# Newton's law of gravity

ttesss
I´ ve seen that Newtons law of gravity is considered and used very accurate to predict planet and satellites motion ( eclipses, etc..), but if space time is actually warped as Einstein told, how come Newtons law be accurate when it only depends on the mass and distance of to planets or stars?? I mean, if the fabric of spacetime is warped then this warping must rely on more than just the mass of the star or planet, has it is shown in einstein´s laws of gravity. To sum up, if Einstein has shown new gravity laws, how can we still consider Newtons law accurate and actually use it?

Mentor
Summary:: law´ s accuracy

To sum up, if Einstein has shown new gravity laws, how can we still consider Newtons law accurate and actually use it?
When you start with Einstein’s law and take the limit of low mass and slow objects then you can derive Newton’s law. So Einstein’s law actually implies Newton’s law as a limiting case.

This is important because Newton’s law has so much experimental support. If Einstein’s law did not reduce to Newton’s law in the appropriate limit then Einstein’s law would have been immediately disproven.

This is a general fact in science. Once a theory has been experimentally validated, like Newton’s laws, then it never goes away. New theories may come along that explain more, but the old theory still works in its domain, and the new theories must contain the old one

vanhees71, DrStupid, etotheipi and 3 others
2022 Award
I mean, if the fabric of spacetime is warped then this warping must rely on more than just the mass of the star or planet, has it is shown in einstein´s laws of gravity. To sum up, if Einstein has shown new gravity laws, how can we still consider Newtons law accurate and actually use it?
First, it's better not to think of this as "warping", since that implies that something is distorted. Nothing is distorted, it's just curved. And definitely don't use the word "fabric" (although there's probably a warp and woof joke in there somewhere), since there's no structure there that we are aware of. You see it a lot in pop sci, but it's very misleading.

You are correct that the source of gravity in relativity is not just mass. It's actually a thing called the stress-energy tensor, which means (loosely speaking) that all forms of energy, including mass, generate gravity. However, mass is by far the most important source in all but the most extreme of circumstances, which is why Newtonian gravity (which, as Dale says, is an approximation to general relativity) only depends on mass. And the difference between the Newtonian model and the relativistic one in the solar system is tiny. For example, an early triumph of relativity was explaining the anomalous precession of Mercury's orbit, a correction of 43 arcseconds (about 0.01°) per century. That's why most of the time you don't bother worrying about relativity when sending spaceships around the solar system. Unless you need really high precision (and the clocks on GPS satellites is the only application I can think of where you do), the error from using Newton's simpler maths is negligible.

vanhees71, etotheipi and Delta2
To sum up, if Einstein has shown new gravity laws, how can we still consider Newtons law accurate and actually use it?
For the same reason that we still use Newton's Laws of motion, and not just Special Relativity: They are accurate enough for most applications and much easier to compute.

vanhees71