# Thread: Mass of the Earth

At first I thought we were discussing a mass increase due to the energy being released by nuclear decay inside the Earth and was getting extremely confused. If mass was being converted to energy of which at least some should be radiated into space, then shouldn't the planet be getting *lighter*?

Then I saw that they were talking about global warming as adding energy which I take is what they mean by mass increase by equivalency. Meaning energy added from the *outside*, i.e. the sun, is trapped by greenhouse gases and is increasing the Earth's mass by m=E/c^2, where E is the additional energy held on to, so to speak, by greenhouse gases as part of AGW.

Did I get that right?
Last edited by Marakai; 2012-Jan-31 at 10:43 PM. Reason: Typing on an iPad on a train combiened with auto-correct does strange things

2. I think that is it. The earth is obviously not a closed system, energy enters from the sun. The greenhouse gases, and other effects such as reflectivity determine how much is trapped and how much is radiated to space. If more is being trapped then the overall mass of the system, being made up of contributions from both matter and energy must increase.

3. Order of Kilopi
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Originally Posted by the giant peach
or have I been guilty of confusing mass with matter and regarding the two as identical concepts?
I think this is the case. As has been pointed out by strange in post #22, there is an amount of energy in a particle of baryons, atoms, molecules, etc, that is part of the mass of that particle. For instance, the matter in a proton is composed of two up and one down quark. An up quark has a mass of ~1.7-3.1 MeV and the down quark has a mass of 4.1-5.7 MeV. As a result, the most mass, as matter, a proton can have is 3.1+3.1+5.7 = ~11.9 MeV. The rest of the proton's mass of 938.23 MeV (~926 MeV) is the energy required to bind the quarks together.

Most people see the algebraic equations of special relativity. However, some clarity may be gained by using four-vectors. The time component of the energy-momentum four vector represents the rest energy and is frame invariant. This has also been called the rest mass. Either way, the value of the two terms (mass, energy) are equivalent.

In Newtonian (or Classical Mechanics) this was the mass of what ever matter was being considered. At the low energies encountered in every day life, the energy and mass can be considered pretty much the same(which is why Classical Mechanics worked, and still works for most things). In SR, the total rest energy is considered, so yes, if there is an increase in heat, there is more energy in the system, so there is a higher value for the time component in the four-vector, or more mass. It's just the the increase due to the heat content, considered on an individual particle basis is so small, it is usually ignored. If you think about it, the fission conversion factor in early weapons was only 2 percent, the thermal conversion is much less. I think it was 200 MeV for fission events and 3-4 eV for thermal events. Those thermal events are going to be extremely hard to detect on their own, but when totaled from an increase over the entire mass of the Earth, huge.

Marakai, you got it right.

transreality, that is it.

4. 1 PV=nRT ? never mind 2 where does Smith attend 3? take 8Oz H2O Boil it & weigh

Originally Posted by Perikles
In BBC news today, there is an article about the changing mass of the Earth. In it, Dr Chris Smith is quoted as saying
What I have set in bold baffles me, and I suspect he is being quoted out of context. But is the statement necessarily true?
once upon a time? i tried to calculate the increase in the mass of earth ?/?
by looking at the deposit //// depth of grand canyon layers v time
i dont remember exacty what i came up with BUT i do remember i thought
Earth in galatic orbit 1 was about 1/2 half of what it is now Orb 18 ? 20
Mass of Earth 2000 ?
this tail is about a period of time some call a galyear that i call 24e7
24e7/1000 = 24e4 Thousands of Earth years / ORb ?/?
at a mass accumulation rate of ? per 1000 Ey'es
however it probably is not linear it probably decreases with time \ ? ~4.5678 By ?
24e7 * 20 = 4.8e9 by by: |/|/
6CABAN changes in Earth parameters with Time Feb guesses
% % % %%% Diameter of the Earth for 20 Orbits (MatLab Script}
d1=6000 %Km
d20 = 13000 %km
ORb = linspace(6000,13000,20);
ORt=1:20;
%%%% now try to apply the Fox { i do think this is WRONG {{ ?/?
fo=ORt.^3;
for j=1:20
fox(j)= 13000-fo(21-j);
end
%%% % volume 4/3*pi-r^3 ?
r=fox/2;
v=4/3*pi-r.^3;
%%% % Earth, Mass (kg): 5.98 × 10 24 kg
V_2000= 4/3*pi*((12756.1/2)^3)
Mass = 5.98*10^24 % kg
KGpKm=Mass/V_2000
mv = KGpKm*v;
mvp = diff(mv);
plot(ORt,fox)
plot(ORt,r)
plot(ORt,v,'go')
plot(ORt,mv,'b+')
plot(ORt(2:20),mvp,'C*')

% % % %%% t_End = 2351 t_Spent = 43
======================PART2
.5 * .3 * (mass of the earth) * (radius of earth)^2 / (86140 sec)^2
Result: Show details
1.89×10^21 kg mi^2\/s^2 (kilogram miles squared per second squared)
.A Input interpretation: Earth | mass ::: Result: 5.9721986×10^24 kg (kilograms)
B. Input interpretation: Earth | average radius Unit conversions: 6367.5 km

.wolframalpha.
Last edited by HUb'; 2012-Feb-02 at 10:02 AM. Reason: 6

5. Originally Posted by the giant peach
so please explain the magic - how does "heat contribute to mass"
If the Earth absorbs more heat then it radiate back out into space then this heat adds to the mass because it is energy being added to the Earth system

If I have a box of photons then I can calculate the gravity of those photons even tho they have no rest mass themselves.

So if you want to know how much mass the Earth gain from incoming solar energy you have to do this

Compute the incoming solar energy ... lets call this E

using E=mc2
we can figure out how much that equates to in mass by rearranging the formula.
m=E/c2

I know c2 is a REALLY big number so you need a LOT of energy to create the same effect as a good just of matter.

You also have to figure out how much energy the Earth radiates back out into space and subtract that from the incoming energy.

The point is with global warming the Earth is absorbing more energy then it radiates back out into space. This also causes more of the atmosphere to be lost and that to should be factored into the equation. But at the end of the day the more energy you pump into the Earth's system the stronger its gravity but really it is such a small amount.

160 tons...compared to the mass of the Earth which is 5.9736x1024
so 1.6x105
that leave you with 1.6/5.9736x1019
which is ~2.67845x10[/sup]-20[/sup]
or 0.00000000000000000267845%
and that is a year's worth of energy.

6. Originally Posted by Perikles
I thought it was the same question as well. Now I am still confused. How would you define the difference between matter and mass?
All matter has mass. Energy not only can be transformed into matter but even staying in the form of energy it has a an equivalent effect as some amount of mass which can be computed via the same E=mc2

Say I take 1kg of matter and 1kg of anti matter and bring them together. They'll annihilate and produce a HUGE amount of photons. But If I'm on the moon when that happens I'll still measure the gravity of the Earth being the same even though 2kg of it was just annihilated. As soon as I see that flash ... well a lot of that energy would have left the Earth. That is the flash I would see. Some of the 2kg of energy would stay on the Earth because some fraction of the 2kg worth of photons would have just heated up the surrounding area. Its only the amount of photons that leave the Earth that reduces the mass of the Earth.

7. Originally Posted by the giant peach
so if all the earth's heat is turning into mass then we should all be frozen solid by now. You can't have it both ways - it can't manifest itself as heat and as mass simultaneously.

As to other's suggestions that heat "contributes" to mass, please explain the mechanism. Just to be clear about the original quote from the BBC:

"Nasa has calculated that the Earth is gaining about 160 tonnes a year because the temperature of the Earth is going up. If we are adding energy to the system, the mass must go up," says Dr Smith.

So Dr Smith is unambiguous - adding energy to a system increases its mass. Apparently.
yes it can. It can't be heat and matter at the same time.
a given amount of heat has an certain amount of mass equivalence

8. Originally Posted by the giant peach
I know he is a broadcaster, he goes by the name of The Naked Scientist. The thing is, he puts himself forward as a specialist. Which he is, just not in that field. In that field he is just a layman.
Just because he's a medical doctor doesn't mean he can't know stuff about other areas of science. You'll find in astronomy lots of specialist that don't have any formal degrees in the field. In fact I personally know a few people who's hobby is astronomy that know more about certain aspects of astronomy then most fully qualified astronomers just because they are focused in a different area. Doesn't matter that my friends don't have 8 years of study under their belts. Hell some of them have a pretty good publication record even for a professional astronomer.

So before you call someone a layman you should find out what their level of knowledge in that area is not just say something like "Oh he's a janitor, he couldn't possibly a great cook" because that is basically what you are saying.

9. Originally Posted by WayneFrancis
All matter has mass. Energy not only can be transformed into matter but even staying in the form of energy it has a an equivalent effect as some amount of mass which can be computed via the same E=mc2.
This is a distillation of various other statements above which was the fundamental issue I was unaware of. What I really don't understand is how I have forgotten this, or was never actually aware of it in the first place, from the SR course I took 50 years ago. It is after all of fundamental significance. I guess I must have had a hangover on the day of a key lecture. I get the impression that the focus and presentation of SR has changed a lot over a few decades.

Thanks everyone for the helpful posts.

10. Originally Posted by NEOWatcher
I think it's a matter of the way it's worded.
Before the phrase "global warming" was common, the accepted term was "greenhouse gas". I've heard of the greenhouse effect all my life (or it seems so).

So; if I project my understanding of this onto the story, then the heat of global warming is not from the warming itself, but from the extra heat that is trapped by the greenhouse effect that causes the global warming.
correct. Note that global warming while is caused by what we dump into the atmosphere it isn't the actual stuff we dump into the atmosphere. It is the photons coming from the sun, heating up the Earth and the Earth re-radiating that back out into space but before it can the green house gases reflect it back to the Earth.

IE there is an excess inflow of energy coming to Earth from the sun. Green house gases just lower the rate at which the heat is radiated back out into space.

11. Again I do not seek to alter the question but since temperature is a measure of energy should the gravitational mass of an object (any and every object) be expressed as a function of (rest) mass and its temperature? Even if the additional term is tiny. And since ( I thought thus far) temperature has a zero but no upper limit what is this expression?

12. Originally Posted by the giant peach
Energy does turn into mass, and mass into energy. That is exactly what E=mc^2 means.
Energy CAN turn into mass but it doesn't have to. Gravity isn't just from matter. This effect we are talking about doesn't turn energy into mass but you still have to account for that energy in the equation to calculate the total mass of the Earth.

Originally Posted by the giant peach
Mass into energy - that is what atomic bombs do, mass converted into energy. Explode an atomic bomb in a closed system and the outcome is less mass that your started with (and a lot more energy).
Yup but if you think that is all that E=mc2 means then you are mistaken and you should listen to people tell you that energy(E) has a m(mass) equivalent even while it is in energy (E) form and you can calculate that by E=mc2. You don't need to actually convert the energies form to get the gravitational effect.

Originally Posted by the giant peach
Energy into mass - happens in high energy particle beam collisions. But, crucially, it isn't hapening when the earth warms up through global warming. The heat energy remains very much as plain old heat, the earth gets warmer (so they say).
No you are wrong. In the LHC there is no extra gravity being created. Some where a power plant is creating energy from a chemical or nuclear reaction. The mass of the molecules, in a chemical reaction, is being reduced when the atoms are being split apart.
I take some source of carbon
I use a little bit of energy to start the reaction

C-C + O[sub]2[sup] => C=O=C

energy to break the C-C bond 83 kcal/mole
energy to break the O[sub]2[sup] bond 119 kcal/mole
total energy required 83 + 119 = 202
energy released tho is 354 kcal/mole
That means we have a release of 152 kcal/mole of carbon burned

The 2 molecules of CO2 have a smaller amount of mass then the original C[sub]2[sub] and 2 O2 molecules

This energy travels to the LHC where it is used to speed up the hadrons
The hadrons gain an equivalent amount of mass based on their speed. Most of the energy tho goes into heating the magnets. The Earths system hasn't lost gravity because of the creation of electricity.

Nuclear power isn't much different except instead of molecular binding energy, which is MASS, being converted it is nuclear binding energy, which is still MASS.

With global warming the energy coming in is from the SUN. External to the system. So that is a certain amount of mass equivalent that is being added to the Earth system.

Originally Posted by the giant peach
You seem to be implying that enegy is (figuratively) like the shadow of mass, the two accompany each other about inseparably, their relative quantitly governed by E=mc^2
But an amount of energy is not at the same time an amount of mass - the two are interconvertible, the equivalence given by E=mc^2
Just like kinetic and potential energy can be converted one to the other, as a mass bouncing on a suspended spring. So you if you start the system with the spring fully stretched all the energy is PE. It is not simultaneously present as KE. But when you release the spring and the mass boings up to its maximum velocity, then all the energy is converted to KE. There is a one-to-one conversion (excepting friction losses etc). So mass and energy are interconvertible.

EDIT
or have I been guilty of confusing mass with matter and regarding the two as identical concepts?
Yes you have been guilty of confusing mass with matter.

The key is the extra stuff is coming in from the sun. It happens to be photons. Think of it this way. Say I'm in a lab and from energy I create some matter. Does the mass of the Earth go up when that matter is created? No, it was already here in the form of the energy that was used to create that matter. Heat is just a form of energy and the heat of global warming isn't from the Earth but from the sun.

13. Originally Posted by profloater
Again I do not seek to alter the question but since temperature is a measure of energy should the gravitational mass of an object (any and every object) be expressed as a function of (rest) mass and its temperature? Even if the additional term is tiny. And since ( I thought thus far) temperature has a zero but no upper limit what is this expression?
Yes but remember that most of the time that is such a small percentage like.... 0.000000000000001% or so for the Earth it really doesn't matter :P
In actuality the amount is so far below the error bars we deal with when measuring large objects that it is treated as 0
And because smaller objects, ie atoms, have almost no measurable gravitational effect on their own it can also be treated as 0

14. Originally Posted by Marakai

At first I thought we were discussing a mass increase due to the energy being released by nuclear decay inside the Earth and was getting extremely confused. If mass was being converted to energy of which at least some should be radiated into space, then shouldn't the planet be getting *lighter*?

Then I saw that they were talking about global warming as adding energy which I take is what they mean by mass increase by equivalency. Meaning energy added from the *outside*, i.e. the sun, is trapped by greenhouse gases and is increasing the Earth's mass by m=E/c^2, where E is the additional energy held on to, so to speak, by greenhouse gases as part of AGW.

Did I get that right?
Yup.

15. Originally Posted by WayneFrancis
Yes but remember that most of the time that is such a small percentage like.... 0.000000000000001% or so for the Earth it really doesn't matter :P
In actuality the amount is so far below the error bars we deal with when measuring large objects that it is treated as 0
And because smaller objects, ie atoms, have almost no measurable gravitational effect on their own it can also be treated as 0
Thank you for this but there also large objects such as galaxies which are thought to have dark matter and dark energy where the percentage might be higher I suppose? Sorry to go on about this but I am having a paradigm shift I think and need another coffee to settle down/up.

16. Originally Posted by Perikles
What I really don't understand is how I have forgotten this, or was never actually aware of it in the first place, from the SR course I took 50 years ago.
It may not have been covered in a course on SR. You might get told that E=mc2 but not that energy is a cause of gravity (as that is GR).

17. Originally Posted by profloater
Thank you for this but there also large objects such as galaxies which are thought to have dark matter and dark energy where the percentage might be higher I suppose? Sorry to go on about this but I am having a paradigm shift I think and need another coffee to settle down/up.
As I understand it Dark Energy can be pretty much ignored on the galactic scale. Not only is is VERY small but it is essentially a negative type of energy. IE it would weaken the gravitational effect of normal mass regardless of the source, energy, normal baryonic matter or dark matter. The amount of energy leaving a galaxy while huge is also very small compared to the mass within that galaxy. Like wise the amount of energy incoming to the galaxy would be very small. I believe, without crunching the numbers that the amount of energy leaving would be greater then coming in. But being that the universe is homogeneous and isotropic at the large scale...I think even then it would be less if for nothing else the energy coming in would be effected by cosmic red shifting

18. Originally Posted by Strange
It may not have been covered in a course on SR. You might get told that E=mc2 but not that energy is a cause of gravity (as that is GR).
Yes, I think that might be the case. So if an increase in energy of a body represents an increase in mass, a rotating Earth has greater mass than a non-rotating one, the mass difference being equivalent to ½Iω2. Is that right?

19. Originally Posted by Perikles
Yes, I think that might be the case. So if an increase in energy of a body represents an increase in mass, a rotating Earth has greater mass than a non-rotating one, the mass difference being equivalent to ½Iω2. Is that right?
I hesitate to just say yes to that because I suspect the rotation may cause complications. After all, the solution of the field equations for a rotating (Kerr) black hole is very different from a non-rotating one (Schwarzschild).

20. If that were the case rotation would be equivalent to temperature???

21. Originally Posted by Perikles
Yes, I think that might be the case. So if an increase in energy of a body represents an increase in mass, a rotating Earth has greater mass than a non-rotating one, the mass difference being equivalent to ½Iω2. Is that right?
I typed this into Wolframalpha:

.5 * .3 * (mass of the earth) * (radius of earth)^2 / (86140 sec)^2

and got 4.895 x 1027 joules. Dividing by the speed of light squared gives

5.5 billion metric tons, about one trillionth of the mass of the earth.

ETA: In case you want to play with it yourself, Wolframalpha keeps track of the conversions too.

.5 * .3 * (mass of the earth) * (radius of earth)^2 / (86140 sec)^2 / (29792458 m/sec)^2 /(mass of the earth)

EETA: Since the Earth is slowing due to tidal friction, about .023 sec per year, it's losing about 2*.023/86140 of that mass each year, or about, let's see, 3000 metric ton per year. Did that make the list?

22. Originally Posted by grapes
I typed this into Wolframalpha:....

5.5 billion metric tons, about one trillionth of the mass of the earth.

EETA: Since the Earth is slowing due to tidal friction, about .023 sec per year, it's losing about 2*.023/86140 of that mass each year, or about, let's see, 3000 metric ton per year. Did that make the list?
No it didn't. Thanks for all that - I had no idea of this relativistic effect on mass.

23. Originally Posted by WayneFrancis
As I understand it Dark Energy can be pretty much ignored on the galactic scale. Not only is is VERY small but it is essentially a negative type of energy. IE it would weaken the gravitational effect of normal mass regardless of the source, energy, normal baryonic matter or dark matter. The amount of energy leaving a galaxy while huge is also very small compared to the mass within that galaxy. Like wise the amount of energy incoming to the galaxy would be very small. I believe, without crunching the numbers that the amount of energy leaving would be greater then coming in. But being that the universe is homogeneous and isotropic at the large scale...I think even then it would be less if for nothing else the energy coming in would be effected by cosmic red shifting
Thanks again, this thread has made things much clearer for me and as i awake from my ignorance I can wonder if these small effects can in themselves be experimentally verified and secondly if the universe is isotropic at large scale but with cosmic red shift, that implies a continual energy loss into the void between matter exactly equivalent to cosmic expansion, doesn't it?

24. kzb
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I make 160 tonnes of energy to be about 46 Terawatt-years. That being the case it is a very small fraction of the energy budget, and in fact is smaller than the uncertainty on how much energy the planet absorbs from solar energy (about 120,000TW).

It's on the same scale as the energy from radioactive decay. But you can treat this as energy produced = energy lost, that is, the decay heat is being lost as fast as it is produced.

But the radionuclides themselves have lost mass in the decay process. The decay products are lighter than their parents. I've not calculated it, but I guess this mass loss completely dwarfs this 160 tonnes per year.

25. Originally Posted by profloater
If that were the case rotation would be equivalent to temperature???
No. Temperature is a measure of the intensity of heat in the body. That heat is the kinetic energy of the internal wiggling and jiggling of the molecules that normally is present even when the body is stationary overall. The act of moving it bodily or spinning it does not necessarily raise the temperature.

26. Originally Posted by kzb
It's on the same scale as the energy from radioactive decay. But you can treat this as energy produced = energy lost, that is, the decay heat is being lost as fast as it is produced.

But the radionuclides themselves have lost mass in the decay process.
Their loss of mass is, of course, exactly equal to the energy released. So if the energy stayed trapped in the earth it would make no difference.

For instance, the Earth's core is like a giant nuclear reactor that is gradually losing energy over time, and that loss in energy translates into a loss of mass.

But this is a tiny amount - he estimates no more than 16 tonnes a year.
I have no idea if that is accurate or not (feels a bit low, for some reason).

27. I think it is apparent from all of this that these changes are vanishingly small in proportion to the total mass of the Earth. If I am not mistaken, there is not an instrument anywhere that is sensitive enough to detect it.

28. Originally Posted by Strange
I have no idea if that is accurate or not (feels a bit low, for some reason).
A few thousand km of rock makes a pretty good insulator. The equilibrium temperate of Earth's surface without the sun heating it would be quite low, despite the high core temperature. With solar input, the heat from below barely makes a difference.

I'm not sure where the analogy to a nuclear reactor comes in, though, since it doesn't sound like he's referring to the speculation about it literally being a natural nuclear reactor.

29. Originally Posted by Strange
Their loss of mass is, of course, exactly equal to the energy released. So if the energy stayed trapped in the earth it would make no difference.
But this is a tiny amount - he estimates no more than 16 tonnes a year.

For instance, the Earth's core is like a giant nuclear reactor that is gradually losing energy over time, and that loss in energy translates into a loss of mass.
.
More confusion on my behalf. So is he saying that the Earth is losing a nett 16 tonnes a year mass in this manner despite the fact that most of the energy is retained in the Earth, or is that the total mass loss due to radioactive decay? The article smacks of being written by a journalist who does not quite understand what's going on.

30. Originally Posted by Hornblower
I think it is apparent from all of this that these changes are vanishingly small in proportion to the total mass of the Earth. If I am not mistaken, there is not an instrument anywhere that is sensitive enough to detect it.
Yes, true, but the thrust of my original question was not the actual values, but the theoretical principles which involve the changes in mass, irrespective of whether these were measurable.

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