准确度和精密度什么我们知道地球的体积吗?- 江南体育网页版- - - - -地球科学堆江南电子竞技平台栈交换 最近30从www.hoelymoley.com 2023 - 07 - 08 - t20:46:27z //www.hoelymoley.com/feeds/question/2632 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/2632 19 准确度和精密度什么我们知道地球的体积吗? gerrit //www.hoelymoley.com/users/6 2014 - 10 - 15 - t21:36:08z 2019 - 04 - 21 - t10:37:04z < p >卫星如GOCE卫星和恩典测量大地水准面以前所未有的精度。与millimetre-precision高度计可以确定当地面高程。这使我疑惑:我们精密度和准确度能测量地球(或计算)的体积?< / p > < p >我是固体地球时,我甚至惊讶地发现,很难找到一个答案的数量级(10 ^ 0米美元吗?10 ^ 3米美元吗?10美元^{3}$米?)。体积< a href = " https://en.wikipedia.org/wiki/Figure_of_the_Earth " >维基百科是极其有限的问题< / >和链接到一个令人惊讶的是可怜的< a href = " http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html " > NASA字幕新闻< / >,不包括任何错误估计,引用没有来源,并不精确提供上下文或定义的讨论。< / p > < p >一个可以使用较计算地球的体积和小轴获得参考椭圆体,但是我不知道这个近似一个错误有多大。< / p > < p >的精密度和准确度是什么我们知道地球的形状吗? < / p > //www.hoelymoley.com/questions/2632/-/2638 # 2638 10 大卫Hammen回答的准确性和精度,我们知道地球的体积? 大卫Hammen //www.hoelymoley.com/users/239 2014 - 10 - 16 - t17:46:53z 2014 - 10 - 16 - t17:46:53z < p >一个方法是把地球作为一个扁椭球。这将意味着错误出现的不确定性在地球的赤道半径和压扁。从< a href = " http://link.springer.com/article/10.1007%2fs00190 - 003 - 0373 - y?李= true " > Groten”,基本参数和电流(2004)最佳的估计参数共同相关的天文学、大地测量学和地球动力学,“< em >大地测量学杂志》< / em > 77:10-11, 724 - 797(2004) < / >,地球赤道半径均值潮流系统是6378136.72±0.10米,逆压扁是1 / f = 298.25231±0.00001。体积的不确定性造成的不确定性在赤道半径大约是$ 3 V \压裂{\δa} {} $, $ V = \压裂4 3 \π(行进)^ 3美元,约< a href = " http://www.wolframalpha.com/input/?i=4%2F3 *π* % 286378136.72 + m % 29% 5 e3 * % 281 - 1 % 2 f298.25231 % 29 * 3 * % % 286378136.72 + 280.1 + 29% m % 2 f m % 29 " > < / > 51000立方公里。体积的不确定性,由于逆压扁的不确定性是小相比,美元V \压裂{\δ1 / f} {1 / f (1 / f - 1)} $,或者关于< a href = " http://www.wolframalpha.com/input/?i=4%2F3 *π* % 286378136.72 + m % 29% 5 e3 * % 281 - 1 % 2 f298.25231 % 2 f % 28298.25231 * 297.25231% * 0.00001% 29日29日" > < / > 120立方公里。< / p > < p > 51000立方公里图听起来很多,但它不是。这意味着地球的体积可以表示七个地方的精度。< / p > //www.hoelymoley.com/questions/2632/-/2641 # 2641 7 回答的方式,准确度和精密度的地球物理学家我们知道地球的体积吗? 的地球物理学家 //www.hoelymoley.com/users/507 2014 - 10 - 17 - t08:29:03z 2017 - 03 - 12 - t06:49:41z < p >讨论地球的体积,我们必须忽略它不是静态的但实际上高度动态。潮汐仅使高度相差50厘米。我的信息是来自2003年的一篇文章< a href = " http://www.esri.com/news/arcuser/0703/geoid1of3.html " rel = " nofollow noreferrer " > esri Witold Fraczek < / >。< / p > < p >正如你所说,我们有不同的理解。近似,简化计算(更快)。我们从球面到椭球大地水准面实际测量。这些椭球模型之一是< a href = " http://en.wikipedia.org/wiki/World_Geodetic_System " rel = " nofollow noreferrer " > WGS84 < / >,仍保持着这一天。不过,当GPS时代开始,卫星,有一些严重的问题得到正确的高度。将不同约30 - 40米的地方。所以开发一个更好的模型。< img src = " https://i.stack.imgur.com/An6Bf.png " alt = " http://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Geoidheight_DE.svg/600px-Geoidheight_DE.svg.png " > (< a href = " https://commons.wikimedia.org/wiki/File: Geoidheight_DE.svg rel = " nofollow noreferrer " > < / >) < / p > < h3 >大地水准面< / h3 > < p >大地水准面不像你会觉得容易计算。 The way it is actually done is by using gravitational measurements and the mean sea level (MSL). The image I used is from GRACE data, the most accurate model up to today. You can now use GIS to compute the variations from the reference ellipsoid.

GRACE gravitational geoid (source)

The errors

Let me just quote from the article:

The maximum range of the Geoid99 undulations with respect to the WGS84 ellipsoid is 192 meters. The biggest anomaly was discovered southeast of India where the geoid is 105 meters below the ellipsoid, and its highest swelling was observed in eastern Indonesia.

The geoid99 is far from perfect (and there are many newer models). However, from this we can see that the maximum error is in the 100m range, very localized too. Earth's topology is rather insignificant compared to the entire volume. I will not put a number down, as I don't have time right now to do any actual computations, but as a qualitative analysis this should give a basic idea.
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