfram [1]. In place of this table, we could mention the gravity at a few places (fewer than in the table) and then just link that widget at the end of the essay rather than give the long table. The table for "Comparative gravities of the Earth, Sun, Moon, and planets" is poorly sourced and possibly original research. Thoughts? Isambard Kingdom (talk) 14:03, 3 March 2017 (UTC)

 Done Isambard Kingdom (talk) 13:50, 9 March 2017 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified one external link on Gravity of Earth. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20080820093812/http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm to http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 19:58, 22 October 2017 (UTC)

Gravity and latitude

Quote, "The same two factors influence the direction of the effective gravity (as determined by a plumb line or as the perpendicular to the surface of water in a container). Anywhere on Earth away from the Equator or poles, effective gravity points not exactly toward the centre of the Earth, but rather perpendicular to the surface of the geoid, which, due to the flattened shape of the Earth, is somewhat toward the opposite pole. About half of the deflection is due to centrifugal force, and half because the extra mass around the Equator causes a change in the direction of the true gravitational force relative to what it would be on a spherical Earth." Does gravity involve ellipsoidal coordinates? The article Latitude#Ellipsoidal coordinates suggests this. If this is the case, then falling objects maybe adhere to a hyperbolic path, not a straight one. Also please review my question on Stack Exchange, as it deals with this exact same question. ➧datumizer  ☎  22:08, 23 August 2018 (UTC)

"Involve ellipsoidal coordinates" is a somewhat nebulous phrase. The gravity can be expressed in terms of these coordinates, but that doesn't mean that the field lines lie on a coordinate surface (unless the body is non-rotating). Also, note well, that a falling body will, in addition, experience a coriolis force, and so it won't, in general, stay in a single meridional plane.

By the way, "Talk pages are for discussing the article, not for general conversation about the article's subject" (see "talk page guidlines"). So your question doesn't really belong here. cffk (talk) 03:30, 24 August 2018 (UTC)

Please don't automatically assume I'm not asking questions with the intention of editing a Wikipedia article. ➧datumizer  ☎  22:46, 24 August 2018 (UTC)

Depth

If, as suggested in the text, the density of the Earth decreases linearly with increasing radius from a density ρ₀ at the center to ρ₁ at the surface, then the acceleration due to gravity at depth d below the surface (i.e., at $r=R-d$ ) is the following integral:

$g(r)=-{\frac {G\int _{0}^{r}4\pi r^{2}\rho _{r}dr}{r^{2}}}$

where $\rho _{r}=\rho _{0}-\left(\rho _{0}-\rho _{1}\right){\frac {r}{R}}$

Noting that ρ_r is also a function of r, the substitution must be made before the integration, and hence this integral becomes:

$g(r)=-{\frac {4\pi G\int _{0}^{r}r^{2}\left(\rho _{0}-\left(\rho _{0}-\rho _{1}\right){\frac {r}{R}}\right)dr}{r^{2}}}$

$g(r)=-{\frac {4\pi G\int _{0}^{r}r^{2}\rho _{0}-\left(r^{2}\rho _{0}{\frac {r}{R}}\right)+\left(r^{2}\rho _{1}{\frac {r}{R}}\right)dr}{r^{2}}}$

$g(r)=-{\frac {4\pi G\int _{0}^{r}r^{2}\rho _{0}dr-4\pi G\int _{0}^{r}\left(\rho _{0}{\frac {r^{3}}{R}}\right)dr+4\pi G\int _{0}^{r}\left(\rho _{1}{\frac {r^{3}}{R}}\right)dr}{r^{2}}}$

$g(r)=-{\frac {4\pi G[{\frac {r^{3}}{3}}\rho _{0}]-4\pi G[\rho _{0}{\frac {r^{4}}{4R}}]+4\pi G[\rho _{1}{\frac {r^{4}}{4R}}]}{r^{2}}}$

$g(r)=-{\frac {4\pi }{3}}G\rho _{0}r-\pi G\left(\rho _{0}-\rho _{1}\right){\frac {r^{2}}{R}}$

This error was fixed by myself and RockMagnetist in May 2013, I don't know when or why it has reverted. See: https://en.wiki.x.io/w/index.php?title=Gravity_of_Earth&oldid=553887481 Please fix it again. George963 au (talk) 11:52, 16 February 2019 (UTC)

@George963 au: It took me a while to notice this post. I have fixed it. Thanks for notifying us, but it would be better if you simply fixed it yourself next time. RockMagnetist(talk) 22:19, 17 March 2019 (UTC)

@RockMagnetist: Thanks, RM. I would have fixed it, but it seems my credibility is not high enough. The last time I tried, someone promptly reversed it. (I'm not sure, but I think it might have been you!) George963 au (talk) 12:40, 6 April 2019 (UTC)

As far as I can tell, our only previous interaction was this discussion on the same subject. I don't find any edits of the article by you in the history. RockMagnetist(talk) 17:18, 6 April 2019 (UTC)

Hi, there is an error in g(r). The linear density is correct, then if we substitute it in the first equation of g(r), and we develop each term with simple math, we see there is an error: g(r) is missing the 4/3 in the second term. Incredibly in Google books, this paragraph is exactly the same in the book “Artificial Gravity: To Maintain Your Foot in the Space …” (2022) by Fouad Sabry. I wonder if it is a first edition and copied directly from Wikipedia or the wiki is copied from earlier editions from that book. IGomezLeal (talk) 08:56, 3 August 2023 (UTC)

It is better to leave the integral of g(r) to avoid this confusion and as this paragraph says the density has to be substituted inside the integral. IGomezLeal (talk) 09:02, 3 August 2023 (UTC)

I will check also the result of the integral, the order of the powers should increase. The first term on the right should be proportional to r^3 and the second r^4. IGomezLeal (talk) 09:21, 3 August 2023 (UTC)

Ok, inside the gravity integral you have forgotten the r^2 in the denominator from the gravity differential. It cancels the r^2 from the sphere volume differential, and then the result of the integral you wrote is almost correct, it is missing a 2 in the second term on the right, since the integral of r is (r^2)/2 and 4/2=2. Do you agree? IGomezLeal (talk) 09:48, 3 August 2023 (UTC)

No, I don't agree. I've put in some of the intermediate calculations above, for your reference. George963 au (talk) 14:02, 9 October 2023 (UTC)

History of the Earth's gravity

What I'm missing on the page is a section about the history and development of the gravity of Earth. What was the Earth's gravity like before the supposed collision with Theia/Orpheus? What was it like in the Mesozoic Age (the "Dinosaur Age")? When and how did it change? Someone please make such a section. --212.186.7.232 (talk) 11:14, 17 March 2019 (UTC)

If you're talking about the value of "g" the acceleration due to gravity at the Earth's surface, then assuming no significant changes in either the radius or overall structure of the Earth, then you would expect no significant change of g with time except in the very early history of the Earth. If you're interested in gravity anomalies in the past, the small scale variations in the field will have been very different then. Mikenorton (talk) 17:16, 17 March 2019 (UTC)

You say "except in the very early history of Earth". This is what I mean by "before the supposed collision with Theia/Orpheus". The collision that allegedly created the Moon. In the Mesozoic/Antediluvian Era, the Earth's surface gravity might have been different too (weaker) since dinosaurs, other animals and plants were so big. 212.186.7.232 (talk) 09:53, 18 March 2019 (UTC)

This post is a very useful look at evidence for changes in gravity with time - in summary there is no evidence that supports lower gravity during the Mesozoic and lost of evidence that supports gravity similar to the present. Mikenorton (talk) 10:52, 18 March 2019 (UTC)

The size of dinosaurs, etc., is no guide to changes in the Earth's gravity; for at least the suggested timing is backwards. The collision with Theia was very early in the evolution of the Earth, over 4 billion years ago; the Mesozoic Era was a (mere) 250-66 million years ago. George963 au (talk) 01:27, 4 November 2023 (UTC)

Yes i agree we need more knowledge on this topic 2601:300:4100:75F0:E8F3:8332:B5B1:EB5C (talk) 02:29, 23 March 2023 (UTC)

Relative gravity backwards?

I have re-read the section related to gravitational anomalies by geography and believe it is backwards. I'm not sure if the mgals are also backwards. It shows red being positive, but red on the map seems to correspond with lower gravity areas.

The lowest gravity falls on the mountain range in Peru on the west coast of South America. That whole range is lit up in red.

The oceans are overwhelmingly blue and should be some of the highest gravity areas. Peter Bailey (talk) 06:16, 27 April 2019 (UTC)

I was going to start a topic on this as well. If you look at the animated globe, all the mountains are in red but the supporting text says red is higher gravity.

And adding to the confusion, your post ends with saying the oceans should be some of the highest gravity areas which other then appearing to be wrong contradicts the point. The WSmart (talk) 10:49, 18 March 2022 (UTC)

Maybe red means higher gravity at the geoid? —Tamfang (talk) 02:39, 29 March 2023 (UTC)

If we're talking about satellite gravity (like the GRACE results) then what affects the satellite is not the same as the value of gravity that would be measured at the Earth's surface directly below the satellite at the same time. The "Altitude" section (third paragraph) attempts to cover this apparent contradiction. In summary a satellite is affected by high elevation areas in the opposite sense to how a ground observer would be. Mikenorton (talk) 16:03, 29 March 2023 (UTC)

Propose to clarify Free Air Correction

"The first correction to be applied to the model is the free air correction (FAC) that accounts for heights above sea level. Near the surface of the Earth (sea level), gravity decreases with height such that linear extrapolation would give zero gravity at a height of one half of the Earth's radius - (9.8 m·s−2 per 3,200 km.[19])"

The reference is not a reference, it says "The rate of decrease is calculated by differentiating g(r) with respect to r and evaluating at r=rEarth."

This was moved here on 27th May 2007 from the standard gravity page, which was moved their from the g-force page 6 March 2007.

We know the earth's gravity acts on Geostationary satellites and the moon, far beyond many times the Earth's radius (and this made someone smart I trust think science is not all it's meant to be). This clarification then needs to give context to where it applies and where it doesn't, or remove it if it's not something the Free Air Correction does actually predict.

I don't like that the reference is just an explanation! I suspect that the approximates used for calculations work very well within the 10km high differential of our crust, but are not meant to be applied over thousands of kilometres. So I want to back that up or find out more context. Any ideas? Greg (talk) 07:44, 4 October 2020 (UTC)

The free-air correction is intended to remove the effects of topography on observations above the reference ellipsoid, which equates with sea level. The resulting free-air gravity anomaly is just one step to reaching the ultimate aim of showing the gravity field as it would be measured if the whole earth was at sea level - the other main correction is the bouguer correction, which accounts for the fact that the material between the point of observation and sea level is rock, not air. The "reference" that you mentioned is actually a "note" to help explain, although I tend to agree that it's not that helpful. Mikenorton (talk) 15:19, 4 October 2020 (UTC)

https://academic.oup.com/gji/article/154/1/35/604237 http://geopixel.co.uk/g4g_lab1.html

So does the "such that" in the ongoing sentence help in any way in understanding? ("gravity decreases with height such that linear extrapolation would give zero gravity at a height of one half of the Earth's radius")

The intent of the sentence's clarification seems to be: "gravity decreases with height. The FAC does not work and is not intended for higher altitudes, a linear extrapolation would give zero gravity at a height of one half of the Earth's radius". Greg (talk) 03:38, 23 October 2020 (UTC)

Equivalence of inertial and gravitational mass

Shouldn't the section "Estimating g from the law of universal gravitation" include a remark that the inertial mass (the term that arises in Newton's 2nd law of motion) is assumed equal to the gravitational mass (the term that arises in the inverse square law). This does strike me as an extremely serious omission Wikipedia ought not be guilty of. Соловей поет (talk) 15:30, 11 August 2021 (UTC)

How long is gravity range

How long is gravity range 2409:4042:785:F569:0:0:29D0:10A1 (talk) 15:57, 21 May 2022 (UTC)

• The acceleration experienced due to Earth's gravity is inversely proportional to the square of the distance from the center of the Earth. The Earth's gravitational field does not abruptly end anywhere. Rather, it gradually fades into nothingness. The "range" is infinite, although if one is far enough from Earth then Earth's gravity will be so small as to be unnoticeable. Crossover1370 (talk | contribs) 17:17, 25 May 2022 (UTC)

Wiki Education assignment: 4A Wikipedia Assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 12 February 2024 and 14 June 2024. Further details are available on the course page. Student editor(s): Maaatttthhheeewww (article contribs). Peer reviewers: WikiIsaacPedia.

— Assignment last updated by Ahlluhn (talk) 00:58, 31 May 2024 (UTC)

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 my attention. We're lucky because the best place to look for and understand gravity is right here on Earth. We have gravity AND the internet.

• 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. 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.

Here’s some basic scientific observations on gravity taken at known locations and altitudes on Earth.

• 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 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. There is more mass underfoot at the equator, but less acceleration.

A contemporary model of what gravitational acceleration looks like at the center of a gravity well should consider the relative time as time dilation and acceleration are interconnected whereas Gravity can sometimes be confused with mass attracting mass such as in orbits. To consider a gravity well's composition we must consider time. It's the 4th dimension, time that is getting stretched and slowed by the total mass present.

We can use identical atomic clocks to map our gravity well's acceleration curve from the surface off into deep space. We'll have to theorize when solving for acceleration from the surface down. We can’t send a clock to the core, but we have approached this topic in scientific literature.

• "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

Time cannot be slower at the core and simultaneously be at zero acceleration. Einstein showed us that increasing time dilation and increasing acceleration are linked. That means that if the core has a slower time than the surface it also must have a faster acceleration.

In this PREM chart there is no consideration for relative time. It's a Newtonian notion of mass attracting mass that has the researchers arriving at an acceleration of zero at the core. This makes the PREM chart for acceleration incorrect.

Here is the principal error

• gravity depends only on the mass inside the sphere of radius r -wiki.com

The total depth of the well depends on the total mass in the gravity well. The acceleration at a given point is a function of all the mass comprising the well and the radial distance from the center of the gravity well decreasing in strength as a function of [/r²]. All the mass is driving the depth of the well, not just the mass under your radial. It's not about weightlessness, it's about the stretching and slowing of the 4th dimension, 'time' by the presence of a large mass. For a stationary object on earth's surface, your warped space time line is a radial extending from the center of the core, through you and in a straight line out into deep space. That stetched radial is the time dimension of 4d space-time

• 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)

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 just as it does above the surface.

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 motionless, the Moon’s curved spacetime line will be a straight, stretched radial right to the center of the core.

Now start the simulation and let the moon go. 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 as the gravity well attains hydrostatic equilibrium again, but the dropped "softball moon" will quickly occupy the core, driving the Earth’s well ever deeper with its added mass. And due to its ultra-density, it will reside at the point of greatest acceleration - the center.

Earth’s surface acceleration is now over 10 m/s² due to being in a deeper gravity well without gaining any significant volume and time at all points got a little bit slower.

An acceleration tapering to zero at the core is a physics recipe for a hollow Earth rather than the home for the densest matter.

Thanks, Joe 2605:59C8:41D:2010:9898:C682:F5C5:EBAE (talk) 15:30, 29 August 2024 (UTC)

I'm pretty sure that Newtonian gravity gives you a very good approximation of the gravity on the Earth. Specifically, where do you think that it fails? cffk (talk) 00:57, 24 October 2024 (UTC)

according to the chart, immediately under the surface 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 18:54, 25 October 2024 (UTC)

or I should say, between the surface and the core. That part of the chart is antiquated theory. The values for the surface and into space have been verified with measurements 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 18:59, 25 October 2024 (UTC)

What's the evidence that the values of gravity below the surface are wrong? cffk (talk) 19:08, 25 October 2024 (UTC)

It's literally in the article, cited. 207.225.209.2 (talk) 19:23, 25 October 2024 (UTC)

Science daily - JILA physicists have measured Albert Einstein's theory of general relativity, or more specifically, the effect called time dilation, at the smallest scale ever, showing that two tiny atomic clocks, separated by just a millimeter or the width of a sharp pencil tip, tick at different rates'

Do you think that the bottom clock would ever tick Faster than the top as it descended to the center of the core?

General relativity says no

The PREM chart says yes, and it's wrong 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 19:19, 25 October 2024 (UTC)

Yes, general relativity is correct; but do the differences between it and Newton's theory for gravity on the Earth ever exceed 1 part in 10^6, say? By the way, you may be ignoring the effect of the earth's rotation. That is why the acceleration due to gravity is smaller at the equator than at the poles. cffk (talk) 19:36, 25 October 2024 (UTC)

Yes, newton's theory for gravity ceases to be accurate once you get under the surface of a gravity well. It considers only the radial mass remaining and then they use that to calculate an acceleration

GR accurately continues to show time slowing all the way to the core. Which would have a corresponding increase in acceleration all the way to the core

So yes, Newton falls apart under the surface. It shows an acceleration of zero, that's where they two theories disagree.

I put my money on general relativity 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 19:46, 25 October 2024 (UTC)

No, Newton doesn't say that the acceleration is zero below the surface of the earth. (But maybe I'm misunderstanding you?) cffk (talk) 19:55, 25 October 2024 (UTC)

And can I ask a silly question? If GR says that the acceleration is increasing all the way to the core, in which direction is acceleration at the center of the Earth. Symmetry (and Newton) says that the acceleration is zero at the center of the earth. cffk (talk) cffk (talk) 20:03, 25 October 2024 (UTC)

Well, the PREM chart on this page says it's zero. I assume the researchers used Newton because they sure didn't use Einstein's general relativity to get to zero. 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 20:02, 25 October 2024 (UTC)

The PREM chart only gives zero at the center of the earth. And, of course, it has to be zero there by symmetry. cffk (talk) 20:05, 25 October 2024 (UTC)

The chart gives a decreasing acceleration as you get closer to the center with the center being zero. this is not accurate

each point of decent made toward the center, the slower the clock is going tot tick. Acceleration will commensurately increase. that's General Relativity.

So it's not a minor error.

And i dont understand what you mean by there having to be zero acceleration for symmetry? Accelerations is highest for all radials at the center of the gravity well. I dont know how to be more clear. SJRarey (talk) 20:12, 25 October 2024 (UTC)

Acceleration is a vector, so it has to be zero in the center of a symmetric object. If you disagree, please tell me in which direction the acceleration points. cffk (talk) 20:17, 25 October 2024 (UTC)

from all radials acceleration points straight down to the center and it increases until it gets there because time is slowing.

Light would blue shift all the way to the core

The PREM chart would have it red shifting once it got under the surface and that is incorrect.

Because the PREM researchers are using acceleration as a measure they have to consider the rules of GR,

Those rules say that time and acceleration are linked. The slower the time the faster the acceleration.

In a gravity well, the highest acceleration and the slowest time will be at the center. 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 20:34, 25 October 2024 (UTC)

Ahh, so you're saying that the acceleration is discontinuous at the center (the magnitude may be continuous, but the direction flips). I'm no expert on general relativity, but I promise you this is not what it predicts. As long as the density of the earth varies smoothly at the center, there can be no discontinuities there. To focus the discussion on more concrete matters, let's focus on the results for gravity above the surface of the earth (where it's easy to measure). Does general relativity ever predict a result for the acceleration which differs from the Newtonian result by more that 1/10^6? cffk (talk) 21:06, 25 October 2024 (UTC)

I didn't say there was a discontinuity at the center

I said the prem chart is incorrect once you get under the surface

Time slows and Acceleration increases considerably from the surface the closer you get to the center. So the acceleration line on the chart should be increasing the whole way down.

for the sake of the thread, id like to keep it focused on that issue. Others will come about once we rectify this error in thinking about the interior earth

I highly recommend jumping into general relativity. It's quite approachable from the thought experiments he's given us. Einstein had a profound canvas to envision what he did. Incredible man. 2605:59C8:41D:2010:5552:DCBB:4A3F:7014 (talk) 21:17, 25 October 2024 (UTC)

If the magnitude of the acceleration is finite at the center of the earth, then the acceleration itself is discontinuous. You said so yourself: "from all radials acceleration points straight down to the center and it increases until it gets there". (The "down" direction flips its sign as you pass through the center.)

To stick with the acceleration inside a body, why don't we consider the simple case of a non-rotating sphere of uniform density far from any other masses; and let's say that the mass and radius of the sphere match the values for the earth. In this case, Newton says that the acceleration decreases linearly from the surface of the sphere to the center. Can you tell me the prediction of general relativity for this case? cffk (talk) 21:52, 25 October 2024 (UTC)

Yes, that's the green line on the chart.

In GR, Time would slow down and acceleration would increase (greater than that measured at the surface of the earth) the deeper you went until you reached the center where acceleration would be highest and time slowest.

Orbital Mechanics do not work inside a gravity well SJRarey (talk) 22:28, 25 October 2024 (UTC)

And what's the magnitude of the acceleration at the surface and at the center? Newton has 9.8 and 0 m/s^2. cffk (talk) 23:18, 25 October 2024 (UTC)

Greater than 9.8.

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 -phys.org,

That's an important citation. He's not speculating. General relativity has been proven right at every opportunity. 2605:59C8:41D:2010:CA9A:D355:8F8C:7AD0 (talk) 23:26, 25 October 2024 (UTC)

Surface acceleration and time are well studied with both falling object in a vacuum and atomic clocks. It really depends on where you are, but on average 9.8m/s2 2605:59C8:41D:2010:CA9A:D355:8F8C:7AD0 (talk) 23:29, 25 October 2024 (UTC)

So we only know that, according to GR, the acceleration at the center is greater than 9.8 m/s^2? Surely it's possible to come up with a tighter bound on the value.

Anyway, we're just going round in circles here. I'm convinced that the acceleration must be zero at the center of a symmetric object while you assert that it's finite, and thus discontinuous. And of course, we can't measure the value at the center of the earth.

So what about the values of g exterior to the surface of a rotating ellipsoid? In the Newtonian limit, this is given by "normal gravity" and this gives a pretty good approximation to the earth's gravity. This is corrected by gravity models such as EGM2008 which is also based on Newtonian physics. Are there any instances where these models are badly off because of GR effects?

cffk (talk) 01:14, 26 October 2024 (UTC)

I'm convinced that the acceleration must be zero at the center of a symmetric object

This might be where you're getting hung up. This is an incorrect assumption.

Do you disagree with freyman that the slower clock would be creating a greater pull at the center? You can't accept his science and an acceleration of tapering to zero. It's wrong headed.

Earth is a rotating oblate spheroid in hydrostatic equilibrium.

it is stratified in density with its densest matter comprising the core.

At each progression out from the core you get less dense matter. They can map this very accurately with p and s waves during earthquakes.

This continues until you get to the exosphere where the lightest element, hydrogen, is escaping off into space.

how would you explain this hierarchical stratification of density with an acceleration tapering from 9.8m/s2 at the surface to zero at the core?

As far as suggesting an acceleration number for GR,i would point you to the paper i referenced. They used a time dilation value to determine that the core's difference in age with the surface was measurable.

Whatever value they used would reveal a commensurate acceleration. They are linked 2605:59C8:41D:2010:CA9A:D355:8F8C:7AD0 (talk) 01:57, 26 October 2024 (UTC)

GR says that the speed of the clock depends on the gravitational potential. The gravitational acceleration is the gradient of the potential. Inside our spherical body, the potential is smallest at the center. The gradient of the potential, the acceleration, is zero at that point. GR and Newton agree on this point. This now leaves the question as to where you believe the GR offers a noticeably different result from Newton for the gravitational acceleration. Please provide an explicit citation (e.g., a DOI) for the paper you're referring to. cffk (talk) 02:46, 26 October 2024 (UTC)

you've done an excellent job of explaining classical newtonian gravity. It's simply incorrect at providing a value for Acceleration within the material body of a gravity well.

I dont have time to teach you general relativity

run my thought experiment with the neutron moon dropping on the earth. How can it merge with the core and reside at the center if there were no increase in acceleration and a commensurate slowing of time? SJRarey (talk) 03:03, 26 October 2024 (UTC)

one more try using your own stuff

A spherically symmetric mass distribution behaves to an observer completely outside the distribution as though all of the mass was concentrated at the center, and thus effectively as a point mass

This clue would not be observed if there were in fact a gravity gradient reducing to zero at the core. you'd get an extreme amount of ambiguity about the center's location because all the dense stuff would be at the point of greatest gravity somewhere below the mantle.

In reality, All 4th dimension (Time) radials extend directly to the center of the gravity well where they are stretched to the maximum by all the matter present.

All the mass present is driving the depth of the well into a point mass. That's why time is slowest there. Just think of it as the radial stretching more the closer you get [/r²] to the center.

Hope this helps SJRarey (talk) 03:31, 26 October 2024 (UTC)

You have confused gravitational potential, a scalar field, and gravitational acceleration, a vector field. In reality, the mass of the earth is small enough that the discrepancy between observable gravitational quantities according to general relativity and Newton is tiny. Well, good luck with your endeavors. cffk (talk) 11:22, 26 October 2024 (UTC)

By the way, I'd like to echo the reply you got from CRGreathouse on Talk:Preliminary reference Earth model: You should continue this discussion somewhere other than on Wikipedia. cffk (talk) 13:28, 26 October 2024 (UTC)

then dont continue replying.

I've made a good faith effort at explaining my view, you've admitted you know very little of GR and you've answered none of my questions that would help you see the conflict in your thinking. not very receptive

If you were locked in a windowless room on a rocket accelerating a 9.8m/s2 there would be no test that you could perform to differentiate that acceleration as being from a rocket or from gravitational acceleration sitting stationary on the surface of earth. none

I've not confused the fields

In general relativity, the gravitational potential is replaced by the metric tensor, which describes the curvature of spacetime. Unlike in Newtonian gravity, where the gravitational potential is a scalar field, general relativity uses the metric of spacetime to describe gravity

have a nice day

PS id like to leave the convo up, the data line on the PREM chart posted here is incorrect, Im trying to sort that out. 2605:59C8:41D:2010:F281:50CF:50A:8C2F (talk) 15:25, 26 October 2024 (UTC)

It happens that you're wrong about general relativity (and much else), but that's not so important here. What's important is that this is WP:NOT what Wikipedia is for; this discussion is inappropriate here.

CRGreathouse (t | c) 17:22, 26 October 2024 (UTC)