On Wednesday, 19 October 2016 21:06:01 UTC+2, Steve Willner wrote:
In article ,
Yousuf Khan writes:
We're still using Newtonian gravity in this day and age because we still
don't have computers strong enough to do a GR calculation for an entire
galaxy.

That's not the problem. GR is mathematically identical to Newtonian
gravity provided gravity is not "strong" and speeds are "low"
compared to the speed of light. The magnitude of the errors can be
quantified for the actual gravitational potentials and speeds in any
particular calculation.

In some sense I have a problem with your reply.
GR is not mathematical identical to Newton's Law.
If you want to use GR the full Einstein equations are extremely difficult.
A typical document to study is: https://arxiv.org/abs/1203.5166
"Numerical simulations of compact object binaries" by Harald P. Pfeiffer
For a different document about my own investigations read this:
http://users.telenet.be/nicvroom/Num..._documents.htm
In this document many articles about numerical relativity are discussed,
but mainly 2 or maximum 3 objects are considered.

I fully agree that in many cases with great succes Newton's Law
can be used.

The real problems are 1) even Newtonian gravity is too hard to
calculate when the system has too many bodies,

It is not so difficult (using 2D configurations) to simulate Galaxy Rotation
curves with 100 objects. I doubt if that is possible using the full
Einstein equations.

Nicolaas Vroom.