Newton's gravity vs Einstein's gravity Hello so if i were to simplify the difference between gravity as seen from Newton and gravity as seen from Einstein, could i say that Einstein's gravity is just adding the fact that gravity does not exceed the speed of light and does not have an instantaneous effect on mass. Also that not not all matter has a gravitational pull with other matter at any distance.
sorry if i look stupid but I'm 14 and I'm really trying my best to figure out the difference between the two different theories as I'm very curious and LOVE astrophysics.
 A: It's tempting to imagine starting with Newton's theory of gravity and trying to extend it to end up with general relativity. The trouble is that Newtonian gravity and GR are formulated in utterly different ways. General relativity is a metric theory with a completely different starting point to Newtonian gravity. While it's fairly easy to show that Newtonian gravity is the low speed, low energy density limit of GR there is no simple way to do the reverse.
A: 
Could I say that Einstein's gravity is just adding the fact that gravity does not exceed the speed of light and does not have an instantaneous effect on mass?

No, you cannot. You are not alone in making this mistake. Laplace made this very same mistake in the late 18th century and calculated that if light does have a finite speed, it must be at least 7 million times that of the speed of light. Poincaré made this same mistake about a century later and calculated that the speed of gravity must be at least 1017 times that of the speed of light. Even as late as 19981, a professional scientist with a PhD in astronomy made that very same mistake.
Suppose it's raining straight down and you run in an attempt to get out of the rain. Instead of just your head and shoulders getting wet, your running makes you get wet (in front) from head to toe. The vertical rain isn't so vertical anymore from your perspective. It appears to be coming from in front of you. This same issue appears when we observe the Sun; it appears to be 20 arc seconds ahead of where it "actually" is thanks to the finite speed of light. This same issue would arise if one merely added a time lag to Newtonian gravity. The solar system would fly apart in short order if that was all there was to general relativity.
General relativity does not make this mistake. There's a lot more to general relativity than a finite transmission speed. But to understand the details, you will need mathematics far beyond even that of a very smart 14 year old.

1 Note to future editors: DO NOT make the cited link into a reference. That author's name is verboten in any answer authored by me.
A: I think the simplest way of thinking about the difference between Newton's theory of gravity and Einstein's is to think about how they think of gravity itself.
Newton says that there is a force which all massive objects feel and gives a rule for what that force is.  There's no explanation for how the force comes about: it just exists.  There's no delay in the force: this is fine in Newton's world (which, but it's not fine in Einstein's.
Einstein says something entirely different: there is no force of gravity.  Instead, massive objects simply move on straight lines.  But as well as doing this, massive objects deform spacetime, which means that 'straight lines' are more complicated than they would be in a non-deformed spacetime.
Einstein's notion of gravity is hugely more compelling than Newton's:


*

*it gives an explanation of what gravity is, in terms of curvature;

*it is compatible with special relativity, as the deformation of spacetime by mass spreads through spacetime at a finite speed (which, of course, is the speed of light);

*but, in suitable limits, it reduces to Newton's theory and so is compatible with it, which is good since Newton's theory works very well in many cases.


Unfortunately, because gravity is treated as a modification of the arena in which things happen, the theory tends to be fairly hard to work with.
(Note: this is not meant as a full description of GR: I'm trying to aim at someone of 14!)
