# Can gravitational potential energy be converted to mass

This may have been answered elsewhere but I couldn’t find it. Is it the case that gravitational potential energy will add mass to an object the same way nuclear binding energy will?

In other words, as I move an object away from Earth is it gaining mass in the form of the stored energy I put into it, albeit considerably smaller than the mass gained/lost in nuclear binding energy?

## Answers and Replies

Related Other Physics Topics News on Phys.org
Mass is not a relative measurement. Weight, however, is (at least relative to the gravitational force experienced by the object).

Ok well... gravitational potential energy can't be converted to rest mass. So if that is the question; it is solved.

I thought the subject was about how gravitational potential energy contributes to relativistic mass.

Ok well... gravitational potential energy can't be converted to rest mass. So if that is the question; it is solved.
Okay let's start here. Why not? The nuclear binding energy can be, and the electron binding energy can be, so why not gravitational energy?

Does a satellite have more mass orbiting the Earth than it does on Earth?

Drakkith
Staff Emeritus
Science Advisor
Okay let's start here. Why not? The nuclear binding energy can be, and the electron binding energy can be, so why not gravitational energy?

Does a satellite have more mass orbiting the Earth than it does on Earth?
I believe it does, as you have to give the satellite a large amount of energy to make it reach and stay in orbit. Once that object starts to fall back towards Earth, it will not lose energy or mass unless it impacts something and slows down. In an highly elliptical orbit the satellites total energy stays the same, but the potential and kinetic energy both oscillate back and forth as the satellite passes between apogee and perigee.

For another example, take two asteroids that are stationary near each other at one point in time and about to collide after attracting each other at another point in time. In their initial position AND right before they collide the total energy and mass will be equal at both points in time. However after they collide the kinetic energy from the collision will be converted into heat and radiation and the two asteroids will lose energy and mass as this energy is radiated out. So gravitational energy has been converted to kinetic energy as the two approached each other, and then it was converted into thermal energy and radiated out after the collision.

I think that's all correct. Someone correct me if I'm wrong.

Okay let's start here. Why not? The nuclear binding energy can be, and the electron binding energy can be, so why not gravitational energy?

Does a satellite have more mass orbiting the Earth than it does on Earth?
I don't see why not. Each particle according to quantum mechanics has a frequency associated with it.

Just like the theoretical light clock of special relativity. If your not familiar See:
http://galileo.phys.virginia.edu/classes/109N/lectures/srelwhat.html

So let us take the light clock and put it in an accelerated frame, like an elevator.

If the clock is parallel to the floor of the elevator nothing happens, it tickets at the same rate since the ray travels both up and down in one cycle. However if it is perpendicular to the floor; the distance the light ray must travel would be slightly longer between each mirror as it ticks away.

So for all components of any quantum mechanical clock perpendicular to a gravitational field the frequency would be shifted (to an outside observer) thus altering it's momentum. The magnitude of the shift would be proportional to the distance squared which is exactly the same function of the potential energy.

Red shifting as the distance decreases and blue shift as it increased to be exact.