# Newton's gravitational formula wrong?

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1. Feb 27, 2015

### akshaya

Hi,
According to Newton, F= (GM¹M₂)/r²

Einstein proved that light bends around massive bodies, due to gravity. (because space bends around these bodies)

Mass of light = zero, but its being affected by gravity. So, is Newton's equation not universal?

2. Feb 27, 2015

### Orodruin

Staff Emeritus
No, Newtons gravity is most often a good approximation, but it is superseeded by general relativity.

3. Feb 27, 2015

### Staff: Mentor

It is not. As Orodruin says, it is a good approximation... but it would be a mistake to take the next step and say that it is "wrong".
I point people at this essay from time to time: http://chem.tufts.edu/answersinscience/relativityofwrong.htm

4. Feb 27, 2015

### VantagePoint72

In addition to what's said above, it should be pointed out that Newtonian gravitation does predict bending of light around massive bodies after making a some very reasonable assumptions. Basically, rather than being combined into the standard force law, you should think of Newtonian gravity as a field equation: $\vec{E} = GM/r^2$ along with a force law analogous to the electrostatic force, $\vec{F} = m\vec{E}$. Now, despite not knowing how, exactly, such a gravitational field affects massless objects, it's fairly clear that if massless objects exist it must affect them. Just start with a massive object and apply these equations plus $\vec{F}=ma$ and deduce that it accelerates at a rate independent of its mass, $\vec{a} = \vec{E}$. Now take the limit of the mass to zero and the acceleration stays the same. You can make the mass infinitesimally small and it will still accelerate at the same rate. It would be exceedingly strange if gravitational acceleration were discontinuous—zero for something massless and finitely small for anything arbitrarily close—so it's reasonable to deduce that the identification of acceleration with the gravitational field is completely general. Then by treating light as massless particles, you can figure out how much it deflects when passing by massive bodies. This was done around 1800 and generally accepted by the scientific community, well before Einstein and relativity.

It's commonly stated that, as Eddington tested, GR predicts light bends and Newtonian gravity predicts it does not. This is not true, or at least doesn't reflect the understanding of Newtonian gravity at the time. In fact, the prediction by GR is that light bends exactly twice as much as Newtonian gravity predicts. It's also now generally accepted that the accuracy of Eddington's experiment was insufficient to support his conclusion in favour of GR; however, since then we've done much more precise tests that have confirmed relativity's prediction over Newton's.

5. Feb 27, 2015

### akshaya

Well, E = GM/r^2 is applicable only IF the particle has mass, even if its infinitesimally small. Since light's mass is zero, it would not be possible to equate this:
>F= (GM¹M₂)/r²
>ma/m= GM/r²
m=0, so the LHS is not defined.

I guess the universal law of gravitation is not applicable to mass-less objects. (Then why is it called a law? haha) It's just a good approximation. And plus, if Newtonian equation already proved light bends due to gravity, I dont think Einstein would have needed to struggle to prove it.
If you think I'm not understanding something here, can you stress on that? Sorry, I'm just a 10 grader :)

Last edited: Feb 27, 2015
6. Feb 27, 2015

### HallsofIvy

Staff Emeritus
You understand, do you not, that Einstein's theory is, at best, an approximation that will, more than likely, be replace by some other theory that is a better approximation.

7. Feb 27, 2015

### zoki85

You know, that Newton was also a smart guy. I've read somewhere he also expected that trajectories of light rays should be bent due to gravity of massive object. He considered light to be particles (lat. corpuscula) in such case. But treatment and calculation of the effect with Einstein equation is much more correct and accurate .

8. Feb 27, 2015

### A.T.

Like all of physics.

Einstein's theory predicts a different amount of light bending, than Newtonian acceleration.
http://mathpages.com/rr/s8-09/8-09.htm

9. Feb 27, 2015

### VantagePoint72

Do you know anything about calculus? I was using the concepts of "limit" and "continuity" which come from calculus. It's with those concepts that the notion of applying Newton's law of gravity to massless particles is justified.

10. Feb 27, 2015

### Staff: Mentor

Really? I had no idea. Interesting...

11. Feb 28, 2015

Staff Emeritus
The observation that led Newton to his laws was that a = g, independent of mass. From that one can infer ma = mg. To then say that this fails when m = 0 doesn't follow. No calculus required.

Last edited by a moderator: Feb 28, 2015
12. Feb 28, 2015

### Staff: Mentor

This is incorrect. There is nothing about that equation that requires m to be non zero, particularly if it is taken as the starting point.

13. Feb 28, 2015

### Delta²

This is how physics is done since the begining of human history, that is, if you have a theory that explains or fits for a wide set (but not everything) of phenomena you can call this theory or law universal though it really isnt. It just gives us right answers for most of what is happening but not for absoletuly everything that is happening out there.

Even general relativity isnt perfect (it is very good-but still not perfect-only for gravity) or quantum physics (very good-but still not perfect-for anything else except gravity). Unification of quantum physics and general relativity hm thats another story (but still not perfect hehe). And ofc dont forget dark matter or dark energy quantum physics or GR dont say much for those either.

Last edited: Feb 28, 2015
14. Feb 28, 2015

### akshaya

How is it incorrect? To derive that equation, m needs to have a value. 1/0 is not defined.

15. Feb 28, 2015

### Staff: Mentor

You don't need to derive the acceleration law, you can take it as the starting point.

In fact, scientifically the force law (dynamics) was derived from the observed acceleration law (kinematics), not the other way around. In other words, you observe the fact that the acceleration is independent of the mass, and then you multiply that by mass to derive the force law.

However, even if you do derive it from the force law the derivation can still be valid under certain conditions. Specifically, if $F=GMm/r^2=gm$ holds for all m and if $F=ma$ holds for all m then $a=g$ as shown here:
https://www.physicsforums.com/threa...onclusions-for-m-0.770703/page-3#post-4852663

The key condition mathematically is the "for all m".

Last edited: Feb 28, 2015
16. Feb 28, 2015

Staff Emeritus
Apparently the mods thought my original post was too strong. Unfortunately, the point seems to have been missed.

There is no division by zero. Newton's starting point is a = g.

Physics is not about memorizing a bunch of equations. You need to understand the line of argument leading to these equations.

17. Mar 1, 2015