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" ... But there ought to be many more stars that are fainter than S2, and many of them should get closer to our galaxy’s central black hole, move faster, and see the position of their closest approach precess more quickly than S2 does. In short, they should provide a better, more restrictive, and more fundamental test of relativity than ever before. Additionally, they should orbit more quickly, on timescales of less than a decade. We want to test relativity more precisely than ever before, and this is one approach to doing so. ... "
" ... Earth's rotational axis will precess over time due to two combined effects: axial precession (shown ... [+] here) and apsidal precession, as its elliptical orbit also precesses. As a result, Earth's axis will sweep out a large circle in the direction it points over ~26,000 year timescales, changing the direction of our celestial poles. ... "
" ... Earth's rotational axis will precess over time due to two combined effects: axial precession (shown ... [+] here) and apsidal precession, as its elliptical orbit also precesses. The combined effects, which have ~26,000 and ~112,000 year periods, respectively, result in a total precessional period of closer to ~23,000 years. ... "
" ... Of course, the Universe isn't ideal. We view the Sun-Mercury system from Earth, which itself moves in an ellipse, rotates on its axis and sees that spin-axis precess over time. Calculate that effect, and you'll find that the shape of Mercury's orbital path isn't a closed ellipse any longer, but one whose aphelion and perihelion precesses at 5025 arc-seconds (where 3600 arc-seconds is 1 degree) per century. There are also many other planets in the Solar System that tug on the Sun-Mercury system. If you calculate all of their contributions, they add an additional 532 arc-seconds per century of precession. ... "
" ... What appears to be a parabolic trajectory (left) is actually a segment of an ellipse (center), but... [+] if the projectile were made of dark matter (or neutrinos) and were allowed to fall through the Earth, it wouldn't make an exact ellipse, and the oval-shape it did make (right) would precess by a small but significant amount with each orbit. ... "