I have been searching everywhere for the first order GR term that describes the gravitational force of a mass.
Could someone kindly show me the term that describes this?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to join this community
Look up the term "precession of the perehelion of Mercury's orbit" in any general relativity text.
The term "gravitational force" is a thorny one in general relativity, and it does not map well to the formalism of the theory, but as mentioned in the comments, the Post-Newtonian expansion is the simplest way to apply that concept.