Einstein’s General Theory of Relativity is what we use to describe gravity and it has passed many experimental tests since Einstein devised it in 1915.
One of the things Einstein postulated is the pseudo-force we feel when we’re accelerated, such as being pressed back into our seats, is equivalent to the gravitational force.
He said that:
Inertial Mass x Acceleration = Gravitational Mass x Intensity of Gravitational Field
This explains why astronaut David Scott’s hammer and feather fell at the same speed on the moon during Apollo 15. The inertia of a hammer (i.e. its resistance to movement) is greater than the inertia of a feather to a degree that cancels out the differing gravitational attraction of the masses due to gravity, hence they fall at the same speed (in a vacuum — we see differences on Earth due to air resistance).
To be fair, Galileo, Kepler, Newton and many others all had ideas about the Equivalence Principle long before Einstein, but Einstein brought it all together, reframed it and expanded it in his General Theory of Relativity.
One bit that Einstein expanded — and is hence called the Einstein Equivalence Principle — is:
The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
This basically states that all the laws of physics are the same everywhere. It’s easy to say “of course they are” because that’s our everyday experience, but these things need to be tested under extreme conditions to be certain a theory holds true.
The details of Einstein’s theory also highlight differences to Newton’s theory of gravitation and many of the proofs for General Relativity set out to find these predicted differences, which are often only apparent in extreme circumstances.
So the article I link to describes an experiment to test things by looking at the light from a star orbiting a black hole, which is a fairly extreme set of conditions.
The experiment found the redshifts of the light it observed are 43,000 times more likely under Einstein’s theories than they would be under Newton’s.
Einstein wins again but scientists still expect his theories to break at some point when they come up against Quantum Mechanics in even more extreme conditions.
One sexy aside to this experiment — for anyone who hasn’t nodded off by now — is the situation with gravitational redshift. An object attempting to climb away from close to a black hole (or any mass for that matter) should lose energy and slow down because the gravitational forces of the black hole will be pulling it backwards.
This applies to light photons too. But the speed of light is constant, so how do we slow it down? Well, we don’t and Quantum Mechanics comes to the rescue. Light can be either a wave or a particle (but not both in any given experiment) and we need to see it as a wave here. The energy of light is related to its frequency, so by stretching out its waves, the frequency drops and so does its energy. This energy is what’s lost to the black hole, and stretched out light waves move from the blue end of the spectrum to the red end, hence ‘redshift’.
So Quantum Mechanics and General Relativity combine to provide the solution, which is ironic given that the theories spend much of their time at loggerheads these days.