Even if the magnitude of the force of gravity and buoyancy were equal, having a different location for the center of mass and buoyancy would mean that the object (or person) would not be in equilibrium. Here’s a quick demonstration for you to try. Take a pencil and place it on a table so that it points away from you. Now put your right and left fingers somewhere near the center of the pencil and push them towards each other. If you push with equal force with both fingers, the pencil just stays there. Now push towards the tip of the pencil with your right hand and towards the eraser with your left hand. Although the forces are the same, the pencil will rotate.

This is exactly what happens to the force of gravity and buoyancy on an underwater person. If gravity and buoyancy forces push with equal and opposite magnitudes, the person can rotate if their center of mass and center of buoyancy are in different places.

There’s another problem with going underwater: the water. Here’s another experiment. Take your hand and wave it back and forth as if blowing some air. Now repeat it underwater. You will notice that in water it is much more difficult to move your hand. This is because the water resistance is around 1,000 kg per cubic meters, but the air is only 1.2 kg/m3.^{3}. The water provides significant traction when you move. This is not what would happen on the moon since there is no air. So it’s not a perfect simulator.

But still, this underwater method has an advantage: you can build the floor of a pool to resemble the surfaces you want to explore on the moon.

The Einstein method

Albert Einstein did much more than develop the famous equation E = mc^{2}, which provides a connection between mass and energy. He also did significant work on the theory of general relativity, describing the gravitational interaction as a result of the bending of spacetime.

Yes, it’s complicated. But from that theory we also get the principle of equivalence. This says that you cannot tell the difference between a gravitational field and an accelerating reference frame.

Let me give an example: Suppose you get into an elevator. What happens when the door closes and you press the button for a higher floor? Of course, the elevator is at rest and must have some velocity in the upward direction to accelerate upward. But what does it do *feel* like when the elevator accelerates upwards? It feels like you are heavier.

The reverse happens when the elevator slows down or accelerates in a downward direction. In this case, you feel lighter.

Einstein said you can treat that acceleration as a gravitational field in the opposite direction. In fact, he said there is no difference between an accelerating elevator and true gravity. It is the principle of equivalence.

OK, let’s go to an extreme case: Suppose the elevator was moving with a downward acceleration of 9.8 m/s^{2}, which is the same value as the Earth’s gravitational field. In the elevator reference frame, one could treat this as a downward gravitational field from Earth and an upward field in the opposite direction due to the acceleration. Since these two fields are the same size, the net field would be zero. It would be *just* like having a person in a box without *anyone* gravitational field. The person would be weightless.