As has been well documented over recent days, there has been great excitement over the recent activity of full and partial solar eclipses, with students, astronomy enthusiasts, etc… all over showing great enthusiasm. However, a vast majority seem to be completely unaware as to *why* these solar eclipses are so important. Their most important purpose is that one can directly confirm as Eddington did in 1919 the validity of Einstein’s theory of General Relativity. When the sun is eclipsed, one can directly observe starlight from behind the sun being bent as should happen according to Einstein’s theory, namely that light bends according to the curvature of spacetime. I document here a brief calculation that demonstrates this:

We will assume that the spacetime under consideration is spherically symmetric and static, and so by Birkhoff’s theorem, outside the spherically symmetric body, the solution to Einstein’s equations is the well-known Schwarzschild metric:

To determine an equation for the path that light should follow in this spacetime, one writes the associated Lagrangian of geodesics as:

Applying the Euler-Lagrange equations and exploiting the fact that the spacetime is spherically symmetric and static, one obtains the *orbit equation* for light as:

This ordinary differential equation is a nightmare to solve!! For example, Mathematica gives:

That is, a complicated function of elliptic integrals. The easier approach is to consider perturbations as per the text of Gron and Hervik, which we do here:

Essentially, without getting into too much detail, taking this approach (See Ch. 10 of Gron and Hervik), we obtain the solution to the ODE above as:

where *b* is defined to be an impact parameter. At *u = 0*, the photon flies out towards radial infinity, and so the deflection angle, can be calculated from the relationship:

Let us perform a Taylor expansion about Pi/2, to obtain the angle by which an astrophysical body causes light to deflect by as:

For the Sun, the deflection angle turns out to be approximately

That is, the curvature of spacetime induced by the Sun causes starlight from behind the sun to be “bent”/deflected by 1.75”. This is precisely what Eddington’s team observed in their 1919 expedition. This test was what finally confirmed Einstein’s theory of General Relativity, and is the true reason why solar eclipses are so important!

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This turned out to be Einstein’s “message in a bottle” he left that no one has discussed since, because even he knew he could not talk about it without losing his scientific reputation…

[See the article titled, “The Einstein Connection: ‘One Step'” as to why on Google+ in The New Meta-physics Paradigm community here:

http://plus.google.com/communities/114246497620313813412

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the same out of date rehashed information.

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