Let’s say we have a system where two objects are rotating each other and one object falls into the other. There is a device in the larger object that is somehow capable of transforming this tapped gravitational potential energy into mass, so the total mass of the system is larger than when the objects were rotating each other.

Would a third object at a sufficiently large distance away from the pair register an increased gravitational effect from the system afterward, despite that the total mass-energy (if you count gravitational potential) of the system was unchanged? Or would some other factor (such as the system pressure?) mean that the gravity is unchanged?

If the objects “fell into each other” (occupied the same space) wouldn’t they no longer have a gravitational potential energy with relationship to each other?

One object falls toward the other, hitting the other at a certain velocity. The second object, in the act of decelerating the second object, converts the realized potential into mass via a yet to be invented device (perhaps a spring attached to some proton-electon generating machine ).

I don’t get what you mean by “gravitational potential energy”. The gravitational pull of the two objects is proportional to their mass and distance from each other. If one object falls into the other, it no longer has any potential energy.

The gravitational forces on the third object would be the sum of the forces of the other two objects and would be dependent on their masses and distances from each other.

The velocities of the object really don’t play a role here.

I’m not sure the physics here are correct. Isn’t gravity a constant attractive force rather than a potential force? The gravity doesn’t disappear when two objects collide; in fact it grows stronger because they are closer.

I don’t think the idea of converting gravity into mass is workable either. Gravity is an inherent property of mass. If you could convert gravity into something else you could create mass without gravity, which I think is impossible. And if you were somehow able to convert a given mass’s gravity into additional mass, that additional mass in turn would have its own gravity. I think at some point, the math breaks down.

Which is why I specified that the third object was at a sufficient distance, since it would be unaffected by the relative positioning of the objects within the system, only the total mass-energy

You’re really converting velocity-energy into mass, which happens sometimes in high-speed particle physics, but I don’t know if it’s even theoretically possible to tap this on subrelativistic and macroscopic objects.

Not if there was some mechanism whereby the total gravitation in a system stays the same

This here is the key part of the question. You don’t need such a device, since the gravitational potential energy was already mass in the first place, and it always will be mass, no matter what you do. Mass is just another word for the energy a body has in the reference frame where it has zero momentum. So long as you maintain a consistent definition of what constitutes your system, mass is always exactly conserved.

I thought this might be part of it. So the only way that the objects could have rotated around each other in equilibrium is if they had a certain velocity, which would increase its mass from the perspective of the third observer, and this would nearly exactly equal the potential energy realized in putting them nearby each other and at rest?

Is that true? When the objects strike, aren’t you converting mass into energy in the form of heat/radiation - so your system will lose a miniscule amount of mass and gravity at the same time.

I don’t believe that gravity or mass exist without each other anywhere in nature. I don’t think that there could be a mechanism that could convert gravity to mass.

If you consider the system to include the radiation given off, then the mass still stays constant. If you don’t count the radiation as part of the system, then the mass of the system changes.

So if I’m understanding the question correctly, what’s being asked is what happens if two objects collide into each other due to gravitational attraction and some of the energy caused by that collision is converted into mass? If so, then I would say that because there is now more mass, the total amount of gravity present would be greater than before the collision.

The source for the gravitational field isn’t mass, it’s total energy(**). It doesn’t matter (heh) what form the energy is in.

The gravitational field of two masses near each other is due to the total energy of the system, including the (negative) gravitational binding energy. As those masses fall towards each other, the binding energy becomes more negative, and the masses gain kinetic energy, but the total energy is constant(*) and the gravitational field far away is unchanged.

When the masses collide, the kinetic energy is converted to heat, but again the total energy is unchanged(*), and so is the gravitational field.

(*) Neglecting gravitational radiation.
(**) It’s actually the Stress-energy tensor. For something like the Earth, the T[sub]00[/sub] component is energy, and is by far the largest component.