On the Importance of Solar Eclipses

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:

More on this calculation can be found in my handwritten notes by clicking the image below: 

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!