Talk:Gravity of Earth

message: 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 . 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)
thread_title:  Propose to remove 2 too-long tables 

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thread_title:  External links modified 

message: If, as suggested in the text, the density of the Earth decreases linearly with increasing radius from a density  at the center to  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  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.wikipedia.org/w/index.php?title=Gravity_of_Earth&oldid=553887481
Please fix it again.
George963 au (talk) 11:52, 16 February 2019 (UTC)
replies: text: 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)
replies: text:  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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Depth 

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: 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)

text: 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)

text: 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)
thread_title:  History of the Earth's gravity 

message: 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)
thread_title:  Equivalence of inertial and gravitational mass 

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

message: — Assignment last updated by Ahlluhn (talk) 00:58, 31 May 2024 (UTC)
thread_title: Wiki Education assignment: 4A Wikipedia Assignment