general relativity - How can gravity affect light?

I understand that a black hole bends the fabric of space time to a point that no object can escape.

I understand that light travels in a straight line along spacetime unless distorted by gravity. If spacetime is being curved by gravity then light should follow that bend in spacetime.

In Newton's Law of Universal Gravitation, the mass of both objects must be entered, but photon has no mass, why should a massless photon be affected by gravity in by Newton's equations? What am I missing?

Answer

Newton's law does predict the bending of light. However it predicts a value that is a factor of two smaller than actually observed.

The Newtonian equation for gravity produces a force:

$$ F = \frac{GMm}{r^2} $$

so the acceleration of the smaller mass, $m$, is:

$$ a = \frac{F}{m} = \frac{GM}{r^2}\frac{m}{m} $$

If the particle is massless then $m/m = 0/0$ and this is undefined, however if we take the limit of $m \rightarrow 0$ it's clear that the acceleration for a massless object is just the usual $a = GM/r^2$. That implies a photon will be deflected by Newtonian gravity, and you can use this result to calculate the deflection due to a massive object with the result:

$$ \theta_{Newton} = \frac{2GM}{c^2r} $$

The calculation is described in detail in this paper. The relativistic calculation gives:

$$ \theta_{GR} = \frac{4GM}{c^2r} $$

The point of Eddington's 1919 expedition was not to show that light was bent when no bending was expected, but rather to show that the bending was twice as great as expected.