Note 4 — EASY LESSONS IN EINSTEIN (continued 2)

If you insist upon seeing just what is the difference between Einstein’s and Newton’s laws of gravitation here it is as given in The Scientific Monthly of January, 1920:

Any particle or light pulse moves so that the integral of ds between the two points of its path (in four dimensions) is stationary where

(according to Einstein) ds² = -(1 - 2m/r)^{-1} dr²-r² d θ² + (1 - 2m/r) dt

or (according to Newton) ds² = dr² - r² d θ² + (1 - 2m/r) dt

These expressions are in polar coördinates for a particle of gravitational mass m.

The new factor introduced by Einstein is, as shown above,

1/{1-(2m/r)}