In order to calculate the acceleration due to the geopotential, I've already implemented the EGM-2008 TideFree model, getting the coefficients from the link.

Is the Earth tides effect already considered in these EGM-2008 coefficients? If not, how to measure the effect of tides?


To implement the effect of harmonics, I calculated the gradient of the geopotential $\nabla$U (equation was taken from Vallado). Using the symbolic math library in Julia language, the program is able to calculate the harmonics effect for any given degree and order.

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    $\begingroup$ While I'm not sure these answer to your question directly as asked, this and this are certainly worth reviewing if you haven't already. $\endgroup$
    – uhoh
    Commented Oct 27, 2018 at 10:43
  • $\begingroup$ Implemented how, and to what end? Since you posted your question in the Space Exploration StackExchange, presumably you are using the model to calculate gravitational acceleration (or maybe the gradient of the acceleration, a second-rank tensor). There are three widely used algorithms for this, one by Lear, another by Pine, and yet another by Gottlieb. Did you use any of these? $\endgroup$ Commented Oct 27, 2018 at 16:52
  • $\begingroup$ @DavidHammen Edited the question. Yes, I'm calculating the acceleration. For the harmonics, I just calculated the gradient of the geopotential. $\endgroup$
    – Leeloo
    Commented Oct 27, 2018 at 17:17
  • $\begingroup$ @Leeloo -- "Just"??? That is one of the most dangerous words in both engineering and computer science. Extreme care needs to be taken in calculating the gravitational potential and its gradient (acceleration). PhD theses have been written on this subject. It is anything but a matter of "I just calculated the gradient of the geopotential". $\endgroup$ Commented Oct 27, 2018 at 21:19
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    $\begingroup$ @DavidHammen Thank you, I'll read the theses. I'm not familiar with the methods you mentioned, I took the equation of Geopotential from Vallado and calculated its gradient, which gave me the acceleration. You may dislike the word "just", however that was exactly what I did and that worked for me. $\endgroup$
    – Leeloo
    Commented Oct 28, 2018 at 20:41

1 Answer 1


Well, taking into account tidal perturbations is not a simple issue. You should familiarize yourself with the IERS Conventions 2010 (chapter 6).

In short, tide-free model doesn't take into account tidal perturbations. You should add them yourself as small corrections to the Stoke coefficients $ C_{nm}, S_{nm} $ of the EGM2008 model.

You will need some formulas to compute perturbations from different types of tides (solid, ocean and polar). These formulas use some additional data like "Love" numbers.

The full description of the algorithm including all needed formulas and coefficients can be found in IERS Conventions 2010 (chapter 6).

Also you will need Luni-Solar ephemeris for that algorithm. You can get them at NASA's web server HORIZONS.


For computing gravity potential and its gradient I can recommend you two very efficient methods:

1) M.V. Belikov, K.A. Taybatorov, 1992

2) S.A. Holmes, W. Featherstone, 2002


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