Modern physics is full of demonstrations which confound our everyday experience. There are some oldies but goodies, like the feather and the hammer. Remember Apollo 15 (1971)?
These demonstrations illustrate the limits of everyday experience and provide interesting historical lessons.
• Physics World > “The legend of the leaning tower” by Robert P Crease (04 Feb 2003).
So why do falling-body experiments continue to be so popular? They were, for example, voted into the top 10 “most beautiful experiments” of all time in my recent poll of Physics World readers (September 2002 pp1920). I think the answer is related to the fact that, as everyday experience suggests, heavier bodies do fall faster than light ones.
Here’s a more recent article on testing the strong equivalence principle (SEP) – in a gravitational field heavy and light objects fall at the same rate. Another shout-out for research using X-ray data.
The same thing happens with you and Earth. When you jump, you fall back toward the planet very quickly. But the planet falls toward you as well — very slowly, due to your own low gravity, but at the exact same rate as a feather or a hammer would if you ignore air resistance.
• Space.com > “Einstein’s core idea about gravity just passed an extreme, whirling test in deep space” by Rafi Letzter (June 17, 2020) – Once again, physicists have confirmed one of Albert Einstein’s core ideas about gravity — this time with the help of a neutron star flashing across space.
“At some level, the majority of physicists believe that Einstein’s theory of gravity, called general relativity, is correct. However, that belief is mainly based on observations of phenomena taking place in regions of space with weak gravity, while Einstein’s theory of gravity is meant to explain phenomena taking place near really strong gravitational fields,” Morsink told Live Science. “Neutron stars and black holes are the objects that have the strongest known gravitational fields, so any test of gravity that involves these objects really test the heart of Einstein’s gravity theory.”
 Astrophysicist Sharon Morsink, University of Alberta, Canada.
 As Wiki says, more specifically:
The strong equivalence principle suggests the laws of gravitation are independent of velocity and location. In particular,
• The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution.
• The outcome of any local experiment (gravitational or not) in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
The strong equivalence principle suggests that gravity is entirely geometrical by nature (that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe. Einstein’s theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle.