Gravitational Model of Tides: Earth and Sun Potential Addition

[frogeraie]

I have a question about the gravitational model used to describe tides:
Is it correct to simply add the tide potentials respectively due to Earth and sun as most people do? (see for instance a good example of this approach in Eq 9 of: http://arxiv.org/PS_cache/physics/pdf/0701/0701301v1.pdf).
The superposition principle, at first, almost convinced me not to go further... when I came across this 1976 paper: http://adsabs.harvard.edu/full/1977SvAL...3...96A,
which is then contradicted in 1981 by:
http://articles.adsabs.harvard.edu//full/1981SvAL...7..281S/0000282.000.html.
Avsyuk's reasoning is appealing:
to calculate the acceleration a0 of M0 in the inertial coordinate system of the three bodies he adds the acceleration a1 of M0 in the mobile system of the earth-moon barycenter to the acceleration a2 of this barycenter with respect to the earth-moon-sun reference system.
Sitnik and Khlystov have the same expression for a2 (Eq. 6) but they differ for a1. I have a hard time to understand their second term in (8). What is M0 acceleration in the mobile refrerence frame of the earth-moon barycenter? Is it Sitnik and Khlystov's Eq.8 or F3/M0 as Avsyuk wants or, as I would prefer, (F1+F3)/M0?
Does someone would care to ponder a bit on these questions? Thanks!

 

[D H]

I have a question about the gravitational model used to describe tides:
Is it correct to simply add the tide potentials respectively due to Earth and sun as most people do?

Yes.

I came across this 1976 paper. Avsyuk's reasoning is appealing: to calculate the acceleration a0 of M0 in the inertial coordinate system of the three bodies he adds the acceleration a1 of M0 in the mobile system of the earth-moon barycenter to the acceleration a2 of this barycenter with respect to the earth-moon-sun reference system.

A word of advice on scientific papers from the old Soviet Union: Read them with a grain of salt. Some of that old Soviet science was very, very good. KAM theory, for example. On the other hand, some of it was very, very bad. Lysenkoism, for example. Anything that proved that those stupid capitalists were wrong was good science. Look at it this way: It took 4 years to publish a paper (Sitnik & Khlystov) that showed Avsyuk's reasoning was wrong; that he made what was essentially a stupid math error.