The method of uniform scaling of coordinates introduced by Schiff in 1960 is reviewed. It is shown that its application to the bending of light during solar eclipses assumes that the light rays travel in perfectly straight lines. It nonetheless obtains quantitatively the same angle of light deflection as General Relativity (GR). Schiff’s failure to obtain similarly accurate results for the advancement of the perihelion of Mercury’s orbit is traced to his ignoring the central role of the acceleration due to gravity g in these computations. When the appropriately scaled g factor is included in the theoretical treatment, the adjusted method obtains quantitative agreement with both GR and experiment for the angle of advancement. The scaling produces a value of g=0 for light by virtue of its moving at speed c in free space, thereby leading to the straight-line trajectory of the waves. However, g has a non-zero value for massive objects and its effect on the velocity of the planet needs to be taken into account explicitly to obtain accurate results. More generally, it is shown that there are two key scaling factors, Q for kinetic acceleration and S for the effects of gravity. These quantities can be evaluated on the basis of a minimum of information regarding the locations in a gravitational field and the states of motion of any object-observer pair anywhere in the universe. The scaling of each physical property is characterized by a specific product QnSp, where n and p are integers. One of the main advantages of the uniform scaling approach is that it is relatively simple to apply. The calculations for light bending and the advancement angle of the perihelion of planetary orbits are carried out with a computer program which differs by only a few statements from the standard one which applies Newton’s classical method.