# Einstein on the orbit of mercury, how does this fix Newton's theory?

1. Apr 29, 2014

### shott92

hi guys,
i have a very limited knowledge of physics, and have an engineering background.
but i saw on a program i was watching yesterday about the solar system, one of the comments made on there was about how newton's equation for gravity was what was used to find "neptune??"
however it worked for all of the other planets but mercury, it said that it was something to do with once we look at the fact gravity is not just a force that attract but bends spacetime itsself then this solves the orbit of mercury mystery...

i have looked on the internet and on youtube but i find the same answer everywhere... "it just does" ive looked at a few equations and the ones i could comprehend appear to mea that if the mass of a plant warps space time it warps it the same amount as Newton's equation f=g*(m1m2/r^2)

also i dont want to jump out of my league to much but if some one could explain in laymens terms that would be cool
my understanding is if we was at the near the centre of the earth (aside from being crushed by the immence pressue) we would actually be ripped apart by gravity as it is much stronger nearer the earth core than it is on its surface... if this is the case then is gravity not more related to density than mass... and how do you define the mass of a planet, is it the planet as a whole then the distance from its surface, just cos my thought was that if you went to jupiter and started falling through the planet as you get nearer the center the mass under you is lower as gravity would reduce...
and that doesn't make sense to me, i assume its wrong but why ??

thanks guys

2. Apr 29, 2014

### ChrisVer

First of all I don't really understand your question about mercury's orbit... The problem with mercury is that, by newtonian mechanics you could not describe its orbit (the anomalous perihelion advance of the planet Mercury without any arbitrary parameters -"fudge factors"). Warping of spacetime can be very misleading, because people tend to think in sheets being bent, while in fact it's a spacetime thing. I prefer the idea of going from a constant metric $n$ to a spacetime dependent metric $g(x^{0},x^{1},...,x^{D-1})$, that way the spacetime can indeed -in general- get curvature etc. The equations for the GR is that generally the metric of your space (simply put, a quantity which helps you measure distances) is not a flat minkowski metric. (the way you measure for example distances on a sphere is not the same you do on a flat sheet of paper, and that's why maps are "strangely" drawn - countries closer to the poles are drawn much bigger than they are in comparison to others closer to equator).
It's that difference in metric's form (and the way it depends on to the mass and energy) which gives GR the ability to calculate orbits/freefalls etc...
I'd always suggest Weinberg's-Gravitation and cosmology principles and applications of GR...
The chapter studying that is
6.Bound orbits: precession of perihelia (in my version)

But for the last one, even Newtonian mechanics give the answer... When you go deeper in Earth, the gravitational force become weaker, not stronger...
The $F \propto 1/r^{2}$
does not hold within the earth.
By using Gauss's law (which is way faster that working with infinitesimal small masses attracting you from the whole earth and adding their forces up to get the net force) you can find that after "drilling in the earth" your force will decrease $F \propto r$. The general idea is that you are being attracted by what exists under you, within a sphere of radius r (your distance to the center). Everything out of that sphere, will give zero net force on you. So in fact you get less mass attracting you...

Last edited: Apr 29, 2014
3. Apr 29, 2014

### homeomorphic

Density basically is mass. It's just how much mass is crammed into a certain amount of space.

I think you are thinking of a black hole when you say we'd be ripped apart. I don't think the earth is that dense inside, although it is more dense than at the surface. If the density is constant, than your reasoning is correct, gravity gets reduced. However, in a situation with very high density, notice that the force for Newton's law goes to infinity as r goes to zero, in the extreme case of a point mass (it doesn't actually do that because you need to think of it as mass density, rather than point mass). Thus, if the mass at the center of a planet were very, very dense, the force there would be strong because r is so small with respect to such a great amount of mass. If it was much less towards the surface, then you would have a bigger r with respect to most of the mass, so there wouldn't be as much force at the surface. That's all inside the planet, though. It doesn't make so much difference once you get away from the planet. And as I said, I believe the earth doesn't get that much more dense inside, so gravity gets weaker inside because all the force from the outer layers cancels out, so it's just the inside that's doing the pulling, so there's less of it, hence, less force in that case.

When I took a class on general relativity, we did the calculation for the precession of the perihileon of mercury, but it wasn't terribly enlightening, as the professor himself even joked about. I'm sure you can put it in more qualitative terms of some sort, but I don't know how--not that I'm the most well-informed person on these things.

Anyway, general relativity is pretty heavy stuff, so there's good reason for not explaining the full reasons for that. Mercury is definitely not the motivation for general relativity--it just provides a confirmation of it.

One reason why you can get clued in that Newton's law needs to be fixed is if you know special relativity. The thought experiment is to imagine that the Sun suddenly disappears. According to Newton's law, instantly, there would be no gravitational field. However, special relativity tells us that information can't travel that fast. There has to be a time-delay. Newton's law assumes instantaneous transmission of force. So, something is fishy with Newton's law. Also, you can do thought experiments that have to do with time-dilation in gravitational fields. Einstein's full solution was only obtained by something like 10 years of hard work. To understand it, you can't look at youtube videos or wikipedia. You'd have to read an actual book about general relativity if you are looking for more than "it just does", although I suppose someone here might give you a better partial answer than mine.

Here's a fun way to get started:

http://math.ucr.edu/home/baez/gr/gr.html

4. Apr 29, 2014

### A.T.

Laymen explanation of the Mercury orbit precession (bottom picture):
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

Towards the center gravity decreases (because of less mass below you), but pressure increases (because of more mass above you).

5. Apr 29, 2014

See this :http://en.wikipedia.org/wiki/Shell_theorem

6. Apr 29, 2014

### WannabeNewton

There is nothing fundamental in physics that demands the perihelion precession be explained by a metric theory of gravity such as GR. It just so happens that the (granted elegant and deep) framework of GR describes the perihelion precession correctly.

7. Apr 29, 2014

### D H

Staff Emeritus
That is perhaps a bit of a misstatement. I'm not arguing with you on the differences between Newtonian mechanics and GR. Newtonian mechanics works just fine even for the orbit of Mercury on a short enough time scale. How short depends on how precisely one wants the orbit predicted. The discrepancy between the predictions of Newtonian mechanics and the reality of Mercury's orbit is very, very small, 43 arc seconds per century.

A better way of answering shott92's question is that this tiny discrepancy, although small, is definitely real. General relativity does a better job at predicting of the orbit of Mercury. Deviations between the predictions of GR and the reality of observed behavior are well within measurement error.

This is not true. Apparently even a number of physics professors believe this, even though this is a result from a freshman level physics problem that makes a spherical cow assumption.

Here's a better picture of gravitational acceleration inside the Earth:

The blue curve represents science's best guess with regard to conditions inside the Earth. Note how gravity *increases* with increasing depth from the surface down to the bottom of the upper mantle, then decreases slightly in the top of the lower mantle, and then starts increasing again to reach a global maximum at the core/mantle boundary. Only then does it decline toward zero.

The spherical cow assumption that leads to F∝r is that density inside the Earth is uniform. This is anything but the case. The Earth's core is significantly more dense than is the rock above it. The iron and nickel at the very center of the Earth has four times the density of surface rock, 1.66 times the density of iron and nickel on the Earth's surface.

Admittedly, it is a nice simple calculation that leads to gravitational force being proportional to radial distance from the center inside an object of uniform density. However, no text takes the next step to say that this isn't how the Earth works. A good next step, still comprehensible at the freshman physics level, is to show that the local density at some point inside a solid spherical object whose density is a function of radial distance must be at least 2/3 of the mean density for the gravitational force to decrease at that point. It's still a spherical cow assumption, but at least it's not a uniform spherical cow.

8. Apr 30, 2014

### PERFESSER

One point which nobody made here is this: it's not just Mercury whose orbit is more accurately described by Einstein than by Newton. All the planets are like that, it's just that, for Mercury's orbit, this effect is more obvious. Why? Because it's nearer to the sun, and therefore in a much stronger gravitational-field

Last edited by a moderator: Apr 30, 2014
9. Apr 30, 2014

### A.T.

And because it's orbit has more eccentricity.

Last edited by a moderator: Apr 30, 2014