# How accurate is Newtonian Gravity?

I know that really fast moving things need Relativity rather than Newtonian physics.

I also know the quirk of the Mercury´s orbit.

But just how much more accurate is General Relativity than Newton´s Law of Gravitation for predicting say the orbit of Earth or Neptune?

Can the "slingshot" effect where we use another planet´s gravity to accelerate a space probe be done with Newton or does that require General Relativity?

Is the speed of Jupiter (18 km/s I think) fast enough to make a difference in the accuracy of GR v Newton´s Law of Gravity?

• Possible duplicate: physics.stackexchange.com/q/52165 – JSQuareD Oct 17 '13 at 17:42
• I read that. It doesnt clearly answer my specific questions. – MikeHelland Oct 17 '13 at 18:04
• Yes you can derive the slingshot effect from Newtonian gravity, I'll post the derivation in an answer soon – Run like hell Nov 7 '18 at 10:47

The key point is that Newtonian physics fails when, roughly, the quantity $v/c > .1$ or $\frac{GM}{c^{2}r} > .1$. You can calculate both of these quantities for the cases of Earth and Jupiter, and you will find that your answer is quite small.
• ... except for cosmological distances, and where $|\Phi|/c^2 \gtrsim 1$ and near the Planck scale ... – Michael Brown Oct 18 '13 at 16:24