# Thread: Mass of the Earth

1. ## Mass of the Earth

In BBC news today, there is an article about the changing mass of the Earth. In it, Dr Chris Smith is quoted as saying
"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,"
What I have set in bold baffles me, and I suspect he is being quoted out of context. But is the statement necessarily true?

2. Sounds right. Remember that energy causes gravity, as well as matter. So, if you add energy you effectively increase the mass.

(I hope that is right because I have had a similar argument discussion on another forum...)

3. Order of Kilopi
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I would expect that thermal energy from deep inside the
Earth (leftover from the planet's formation, from decay of
unstable isotopes, or whatever) would reach the surface
and radiate away at a much higher rate than the increase
from increasing temperatures at the surface. And a few
tons of meteoritic material are added each day. I don't
remember how much air is lost each day, but probably

Okay, that's what the BBC article is all about.
Never mind.

-- Jeff, in Minneapolis

4. The article does go on to say that more energy is being lost in these and other ways than is being gained.

5. Yes, but disregarding the main thrust of the article and whether energy is being gained or lost, why would an increase in energy necessarily mean an increase in mass? Why would the rest mass of the Earth change if, say, an increase in energy is due to an increased angular rotation?

6. Originally Posted by Perikles
Yes, but disregarding the main thrust of the article and whether energy is being gained or lost, why would an increase in energy necessarily mean an increase in mass? Why would the rest mass of the Earth change if, say, an increase in energy is due to an increased angular rotation?
Energy is energy; it doesn't matter whether it's kinetic or thermal (which is the kinetic energy of molecules).

7. In the scheme of things, according to the article, where does 160 tonnes fit in? I mean, in comparison to meoterites gain and atmosphere loss.

8. Originally Posted by grapes
In the scheme of things, according to the article, where does 160 tonnes fit in? I mean, in comparison to meoterites gain and atmosphere loss.
It is a really, really tiny contribution.

I have only skimmed through the article but it looks quite good.

Originally Posted by BBC
But overall, Dr Smith has calculated that the Earth - including the sea and the atmosphere - is losing mass. He points to a handful of reasons.

9. Originally Posted by Perikles
Yes, but disregarding the main thrust of the article and whether energy is being gained or lost, why would an increase in energy necessarily mean an increase in mass? Why would the rest mass of the Earth change if, say, an increase in energy is due to an increased angular rotation?
How are you defining or thinking of the mass of the earth? Are you thinking of it as the amount of "stuff" in there (the number of atoms, or something similar)? In which, case, it may not make sense. Mass is not just a measure of how much matter there is; it is also a measure of the gravity caused by (or experienced by) something.

Both matter and energy are causes of gravity. Add energy and you increase the "amount of gravity produced". That is the same as adding mass; no, it is adding mass.

10. Originally Posted by Strange
Both matter and energy are causes of gravity. Add energy and you increase the "amount of gravity produced". That is the same as adding mass; no, it is adding mass.
I'm not disputing anything, I'm saying I don't understand it (hence the Q and A section). Is your statement a direct consequence of GR, and if so, could you point me to where I might read more about this?

11. There is an overview here: http://en.wikipedia.org/wiki/Introdu...ces_of_gravity (I'm sure there is a better description somewhere)

I'm not disputing anything
I didn't mean to suggest you were, I just wasn't sure where your doubts came from.

12. Order of Kilopi
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There are two fundamentally distinct ways of defining mass:

Inertial mass is the measure of how strongly matter resists
being accelerated by a force. Newton defined it as m=F/a.

Gravitational mass is the measure of how strongly matter
attracts and is attracted by other matter gravitationally.
Newton defined it as m1 = F * r2 / G * m2, where
m1 and m2 are two masses, r is the distance between
their centers, F is the force between them, and G is the
universal gravitational constant.

No difference has ever been detected between inertial
mass and gravitational mass. Einstein asserted, as a
postulate of general relativity, that they are one and the
same thing.

General relativity says that gravity is curved spacetime,
and that energy is what curves otherwise flat spacetime.

Mass is the most compact form of energy: A little bit of
mass contains a lot of energy. So mass is very effective
at producing gravity.

-- Jeff, in Minneapolis

13. I obviously need to do a considerable amount of homework and catch up on GR. Half a century ago, my physics degree course included SR, but the equivalence of energy and mass seemed restricted to variation of mass with speed. The equation was E = mc2/sqrt(1-v2/c2). A binomial expansion of that gives E = mc2 + 1/2 mv2 + ... I always took the mc2 to be a fixed rest energy, to which kinetic energy was added. So either that was the thinking at the time, or I just misunderstood. Or that is the difference between GR and SR.

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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?
Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it. A few questions to illustrate the foolishness of his assertion:
• what kind nuclear process is converting the heat into mass?
• what drives the process counter to entropy? What stops it running the other way about?
• if Global Warming heat is turning into mass, how come it is nevertheless still there as heat also?
• ..and how come only 'special' GW heat is converted into mass - what stops all the rest of the heat in the world disappearing down that rabbit hole?
• So have we finally found the answer to Global Warming - just package it all up as mass?

The man is talking rubbish. Without a nuclear reaction we have that mass and energy are each conserved. With a nuclear reaction mass and energy are related through Einstein's E=mc^2. But there is no nuclear reaction going on here!

15. Originally Posted by the giant peach
Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it. A few questions to illustrate the foolishness of his assertion:
• what kind nuclear process is converting the heat into mass?
• what drives the process counter to entropy? What stops it running the other way about?
• if Global Warming heat is turning into mass, how come it is nevertheless still there as heat also?
• ..and how come only 'special' GW heat is converted into mass - what stops all the rest of the heat in the world disappearing down that rabbit hole?
• So have we finally found the answer to Global Warming - just package it all up as mass?
• No nuclear reaction is necessary.
• There is no process. Nothing is counter to entropy.
• The heat is contributing to mass, not turning into mass.
• All heat contributes. What is being discussed is specifically the additional contribution due to global warming.
• That you ask this shows a fundamental misunderstanding of what is being discussed. There is no "rabbit hole" that heat is disappearing into.

Originally Posted by the giant peach
The man is talking rubbish. Without a nuclear reaction we have that mass and energy are each conserved. With a nuclear reaction mass and energy are related through Einstein's E=mc^2. But there is no nuclear reaction going on here!
The lack of nuclear reactions is completely irrelevant. E = m*c^2 does not imply or require any such thing. The misunderstanding is yours.

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so please explain the magic - how does "heat contribute to mass"

17. 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.

18. Originally Posted by the giant peach
Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it.
I assume he is talking about it because he is also a broadcaster; this is a summary of a story from the BBC's "More or Less" radio program, which is always worth listening to.

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Originally Posted by Strange
I assume he is talking about it because he is also a broadcaster; this is a summary of a story from the BBC's "More or Less" radio program, which is always worth listening to.
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.

20. 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.

21. This is very interesting but does not the original quote kind of suggest that energy is being converted into mass as a corollory of (or evidenced by) the surface temperature going up? Surely that interpretation is incorrect isn't it? (I don't mean to start a new question).

22. Originally Posted by profloater
This is very interesting but does not the original quote kind of suggest that energy is being converted into mass as a corollory of (or evidenced by) the surface temperature going up? Surely that interpretation is incorrect isn't it? (I don't mean to start a new question).
I think it is basically the same question. The important point is that the energy is not being converted to matter but it does contribute to the total mass of the Earth. The energy in that paragraph is the extra thermal energy due to global warming. (Or have I missed your point completely?)

23. Originally Posted by Strange
I think it is basically the same question. The important point is that the energy is not being converted to matter but it does contribute to the total mass of the Earth. The energy in that paragraph is the extra thermal energy due to global warming. (Or have I missed your point completely?)
I thought it was the same question as well. Now I am still confused. How would you define the difference between matter and mass?

24. 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?
I suppose matter would be defined as stuff made from leptons (http://en.wikipedia.org/wiki/Elementary_particle). Mass is a property of matter. Some of it comes from the mass of the leptons, a large part of it comes from the binding energy holding those together.

25. 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.

26. 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.

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Nobody needs to do any homework!

The OP is correct to be baffled. You don't even have to ask how the heat gain is supposed to be converted into a mass gain. Just the fact that the quote in the BBC assumes that the energy gained through global warming presents both as heat (global warming) and as mass - both at the same time - should be enough to convice you that the BBC has got this embarrassingly wrong.

Then a little school physics will tell you that there is no nuclear process going on here to drive the E=mc^2 equation anyway. And if it did, and it ran in the direction suggested (energy to mass) then that also would be a first for science. I'm sure entropy would come into that somewhere, and it points the other way.

And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.

28. Originally Posted by the giant peach
And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.
It is. I did a rough calculation for a similar discussion on another forum and came up with the total thermal energy of the earth being about 2x1014kg which is about 0.000000003% of the total mass of the earth.

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Originally Posted by Strange
It is. I did a rough calculation for a similar discussion on another forum and came up with the total thermal energy of the earth being about 2x1014kg which is about 0.000000003% of the total mass of the earth.
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.
Last edited by the giant peach; 2012-Jan-31 at 09:00 PM.

30. 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

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