# Relativistic Mass and Energy Convservation

## Main Question or Discussion Point

Does relativistic energy contribute to gravitational 'pull'?

If so, then does the acceleration of a body being 'pulled' by gravity cause it to increase in mass, thus weighing more and accelerating even faster? Does an object have greater mass because it's original mass pulled it toward another body?

If kinetic energy counts as energy, contributing to relativistic mass, then does potential, as in gravitational potential energy? Does a body's mere position in space make it weigh more?

If all of this is true, then what happens when a body is suspended between two gravitational bodies? What's it's potential energy then?

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Ok, the third question answered the second and i just noticed it, but the fourth remains.

What happens when potential energy is nullified through complex gravitational systems?

In the example you gave of an object between two massive objects the GPE is still there. The object has the potential to fall towards either mass, thus they have GPE. You should remember that the mass gain with GPE is for the system as a whole. In other words lifting a mass won't increase its mass, but will increase the total mass of the system as a whole when observed from far away. Another note is that energy is still conserved in all this. Whatever additional energy a system has in GPE it gain from whatever force separated the two masses in the first place.

Dale
Mentor
Does relativistic energy contribute to gravitational 'pull'?
Energy is the 0,0 component of the Stress-Energy tensor, which is the source of gravity. However, there are 9 other independent components. So you can't just naiively calculate the "relativistic mass" and stick that in the Schwarzschild solution to gain any insight.

If kinetic energy counts as energy, contributing to relativistic mass, then does potential, as in gravitational potential energy? Does a body's mere position in space make it weigh more?
ALL forms of energy contribute to gravitational attraction, even dark energy, whatever it is. For example a coiled spring (higher PE) at a given height from the center of the earth theoretically weighs more than when uncoiled (lower PE).

Of course the position of an object in space causes it to weigh more or less....W = Mg.
A lead weight is heaver at the earth's surface than it is at an elevation of,say, one mile above the earth's surface.

The GPE of a body is the work done against gravity in displacing the particle from a reference position to its given position. The reference position will typically be zero at an infinite distance from a body, and NEGATIVE closer to the body since gravity attracts. This has almost no effect on weight since the force gravity varies so much faster than the potential energy of a particle/body or whatever.