# Gravity re Newton & Einstein

• John15
In summary, the perihelion shift applies to all non circular orbits but the effect is largest for Mercury because Mercury is closest to the Sun. Newton's theory is pretty accurate already, the error is only about 1 part in 107.

#### John15

I understand there is a slight difference in the value of gravity when worked out using Newton or relativity. The obvious example being mercury where Newtonian is slightly out and relativity accurate.
Does relativity show a higher or lower figure or does the difference in working out mean you cannot compare the 2.

John15 said:
I understand there is a slight difference in the value of gravity when worked out using Newton or relativity. The obvious example being mercury where Newtonian is slightly out and relativity accurate.
Does relativity show a higher or lower figure or does the difference in working out mean you cannot compare the 2.
The only effect you can directly compare it the gravitational acceleration. Here is a thread about it:

But GR predicts other effects that also affect trajectories like time dilation and space distortion.

Why do Newtons equations not correctly describe the orbit of mercury. How precise are they with the other orbits.

John15 said:
Why do Newtons equations not correctly describe the orbit of mercury. How precise are they with the other orbits.
Newton's theory is pretty accurate already, the error is only about 1 part in 107.

The perihelion shift applies to all non circular orbits but the effect is largest for Mercury because Mercury is closest to the Sun.

We can actually express equatorial orbits in common form both for GR and Newton's theory:
$$\Large {\frac {{d}^{2}u}{{d\varphi }^{2}}}=1/2\,\mbox {D} \left( f \right) \left( u \right)$$

Where f(u) is:
$$\Large f \left( u \right) =2\,{\beta}^{2}u+2\,k-{u}^{2}$$
for Newton and

f(u) is:
$$\Large f \left( u \right) =2\,{\beta}^{2}u+2\,k-{u}^{2}+2\,{u}^{3}$$
for GR.

The only difference is an extra term (u is defined here as m/r).

For details see for instance "General Relativity" - Woodhouse, chapter 8.2

With a lot of hand waving we get an approximate advance of:
$$\Large 6\,{\frac {Gm\pi}{r_{{0}}{c}^{2}}}$$
where r0 is the approximate radius.

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Have looked at the other thread, I personally don't like the cone idea, it is similar to the rubber sheet example unfortunately for me it does not work in 3d space all the cones cancel out leaving a series of expanding spheres and, for example, the Earth ofbits the suns equator not around its top.
Out of interest if the distance in Newton was taken from the shwartzchild radii rather than exact centers would it bring Newton and einstein any closer, it would obviously slightly increase g in Newton especially close to a large body like the sun.
Not sure if the +2u3 above causes an increase or decrease in GR.

## 1. What is gravity according to Newton and Einstein?

According to Newton's law of universal gravitation, gravity is a force of attraction between two objects that is directly proportional to their masses and inversely proportional to the distance between them. Einstein's theory of general relativity describes gravity as the curvature of space-time caused by the presence of mass and energy.

## 2. How did Newton and Einstein contribute to our understanding of gravity?

Newton's law of universal gravitation helped to explain the observed motion of the planets and other celestial bodies in our solar system. Einstein's theory of general relativity revolutionized our understanding of gravity by providing a more accurate and comprehensive explanation of its effects on space and time.

## 3. What is the difference between Newton's and Einstein's theories of gravity?

The main difference between the two theories is that Newton's law of universal gravitation is a classical, or non-relativistic, theory that only applies to objects with relatively low masses and speeds. Einstein's theory of general relativity is a relativistic theory that can account for the effects of gravity on objects with high masses and speeds, such as those found in space.

## 4. Can Newton's and Einstein's theories of gravity be reconciled?

While there are some differences between the two theories, they are both considered to be valid and accurate descriptions of gravity in their respective domains. In fact, Newton's law of universal gravitation can be seen as a special case of Einstein's theory of general relativity under certain conditions.

## 5. How has our understanding of gravity evolved since Newton and Einstein?

Since the time of Newton and Einstein, our understanding of gravity has continued to evolve through ongoing research and discoveries. For example, Einstein's theory has been tested and confirmed through various experiments and observations, and scientists are still working to refine and expand upon it. Additionally, new theories, such as string theory and loop quantum gravity, are being developed to further our understanding of gravity and its role in the universe.