Math Applying Einstein's Theory of General Relativity

[AJ Allen]

Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and solve these types of problems in a whole different way.

 

[ChrisVer]

[first of all, to be precise, what you give is the acceleration and not the force]

Now, in general the constant force that you are talking about is not even true for the Newtonian mechanics. Gravitational force there follows the inverse squared distance law. At small trajectories then you can consider the force to be constant [as an approximation].
Also Newtonian mechanics are an approximation of general relativity for a weak force and low speeds...

GR then, would just add up corrections to these solutions...now whether these corrections are important or not, is a matter of the wanted accuracy/precision of your measurements. If the corrections were actually large, Newtonian mechanics wouldn't have survived for 400 years.

 

[pervect]

Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and solve these types of problems in a whole different way.

Newtonian theory doesn't really predict a "constant force" for gravity either, you can approximate the force of gravity on the Earth as a constant as long as your distance from the Earth's center doesn't vary much.

GR wouldn't exactly "denounce" the idea, but it would calculate things in ways that would be unfamiliar if you haven't studied GR. One way of computing the path of an object under no non-gravitational forces would be to use the geodesic equation. There are a coupe of ways of arriving at the geodesic equation which are equivalent in GR (though they are some circumstances in which these two ways are not equivalent). One computes geodesics as paths that maximize (more properly, extremize) proper time, another calculates them via techniques of parallel transport. The details are probably not going to make sense without a great deal of mathematical background, I'll refer you to Caroll's GR lecture notes http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html for more details with no guarantee that they'll be at a comprehensible level for you.