The advance of the perihelion of Mercury is one of the four classical tests of general relativity. I wonder what's the most precise modern measurement of it. However, while scanning the literature, the most precise measurement seems to date back to a paper by Clemence in 1947:


The 50 papers that cite it are merely theoretical ones:


There is just one reinterpretation by Nobili and will in 1986,


but no new measurement. I know that there are other periastron shift data from the binary pulsar and others, but I'd be curious about the plantes of which Mercury shows the most pronounced effect. Messenger was a mission to Mercury in 2009, but I didn't find perihelion data from it. With all the precision telescopes built in the last decades, I cannot believe that or best data of this important test is 60 years old. Explanations of the technical difficulties of the measurement by an expert are also appreciated.

  • $\begingroup$ The ephemeris used to guide Messenger to Mercury is fully relativistic. $\endgroup$ – David Hammen Nov 8 '14 at 12:30
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    $\begingroup$ I believe that e.g. this 1972 paper journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.1594 is more accurate, isn't it? $\endgroup$ – Luboš Motl Nov 8 '14 at 12:31
  • $\begingroup$ @ClassicalPhysicist - Quick note, MESSENGER is an acronym so it should be capitalized. Regarding your question, there is a paper by Fränz and Harper, [2002] in Planetary and Space Science discussing the orbital ephemeris of the planets and how they are calculated. The data are updated at specified epochs (basically every 10 years) to remove issues associated with rounding errors, uncertainties, and compounding errors. $\endgroup$ – honeste_vivere Jan 11 '15 at 20:44

A recent overview can be found in Pireaux et al (2001). I quote the authors on page 3:

However, the perihelion shift of planets, and hence Mercury, can not be measured directly because the perihelion is a Keplerian element whereas the motions of the planets are not exactly Keplerian due to mutual gravitational interactions and figure effects. So, only an indirect determination can be done. One can proceed as follows. The motions of planets, from numerically integrated ephemeris, are computed over an interval of time. The time evolution of osculating elements is then plot and a polynomial fit of the parameters gives the rate of the perihelion advance. If one repeats this procedure in the classical Newtonian limit, one gets another set of rates. The difference between the two computations, and taking into account the constant general precession of the equinoxes, gives the combined effect due to relativistic gravitation and the Sun’s quadrupole moment, $\Delta\omega_{\text{obs}}$.

In other words, the perihelion shift of Mercury is a numerically derived quantity, based on ephemeris data and calculated by integrating a Newtonian $N$-body model of the solar system with and without a relativistic contribution, over several centuries. This eliminates the perturbations from other planets, but not the influence of the oblateness of the Sun. To correct for this effect, one has to either measure the solar oblateness directly (using e.g. SOHO data) or calculate it using a theoretical solar model.

The paper references several results from other authors: an unpublished value from M. Standish (2000), and data from Anderson et al (1992), Pitjeva (1993), and Krasinskii et al (1993).


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