Geopotential Zero-Tide Coefficients Final Correction

[3allan]

The geopotential coefficients describing the gravitational potential of the earth (sourcing its gravitational field) come in 2 common flavors within EGM08. These 2 flavors are called "tide-free" and "zero-tide." They concern effects of the permanent Earth tide and are identically the same except in their C20 coefficient (the fully normalized cosine coefficient of degree 2 and order 0). The difference between the two is on the order of ~1e-9, and in both cases, C20 ~ -0.0004841.

Section 6.2(.1) of the IERS TN36 provides a 3-step procedure for correcting these geopotential coefficients due to solid Earth tides, allowing for more precise orbital dynamics to be done. Step 3 of this procedure applies to the zero-tide model only.

The implemented zero-tide model has its coefficients currently skipping step 3 of these corrections which should be addressed for completeness (and correctness). The relevant section of code where this correction would take place would be here.

Priority: Low

• The amount of accuracy gained by correcting the coefficients for the zero-tide model (by implementing step 3) will likely be irrelevant by the amount of uncertainty in aerodynamic drag in LEO.
• The tide-free geopotential model is already corrected according to this 3-step procedure and therefore offers an immediate alternative
• These corrections are supposed to be applied at every dynamical time t, but instead are currently implemented only once at launch (t = 0). Therefore, attained accuracy of applying these corrections (which are very small) is lost anyways on the order of hours due to lunar and solar tidal effects.