Tuesday, 18 September 2018

general relativity - Confusion regarding gravity not being a force


In high school, it was taught that formula for describing circular orbital velocity around a central body is derived by equating Newton's law of gravity with the centripetal force formula (under the logic that the inwards centeipetal force required is provided by the gravitational "force").


It was only recently that I discovered that gravity isn't actually a force but is actually a distortion of space time. (I came across this while wondering why light bends around large masses). Does the fact that gravity is not a force make the above derivation of orbital velocity any less valid? Because the above derivation assumes that gravity is a force.



Answer



You cannot longer use Newton's formalism $F = m a = -GMm/r^2$ if you introduce the fact that the geometry of space time is changed by the presence of the central body $M$.


It is true that the test mass $m$ still moves around $M$ because of gravity, but you should think of gravity not as a force any more, but as an emergent property of the curvature of space-time. Fortunately there's a whole body of mathematical tools that allow you solve this problem in particular.


Actually, it is one the most well known problems you can analytically solved using general relativity: the two body problem


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