[chris (OP)]

Dave and I were doing a calculation for another radio programme today and the stats we looked up suggest that Earth is losing hydrogen at the rate of up to 3 kg per second! Multiplied by 31.5 million (the number of seconds in a year), this adds up to an alarming 90,000 tonnes a year! Luckily it will still take a trillion years or so to empty Earth's oceans, even at this rate. I was, however, quite gobsmacked that the number was so high...

[RD]

someone agrees with your 3Kg of Hydrogen per second figure ...

The loss rate is currently tiny, only about three kilograms of hydrogen and 50 grams of helium (the two lightest gases) per second,

http://www.scientificamerican.com/article.cfm?id=how-planets-lose-their-atmospheres


It's not all loss though : gases like Helium are created through radioactive decay of sold matter.

[CliffordK]

I presume some hydrogen is also gained from cosmic rays, which is the primary source of tritium on Earth.  Although, I thought the tritium was coming from the sun, but it may be that the tritium is being formed on Earth from proton/nitrogen impacts from cosmic rays.

Hmmm, ¹⁴C is also produced on Earth.

¹n + ¹⁴N → ¹⁴C + ¹p

Which results in 1 proton being released.  Perhaps ¹⁴C and Tritium could help with an estimate about the amount of Hydrogen that is being absorbed on Earth, although I would imagine that there is a real cascade of interactions with cosmic arrays including ejecting some of our atmosphere.

Luckily it will still take a trillion years or so to empty Earth's oceans, even at this rate. I was, however, quite gobsmacked that the number was so high...

I'm doubtful there will be much left on Earth in a trillion years...  if there is, it will either have to jump stars somehow, or will be engineered into something very different than we have today (moved to a Jovian orbit or converted into a Dyson's sphere?)

The Scientific American article suggested that the oceans could be depleted in a few billion years which is on a scale that could impact humanity or our progeny if it in fact comes true.

[Soul Surfer]

That is a calculated loss based on the abundance of these gases in the upper atmosphere and the escape velocity and temperature together with the statistics of the particle velocities.  It takes no account of the rate at which material is being added to the earth from meteors and there are strong suggestions that there are quite a lot of small "snowflake" meteors still coming into the upper atmosphere almost unobserved so the influx of hydrogen may exceed the loss

[CliffordK]

there are strong suggestions that there are quite a lot of small "snowflake" meteors still coming into the upper atmosphere almost unobserved so the influx of hydrogen may exceed the loss

If you are talking about ice crystals, I'm doubtful. 
While some of our meteor showers are blamed on comets, I would have to assume that most of the ice crystals are melted by the time they would get to Earth.

However, melted doesn't mean that the matter is lost.  So, even individual gaseous H₂O molecules might be trapped by our atmosphere, especially if they could penetrate through the thermosphere.

[peppercorn]

Dave and I were doing a calculation for another radio programme today...

Was pleased to hear this snippet of Chris talking on "More or Less" on the BBC World Service just a moment ago!  (Thought the interviewer sound doubtful of his analysis though [])

[chris (OP)]

This is a more detailed account of the calculations that Dave and I did in producing the numbers for More or Less, the programme that likes "trying to explain" numbers to the general public, in much the same way that we like "trying" to explain science...

http://www.bbc.co.uk/news/magazine-16787636

We're already receiving some interesting points and feedback from readers. Thank you to them. I'll attempt to post answers to their queries, as they come in, below.

Chris

[chris (OP)]

Dear Chris,

I have just read your comments regarding the loss of mass in the earth.  I feel that you have forgotten a key amount of gains that are causing the planet to grow in size.  This is the mass generated by plants.  Plants take in the suns energy to grow.  As the plant grows it sheds leaf and branches these cause the surface to raise.  This can be proved by the depth you must dig down to find archaeological finds. 

On this note, I have been looking for some time for evidence or theory of the amount of gravity today compared to 50 million years ago.  I would be happy to receive your comments on the above.

Kind Regards,

MARK SCOTT

Dear Mark

Thanks for writing; you are right to highlight photosynthesis as a source of mass gain, and indeed it is; but the carbon dioxide level in the atmosphere is rising, not falling, indicating that the energy being released from fossil fuels must outstrip the chemical potential energy being captured by photosynthesis.

Therefore the net change is negative; we approximated this in our "lost energy" entry on the table, which we calculated from the 500 exajoules being consumed planet-wide annually.

Chris

[chris (OP)]

Here's an update on the evolving story, spawned by our appearance on More or Less, of Earth's annual mass change:

This is the reference cited by NASA indicating a net warming:

http://www.sciencemag.org/content/308/5727/1431

This is NASA's article based on the above:

http://www.nasa.gov/vision/earth/environment/earth_energy.html

You'll see that the figure they arrive at is about 0.8W/m2.

Here, now, is reasoning behind our assertion for the Earth gaining mass through global warming...:

"As it is in a vacuum, the only significant way the earth can gain or lose energy is by radiation. So if the earth is gaining more energy than it is losing, its total energy must be increasing, whether that energy remains as
heat or gets converted into another form.

One result of Einstein's theory of relativity is that if something moves quickly (i.e. has a lot of kinetic energy), its mass increases. This mass increase may be caluclated by [increase in kinetic energy]/[speed of light,
c]^2.

And in fact, it turns out that any increase in energy also produces an increase in mass, so if the earth is gaining 0.84W/m2 in energy it must be gaining a corresponding (0.84W/m2 /c^2) in mass/s, which, when you multiply it up by the area of the earth, comes out as 160 tonnes/year. Compared with the mass changes from other parameters (debris input from space, hydrogen outgassing to space and so on), however, this is trivial."

[chris (OP)]

Hopefully the above will assist the person who sent me this:

Dr Smith

Fascinated by the assertion, attributed to you in:

http://www.bbc.co.uk/news/magazine-16787636

and on the BBC's 'More or Less' programme

that global warming contributes mass to the earth. According to the BBC, you cite NASA and the source of this gem. I wonder if you could provide the reference?

In case you are wondering why I ask, I confess that I believe the assertion to be absolute poppy-cock, but would be delighted to be proved wrong.

Reason: even if I can be made to believe that via E=mc^2 that the energy gained via global warming converts to mass, then it would no longer be manifest as energy, hence the globe would not be any warmer. It can not
be accounted for twice. (Maybe that is the answer to global warming - convert it all to mass?) But of course I don't believe there is any nuclear reaction going on anyway - the extra heat remains as heat.

Understanding that you might get lots of correspondence on this and can't reply to them all, perhaps you could just ask the BBC to correctly reference the assertion in their quote on their webpage instead?

Kind regards

SI

Although he did follow with...

Dr Smith
I've been educating myself, and it seems I owe you an apology. I have been confusing mass with matter and regarding them as interchangeable concepts. I still find it unnerving to consider that warming a body up increases its
inertia and gravitational pull.

Regards

[chris (OP)]

Further clarification (kindly written out long-form by Dave Ansell)

According to Einstein's theory of special relativity the energy of a moving object is:

E²-(pc²)² = (mc²)²

where E is its energy, p is its momentum, m is its mass and c is the speed of light.

If the object is not moving and has no momentum, this simplifies to:

E² = (mc²)²

or, simplifying further:

E=mc²

...one of the most famous equations in the world, and is used and therefore tested by high energy physicists every day.

It doesn't just hold for kinetic energy, but potential energy as well.

This can be shown by measuring the mass of a radioactive atom, and all of its decay products, you will find that the decay products are slightly too light, by the amount of energy released divided by c².

The same applies to any other form of energy.

Heat energy is in fact a mixture between kinetic energy of the particles jiggling around and electrostatic potential energy between them, both of which will add to the energy term in E=mc².

NASA has calculated that more energy is entering the earth than leaving it by 0.84W/m². Whatever form that energy ends up taking, whether it is heat, chemical potential, or anything else, this means that the total energy of the earth must be increasing.

If the total energy of the earth is increasing by E=mc², unless the speed of light is changing (which would be Nobel Prize territory) the mass of the earth must also be changing.

[daveshorts]

The NASA reference is here:

http://www.nasa.gov/vision/earth/environment/earth_energy.html
http://www.sciencemag.org/content/308/5727/1431

[Titanscape]

What do the solar wind and storms contain, and how much does the Earth gain of it each year?

I was under the impression the Earth had no tail, unlike Venus and comets. That the magnetosphere contained all, tested over a billion years. So anything that could be stripped away already was.

[chris (OP)]

The loss of light gases from the upper atmosphere is occurring because the particles have energy and a fraction will have sufficient energy to achieve escape velocity and exit. As you contend, the solar wind can remove material but its impact is mitigated by the magnetic field. Mars, on the other hand, lost its magnetic field fairly soon after it formed and consequently became dessicated billions of years ago...

[Jim Grozier]

The derivation, above, of the equation E = mc² from E² = p²c² + m²c⁴ (note that that is the correct form of the equation – the slightly different version quoted is dimensionally inconsistent) has one very important caveat – that “the object is not moving”. As such it will only work in the rest frame of the object, and cannot be used to model situations where a body gains energy by, say, absorbing or scattering a photon. In fact the interpretation of E = mc² used by Einstein was somewhat different since he redefined mass as mγ – the “relativistic mass” – although he later regretted this. Relativistic mass is not used today, although some physicists still hold onto the concept.

Using this latter interpretation does indeed compel one to say that energy has mass. This is what is known as the “concomitance” view. Those who take this view will say that both energy and mass are conserved at all times, and they would not agree with the statement that by “measuring the mass of a radioactive atom, and all of its decay products, you will find that the decay products are slightly too light, by the amount of energy released divided by c²”. They would say instead that the mass of the system, and its energy, are the same before and after the decay, they are just “rearranged”.

Taking the more modern line, that mass is Lorentz invariant, one arrives at the “interconvertibility” view, which is at odds with the idea of energy having mass. Which line you take depends on how you define momentum, and it is to some extent a free choice. The one sure thing is that you can’t have it both ways – you cannot say that energy and mass are interconvertible whilst simultaneously holding that energy has mass. Yet such confusion is widespread – not only on this forum but in the press, popular books and even textbooks.

One of the problems with the interpretation of special relativity is that Einstein’s models, from which he derived his equations, were incredibly simple. They were based on “rigid bodies” with no internal structure; they therefore had no capacity to heat up, and so one should not expect to be able to use them to model a situation where something is being heated. You only get out of a model what you put in. We might hope to be able to use SR to approximately model a simple collision between, say, a single photon and a single atom (although even a single atom is more complex than Einstein’s model allows, since it can absorb energy by excitation to a higher energy state, which again is not provided for in the model). But if we apply E² = p²c² + m²c⁴ to such a collision, then whichever reference frame we use, there will be motion, and hence momentum; so you can never say that “the object is not moving”, even at this simple level.

[yor_on]

Very nice explanation Jim. Energy is a very weird word, and seems more to have with transformations than with anything tangible, as in touchable, to me. So, assuming that you can transform all matter into 'energy', what happens to 'gravity'?

[Titanscape]

Actually what I meant was that the solar winds finished stripping away earth gas down to the point of the magnetosphere millions of years ago, just like Mars has long had next to no atmosphere.

Venus is still going.

Unless the sun is getting more intensely active, and is not constant, then we should not be losing anything and should not have a tail.
 
And the solar winds and storms contain materials that the earth's gravity captures.

[CZARCAR]

thinx escaping H from earth forms a shell?

[Titanscape]

Shell? What kind of shell?