Sir Isaac Newton developed the first theory of gravitation. It was universal: it explained the motion of objects near the earth and the motion of the planets and moons. Using his theory, one could predict the trajectory of a cannon ball or the positions of the moon or any other celestial body. One only needed to know the initial conditions of the objects (masses of the objects involved, the speed, and the direction of relative motion between the objects), and one could calculate the future relative positions of the objects. As an example, if one knows the speed and direction that Mercury is traveling relative to the Sun, the distance between the Sun and Mercury, and their masses, then one can calculate the shape of Mercury’s orbit about the Sun by using Newton's equations of motion and theory of gravity. One also can calculate and predict the future position of Mercury at any time in the future.
By the 19th century, the accuracy of measurements had improved enough to tell that Newton's theory had a small but measurable error when used to calculate the precession of the orbit of Mercury. Einstein's General Theory of Relativity was able to account for the observed precession within the error bars of the then available measurement accuracy. Note that Newton's equations represent the equations one derives from GTR when one does not consider large masses that are close to each other and speeds are much less than the speed of light. When these conditions are met, Newton's equations are still accurate enough to calculate the motion of objects. This applies to bullets, baseballs, ballistic missiles, the Moon, and most space probes. GTR must be used for objects traveling at speeds approaching the speed of light, objects separated by long distances (e.g., space probes to Jupiter and beyond), and massive objects close together (Mercury and the Sun).
Now, measurement accuracy has improved enough to find that there appears to be a small but measurable error in GR calculations. If this apparent error is validated and the GR calculations are validated and the error remains, this indicates that GR theory needs refinement, there is an anomaly in the mass distribution of the sun or Mercury that isn't being accounted for, or there is a new phenomena awaiting discovery.
