... Like in the first citation that Farsight used to introduce "tilt", the author(s) describe gravity as spacetime curvature. ...
Yes that POV is necessary for complete accuracy as Newton's inverse square is very slightly wrong, but still good enough that the New Horizons space craft that my 30 year employer, APL/JHU launched 10 years ago towards Pluto only used Newton's version of gravity and will pass thru, after more than 3 billion miles of travel to its target, a 120 mile diameter circle before its close fly by on 15 July 2015. That aim accuracy is equivalent to an arrow fired from 100 miles away hitting a dime!
They will try to "wake up" the satellite again in a few days and then reflected Pluto light will guide it to a very close fly-by. I think, soon after wake up it will begin taking photographs. When closer*, many non-photographic data will be collected too. After the fly-by, when power is available for telemetry, it will take nine months just to send the huge volume of data back to earth - low power from its radio-isotope "battery" and the great distance limits the data rate.
Newton may be wrong about the math of gravity, but is "good enough for government work" as we say, and
it is still mass that is the source of gravity.
The only AFAIK astronomical observations not well described (to experimental accuracy limits) are (1) the very slight bending of star light (appearant positon of the star) during a total eclipse of the sun** and (2) very fine details about Mercury's rate of precession.
* APl's 10 year old MESENGER satellite has orbited mercury only 16 miles above the surface! but on 24 October 2014 needed and got a boost to higher altitudes as atmospheric drag would soon send it crashing into the surface. It took radar photographs of, thru the constant thick clouds, with each pixel only 100 miles wide. It surprisingly is energetically more difficult to go to Mercury than Pluto. APL I think is the only organization that has done both. APL has designed about 250 or more satellites that have been launch with a specular success record that caused NASA to take this Pluto missions away for JPL. Often APL has delivered on time an under budget! Compared to JPL, APL is tiny.***
** Observation of that tiny shift were first made in Brazil and Africa. In one the shift was too small to be measured with the film's resolution and the dynamic atmospheric refraction or "twinkle" of the star. (Conditions for observing were poor.)
*** More details of some of APL's amazing history in space here:
http://www.sciforums.com/threads/interesting-facts-of-the-space-age.135996/#post-3251191