Variation in mass with gravitational potential energy [duplicate]

As we lift object above planet, it's gravitational potential energy increases so according to E=mc^2 will it's mass increase?

• Does this answer your question? Why does my apple not weigh 500 tons? Dec 27 '19 at 16:20
• So, from the dupe question suggested by Kyle, if some system external to the (Earth + object) system does work to lift the object, the amount of work E will equal the change in the gravitational potential energy of the object relative to the surface of the Earth, and the rest mass of the (Earth + object) system will increase by $E/c^2$. Dec 27 '19 at 16:33
• Even in pure classical physics potential energies should be associated with the system that generates them rather than with a one part of that system; the potential energy is due to the relative position of the apple and the Earth and if you take the Earth away there is no positional energy just as much as if you take the apple away. Dec 27 '19 at 19:24
• That said, we regularly violate this rule in intro classes when we ascribe the energy to the apple, but (a) it is a lot shorter than saying "the potential energy of the Earth-apple system", and (b) in out day to day life the earth is the other half of every gavitational system and naming it is a bit redundant. Dec 27 '19 at 19:24