Special Relativity and Gravity

[geordief]

I think I may have heard  that Special Relativity  is able to cope with accelerating frames of reference.

If this is correct is it also possible for Special Relativity ,allied simply  to the Newtonian  formula for gravity -as being inversely  proportional to the square  of the distance between centres of mass of 2 objects -to actually make  predictions that are as good as GR?

 

Suppose the internal mass  density distributions  of Mercury , the Sun and the other bodies were known  accurately enough  could the predictions of Mercury's perihelion precession be calculated   as accurately as was done by GR ?

 

Since Special Relativity would be applicable , spacetime distances would be used rather than  "Newtonian" **units of space and time  .

 

I do not have(or am likely to acquire)  the maths skills (or the theoretical knowledge) so I am just fishing here -and hoping perhaps to pick someone's brain if my question has any merit.

 

** just calling them "Newtonian" as shorthand. I mean the way space distances and time distances  were treated separately before Special Relativity  "fused" them  together.

[Mordred]

SR handles acceleration via a type of rotation called Rapidity.

https://en.m.wikipedia.org/wiki/Rapidity

I see someone has updated this link lol. They may have gotten a bit complex for the average reader.

Lets simplify this and apply the more generally applied indices instead of the unit vectors i,j,k

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

Edited November 28, 2017 by Mordred

[swansont]

10 hours ago, geordief said:

Suppose the internal mass  density distributions  of Mercury , the Sun and the other bodies were known  accurately enough  could the predictions of Mercury's perihelion precession be calculated   as accurately as was done by GR ?

How much of a difference can that make?

[geordief]

11 minutes ago, swansont said:

How much of a difference can that make?

That is why  I am asking . I don't have the maths skills to have a "hands on"  feel to be able to say.

 

From your answer it appears to me that it would make little difference (although  I assumed -again  without the maths-that the difference between the Newtonian calculation and Einstein's might also have been extremely small)

 

[swansont]

4 minutes ago, geordief said:

That is why  I am asking . I don't have the maths skills to have a "hands on"  feel to be able to say.

 

From your answer it appears to me that it would make little difference (although  I assumed -again  without the maths-that the difference between the Newtonian calculation and Einstein's might also have been extremely small)

 

The radial distribution doesn't matter, since you can treat these as point masses in Newtonian gravity. It has to be deviations from this, in the other dimensions, that would matter. 

[geordief]

1 minute ago, swansont said:

The radial distribution doesn't matter, since you can treat these as point masses in Newtonian gravity. It has to be deviations from this, in the other dimensions, that would matter. 

I think I see what you mean . There would have to be    (stable,presumably) cavity or volumes of lower/higher  density material in Mercury for an effect to be noticeable.

 

 

 

[swansont]

2 hours ago, geordief said:

I think I see what you mean . There would have to be    (stable,presumably) cavity or volumes of lower/higher  density material in Mercury for an effect to be noticeable.

And these mass deviations from uniformity would lead to wobbling, which would potentially be measurable.

[geordief]

As a generality ,is there anything that GR can predict that SR cannot?