## Wednesday, September 19, 2012

### Astronomical unit (AU) redefined

We visited an old astronomer yesterday: I could see the sunspots exactly as you can see them on the web, except that the image was left-right-reflected and somewhat rotated. By the way, if you click at the link, there's a tiny sunspot between 1569 and 1571, 2 times closer to 1569, that I could see as well.

But I want to mention another astronomical report. A few days ago, Nature told us that the astronomical unit has been redefined after a vote in Peking (yes, because it's Peking, it was an unanimous vote):
The astronomical unit gets fixed
Similar people who gathered in Prague 6 years ago and decided that Pluto no longer belonged to the elite club of planets met in Beijing and reformed the definition of 1 AU.

What was it before?

The most recent previous definition of the constant – which should be the average distance between the Earth and the Sun, just to be sure – said this:
[1 AU is] “the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (known as the Gaussian constant)”
Of course, the orbit described by this definition is meant to be a circularized averaged Earth's orbit. Much like many "historical definitions" of units, this definition was linked to particular objects, in this case the Sun, which is not a terribly stable choice. In 7.5 billion years, there will be no Sun as we know it. But even long before that, the mass of the Sun will be changing.

How much is it changing?

Well, throughout its life that lasts about 10 billion years, only 0.7% of the mass is converted to radiation via $$E=mc^2$$ and fusion: that's a typical percentage for thermonuclear processes. If you care about the numbers, the Sun is converting 4.2 million tons of matter to pure energy each second (it converts an Earth mass to pure energy each 45 million years).

If you check some literature, it will assure you that this is pretty much the whole loss. At the current rate, it would take 10 trillion years for the solar mass to drop to zero. That's a slow process but at the accuracy we need, it actually can't be neglected. In 100 years, the solar mass decreases by 1/100 billion of its value, changing the figures by $$10^{-11}$$ or so. Certain distances – although not really distances of celestial objects – may be measured much more accurately.

So the new 2012 definition is
1 AU is 149,597,870,700 meters.
That's simple enough; the usual value of the distance, 150 million kilometers, was just expressed a bit more accurately and the number has been fixed. Note that 12 digits are listed but only 10 significant figures are nonzero – and those probably express the precision with which we may measure this distance. Recall that 1 meter itself is defined as 1/299,792,458 of a light second and 1 second is still defined via some atomic-clocks-related radiation of an atom.

In a few million years, if people will still respect the 2012 vote in Peking ;-) and if they will use the AU unit at all, and if there will be any people at all, people will have to get used to the fact that the average Earth-Sun distance differs from 1 AU by a fraction of a percent.

The decreasing solar mass wasn't the only problem of the old definition. Another problem was that it completely ignored relativity. The definition doesn't make it clear whether the radius is measured as $$1/2\pi$$ of the circumference or the proper radius itself: in general relativity, due to the spacetime curvature, these two definitions don't quite agree.

Also, the definition depended on a (solar) day which is fluctuating, changing, and whose "corresponding time period" is differently interpreted in different reference frames, due to time dilation of special relativity as well as the gravitational red shift of general relativity. If you had wanted to interpret the old definition too accurately, you were entering a minefield.

Of course that all these changes are small enough and the numerical constant in the new definition was chosen in such a way that nothing will really change in practice.

Negative implications

I would endorse this simplification of the definition as well but I don't share the enthusiastic comments suggesting that the new definition is a win-win situation. In reality, every time we liquidate one of those historical units and replace it by a pure number, a numerical multiple of the modern units, we're making the users of the units less familiar with some part of science or astronomy that used to be very important and that is still arguably important.

In this case, for example, people who would have learned what 1 AU was automatically learned something about the Earth-Sun distance and how it can be used to measure the distance of nearby stars as multiples of 1 AU, by the parallax method, and perhaps a few related things. If you tell your students that 1 AU is just the number (in meters), they may conclude "that's it, it's very simple, there's nothing else to learn, why did the people ever define it differently".

But that's really missing the point because doable experiments we may do with the telescopes during different seasons produce distances of the stars that come out as multiples of 1 AU, not 1 meter. Because the Earth-Sun difference wasn't terribly accurately known in the units of meters or feet and because the measured distances of the stars in the units of 1 AU could in principle be more accurate, it has made a complete sense to disentangle 1 AU from 1 meter and consider them two independent units of distance. By suppressing this independence, we're really allowing people to ignore the actual methods how certain things are measured (in astronomy, in this case).

The history of units in physics is of course full of additional examples. Because 1 meter looks so easy and its numerical multiples are trivial and dull, people feel that there's nothing to learn. But then they can't do many other things that were simpler and more logical in the historical units. So reforms of the units are always a mixed baggage. Such simplified definitions shouldn't be viewed as a justification of a reduction of stuff that is taught because the knowledge of the old units "almost automatically" included some actual science and methods that went beyond pure conventions, some science and methods that were looking simpler in the old units. And not all of those things should be forgotten because such forgetting weakens the people's contact with the world of physics and astronomy.

And that's the memo.

1. Hi Lumo, thanks for this interesting report :-)

2. hmm... are you gay or a female? I've never been able to tell...

3. Interesting article Lubos. Does the speed to which the Earth orbits around the Sun remains the same ? I learned in the book "Quantum Theory cannot Hurt You" Marcus Chown, that it is approximately 107228 km/h (variable since the orbit is elliptic).
The speed of the Earth spinning at the equator is 1669km/h... in Paris it is 109 km/h... I wonder what it is in Dublin, 90 km/h maybe ?

4. Dear Shannon, as the Sun is getting lighter and as the spinning of the Earth is slowing down - because of tides whose friction consumes a part of the rotational energy - the Earth is getting further from the Sun and the orbital speed in km/h correspondingly decreases. It's of course an extremely slow process again, producing changes of order one percent in millions or billions of years - I don't want to think too much right now.

The Earth's spinning motion is simply 40,000 km per 24 hours - the circumference of the equator. That's your 1,669 km/h at the equator, when precise figures are inserted. Your Paris figure is clearly an underestimate - it can't be 16 times slower than at the equator, can it? ;-) The right figures for Paris and Dublin and the formulae are:

http://www.wolframalpha.com/input/?i=sinus%28latitude+of+paris%29*1669

http://www.wolframalpha.com/input/?i=sinus%28latitude+of+dublin%29*1669

5. Thanks a lot Dilaton but I wish it were this simple. What makes me not-quite-healthy is some brutal physics/biology, not the amount of meetings with other people. I could even bike there, I can do my regular pushups, I am in no bad mood relatively to what I can imagine or I have experienced, but I am still not as physically healthy as desired and I of course continue with my tough sugar-free diet, hoping that it could be abandoned on a nice sunny day in the future.

6. Wow, that's much faster then. I think that I (or Chown ?) must have forgotten to put the last digit for Paris : 109 instead of 1098 km/h... So I'm going 997km/h right ?... that is faster than my Skoda ;-)