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I'm doing a physics project about the following: according to special relativity, what appears as momentum to one observer can be inertial mass to another; i.e. mass is relative.

But mass and energy curve spacetime.

I've read (in Gravitation by Thorne, Wheeler, et al.) that the energy-momentum tensor is the source of gravity, and this determines the differential geometry of the spacetime region around mass and/or energy.

So my issue is this: When very massive objects speed up, their masses and gravitational fields increase. I want to calculate the effect of their increasing mass due to kinetic energy increases on an object for which I have the precise trajectory data and distance from the massive objects as a function of time.

AbstractIf a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that Mrel = g(1 + b)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not gM but is 2gM .

I know that substituting the relativistic masses into the Newtonian gravity formula would be terribly wrong. Is my only option to learn tensors?

Nowadays physics don't define mass that way.