# Does Mass Increase with Height?

Gold Member
Hello;

According to the GPE formula you gain gravitational potential energy as you go higher up (further from the centre of gravitation). Does this mean that your mass increases with distance?

Thanks.

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Doc Al
Mentor
Does this mean that your mass increases with distance?
Why would you think that?

Yes. (But of course its a very small increase, as Im sure you know. Even though we cant observe it in the case of a rock and small hill, we assume that it happens because we do observe it in other cases.)

Gold Member
Why would you think that?
Because I thought that mass was a form of energy, and the equation for GPE is;

Change in GPE = Weight x Vertical Height Difference

So increasing height difference = increasing GPE = increasing mass?

It is a good question, does potential energy increase mass as well as kinetic energy. You could apply any amount of potential energy to any object depending on where you set V_0.

Say you set V_0 an infinite distance away. Would you become infinitely massive?

Doc Al
Mentor
Because I thought that mass was a form of energy, and the equation for GPE is;

Change in GPE = Weight x Vertical Height Difference

So increasing height difference = increasing GPE = increasing mass?
The increase in gravitational potential energy as you move away from the center of the earth is a property of the entire earth+you system, not just you. You can think of the energy as being stored in the gravitational field. So your mass doesn't increase, but the mass of the earth+you system taken as a whole may theoretically increase.

But that would only be the case if something external to the system lifted you up and added energy. If you just walked up a hill, the total energy of the system hasn't changed--you've just transformed some of your internal energy (food, etc.) into gravitational PE. I would not expect a theoretical net mass increase since there's been no input of energy.

hmm, interesting. Is the same idea true for chemical and nuclear things?

It is a good question, does potential energy increase mass as well as kinetic energy. You could apply any amount of potential energy to any object depending on where you set V_0.

Say you set V_0 an infinite distance away. Would you become infinitely massive?
No, at infinity you’d only reach your maximum mass. A gravitational bond is a negative energy bond, so you start with your rest mass at infinity where there’s zero attraction, then subtract the negative potential energy of the bond as you approach the gravitational body (the Earth in this example, I presume).

hmm, interesting. Is the same idea true for chemical and nuclear things?
Absolutely. In fact at the nuclear scale, the binding energy between nucleons is so intense that the drop in net mass when nucleons bond together can be easily measured as a significant fraction of the overall mass (and the ‘rest mass’ that’s lost in the process always appears in the form of photons and/or kinetic energy). Also, it’s the intensity of some chemical bonds that causes a great deal of heat to be released (sometimes even explosively) when some compounds are formed.

Whenever two bodies interact attractively, the strength of the bond can be measured by the amount of mass reduction (or equivalently, by the amount of energy released) in the binding process.

The rather absolute notion that we have of bodies of constant mass is mistaken, in the context of the flux of varying interactions all around us all of the time. Mass is actually a variable within this context - we just don’t usually account for it because the variation is more or less negligible in all but nuclear interactions.

Yea, I get that much. I mean the part where he says the extra mass is stored in the field. I never heard that before, is that the case in chemical and nuclear? Im suspicious.

Yea, I get that much. I mean the part where he says the extra mass is stored in the field. I never heard that before, is that the case in chemical and nuclear? Im suspicious.
To say that the ‘extra mass’ is stored in the GPE field is a fair way of talking about it, since we know that all fields possess mass-energy.

Consider a particle with a positive electrical charge. Part of its mass is stored in the field of charge that surrounds the central mass of the particle. So when the positively-charged particle captures a negatively-charged particle, some of both charge fields are nullified, and both particles reach a lower mass-energy state together (a bound condition).

You can look at any attractive field interaction this way, whether it’s a gravitational, an electromagnetic, or a nuclear strong force interaction.