Talk:Geopotential spherical harmonic model

Math formatting

Why do people put immense amounts of effort into violating WP:MOSMATH in ways that produce inferior results? Various things in TeX formatting are complicated in ways that make the results inferior, and then the double backslash shows up repeatedly after the LAST line of an "align" or an array, and such things as

km**2

appear where

km²

should appear, and

n=0,1,2,3

appears where

n = 0, 1, 2, 3

should appear (with n italicized, and proper spacing). Numerous instances of "displayed" TeX are not even indented. Michael Hardy (talk) 05:56, 23 February 2011 (UTC)

The first Goddard Earth Models

Could somebody, for example somebody working in Goddard, by consulting

Lerch, F.J., Wagner, C.A., Smith, D.E., Sandson, M.L., Brownd, J.E., Richardson, J.A.,"Gravitational Field Models for the Earth (GEM1&2)", Report X55372146, Goddard Space Flight Center, Greenbelt/Maryland, 1972

or in another way find out how many terms was used, i.e. what was Nz and Nt? I only have "Joint Earth Gravity Model 3" handy.

Stamcose (talk) 18:04, 1 March 2011 (UTC)

Removal of "tags"

I will remove the "tags" because:

"Clean up" - Neither I nor (until now) anybody else (also not the user that put in the tags) has had any idee what kind of "Clean up" is required!

"Lead section" - There is and has always been a "lead section" what also is recognized by the automatic software function!

Stamcose (talk) 09:41, 16 March 2011 (UTC)

Problems with the article...

1. First - there is not even a lead sentence for what the article is. It jumps into the Newton's law, some blether about measuring the gravitational field, then some vague formalities of solving the gravitational potential using Laplace’s equation. Then there is excessive detail on spherical harmonics - why not link there? Just because the notations in the article are used again in the section, doesn't imply this amount of detail (which a typical reader will NOT read anyway) is necessary - it should be summarized or at the very least use show/hide boxes like at Gauss's law.
2. No sources are inline-cited
3. Notation is non-standard, people will expect g rather than F (also conflicts with F for force), and V or U instead of u, but this is a minor detail.

For now I'll just try to fix the above, but it needs picking up. F = q(E+v×B) ⇄ ∑_ic_i 07:45, 14 April 2012 (UTC)

Just tried to fix more... They were:

• grammatical errors (for instance in some places NO FULL STOPS/COMMAS!!! sentences split in half, words in clumsy order)
• exclamation marks! not needed,
• excessive use of slash spacing in the LaTeX formulae - it doesn't really improve spacing at all, just adds little by little to the byte count...
• I have no clue what these values are:

For JGM-3 the values are:

μ = 398600.440 km³⋅s⁻²

J₂ = 1.7555 10¹⁰ km⁵⋅s⁻²

J₃ = −2.619 10¹¹ km⁶⋅s⁻²

With a "reference radius" R of 6378.1363 km corresponding dimensionless parameters are

${\tilde {J_{2}}}=-1.0826\ 10^{-3}$

${\tilde {J_{3}}}=2.532\ 10^{-6}$

Are these in scientific notation or not? If so shouldn't there be a times sign??

Problems which remain:

• incoherent use of spherical coord conventions - numerous notations are used: the polar angle is λ and θ, azimuthal angle is φ or ϕ... just one would really help not confuse the reader.
• more clean up could be done... (and NO I didn't add the clean up banner as previously stated above).

F = q(E+v×B) ⇄ ∑_ic_i 22:12, 29 May 2012 (UTC)

Irony of ironys...

The section Spherical harmonics says:

"The following is a compact account of the spherical harmonics used to model the gravitational field of the Earth using the precisely the same notations as above.

The spherical harmonics are derived from the approach of looking for harmonic functions of the form

$\phi \ =\ R(r)\ \Theta (\theta )\ \Phi (\varphi )$ (16)

where (r, θ, φ) are the spherical coordinates defined by the equations (8)."

(section later uses (r, λ, ϕ) occasionally anyway) when the "notations above (equations 8)" in section The deviations of the gravitational field of the Earth from that of homogeneous sphere are in fact

"where (r, λ, ϕ) are the spherical coordinates

${\begin{aligned}&x=r\cos \lambda \cos \phi \\&y=r\cos \lambda \sin \phi \\&z=r\sin \lambda \end{aligned}}$ (8)

..."

This is what I'm talking about. Why are we duplicating symbols? F = q(E+v×B) ⇄ ∑_ic_i 22:20, 29 May 2012 (UTC)

Another point is the incoherency and ambiguity of this segment in section The deviations of the gravitational field of the Earth from that of homogeneous sphere:

"Functions satisfying the partial differential equation (6) (the Laplace equation) are called harmonic functions.

The functions

${\begin{aligned}g(x,y,z)&={\frac {1}{r^{n+1}}}P_{n}^{m}(\sin \theta )\cos m\varphi \,,&\quad 0\leq m\leq n\,,&\quad n=0,1,2,\dots \\h(x,y,z)&={\frac {1}{r^{n+1}}}P_{n}^{m}(\sin \theta )\sin m\varphi \,,&\quad 1\leq m\leq n\,,&\quad n=1,2,\dots \end{aligned}}$ (7)

where (r, λ, φ) are the spherical coordinates

${\begin{aligned}&x=r\cos \theta \cos \varphi \\&y=r\cos \theta \sin \varphi \\&z=r\sin \theta \end{aligned}}$ (8)

P⁰_n are the Legendre polynomials, and P^m_n for 1 ≤ m ≤ n are the associated Legendre functions satisfy the partial differential equation (6) and are consequently "harmonic". They are called the spherical harmonics..."

Apart of reading unclearly, where are g and h used later in the article?? What exactly are "these functions" (solutions of the Laplace equation? will a reader with no knowlege on the subject mind-read the editor who wrote this?) and WHY should the reader care?? F = q(E+v×B) ⇄ ∑_ic_i 22:50, 29 May 2012 (UTC)

If no-one objects soon, I'll delete the section on Geopotential model#spherical harmonics: it is purley mathematical and is covered in the main article. F = q(E+v×B) ⇄ ∑_ic_i 23:03, 29 May 2012 (UTC)

A re-formulation and an addition

The text saying "Functions satisfying the partial differentia equation .. are called Spherical Harmonics" is not correctly formulated. The Spherical Harmonics or even the finite sums of Spherical Harmonics are not the only harmonic functions. They are the only of the referenced "product form" ("separation of variables!"), though!

Added a section of recursive algorithms for the efficient computation of the gravitational force used by orbit propagation software. These non-trivial algorithms of fundamental importance for spacecraft flight dynamics could be expanded further! It is not easy to find the mathematical derivation of these algorithms in the litterature!

Stamcose (talk) 14:32, 6 January 2013 (UTC)

Effects of sun and moon on earth

Do any of the models account for the tidal effect of the sun and moon on the shape of the earth and oceans ? Are the tidal effects handled separately or are they so small as to be insignificant ? - Rod57 (talk) 14:25, 8 April 2017 (UTC)

Extension of section "Available Models" and correction of some numerical values specified

I was again looking into this matter using JGM-3 for a special purpose. I then realized that some extension of section "Available Models" simplifies the correct use of gravitational models. I also detected that some numerical values which I myself specified some 6 years ago were not correct! This error was only possible because these parameters are not directly used in common software

Stamcose (talk) 10:38, 3 January 2019 (UTC)

Numerical values for the JGM-3 model

Now the numerical values are precisely those used operationally for several spacecraft! They are "flight proven".

Actually http://www.csr.utexas.edu/publications/statod/TabD.3.new.txt lists (essentially!) the same values with one exception! As C21 and S21 the coefficients -0.24140000522221D-09 and 0.15430999737844D-08 are specified on that WEB page. Corresponding values in this Wikipedia article are -0.3504890360D-09 0.1635406077D-08. The Wikipedia values are the operational ones used in European Space Agency for high accuracy orbit determination and are the correct (official!) JGM-3 values

Stamcose (talk) 19:11, 8 January 2019 (UTC)

Clarification required

Why are these coefficients very different from those reported in https://earth-info.nga.mil/GandG/wgs84/gravitymod/wgs84_180/wgs84_180.html or the more recent https://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/first_release.html?

n	m	Cmn	Smn
2	0	-0.48416685E-03	0.00000000E+00
2	2	0.24395796E-05	-0.13979548E-05
3	0	0.95706390E-06	0.00000000E+00
3	1	0.20318729E-05	0.25085759E-06
3	2	0.90666113E-06	-0.62102428E-06
3	3	0.71770352E-06	0.14152388E-05

Merging "Geopotential" with "Geopotential model"

Comments about article "Geopotential"

Section "Definitions" is OK! Obviously written from the point of view of a meterology stressing the "centrifugal force" and the distinction between between gravity/gravitation. Simple definitions of simple concepts like "geoid" etc are given. Fine!

Section "Mathematical formula" is a bit pointless and not good. This "z" variable is for example rather pointless! If kept at all it should be replaced with the text of section "Newton's law" of article "Geopotential model"

Comments about article "Geopotential model"

This article is very important because it documents the advanced mathematical concepts on which the gravitational models are based THAT ARE VERY DIFFICULT TO FIND IN THE LITERATURE. The orbit propagation software used by space agencies all over the world are based on these concepts but the theory is "hidden in the software" and the generation that originally developed the concept is not around anymore. New improved coefficients are fitted to observed spacecraft orbits but this does not require the full detailed understanding of the internal mathematical algorithms the orbit propagation software is based on.

Conlusion: A justification for having two distinkt articles could be that the first is a very elementary one for the layman and the second an important reference for the expert

Stamcose (talk) 10:36, 13 January 2019 (UTC)