Q: Why is the SI second defined as 9,192,631,770 periods of the transition between two states of cesium-133?

In 1895, the astronomer Simon Newcomb published his "Tables of the Sun," based on observations of the sun's position from 1750 to 1892. (http://en.wikipedia.org/wiki/Newcomb%27s_Tables_of_the_Sun) These calculations turned out to be reliable enough that astronomers continued to use them until the 1980s.

Before 1956, the second was defined as the mean solar second, or in other words, 1/86,400 of the time the earth takes to spin around on its own axis and see the sun again each day. But because the moon's gravity and the tides are slowing down the earth's spin, this is not a stable quantity.

From 1950-1956, the international authorities agreed to redefine the second to be the "ephemeris second," based on the speed of the earth's orbit around the sun in 1900, as predicted in Newcomb's tables. The earth's orbit around the sun is not slowing down, at least not on anything like the effect on the earth's spin around its own axis. (In practice the ephemeris second is measured by looking at the moon's orbit around the earth and taking pictures of what stars the moon is near.)

Because Newcomb's tables cover observations from 1750 to 1892, the "ephemeris second" corresponds to the mean solar second at the middle of this period, or about 1820. (http://tycho.usno.navy.mil/leapsec.html)

Meanwhile, from 1952 to 1958, astronomers from the U.S. Navy and the British National Physical Laboratory measured the frequency of cesium oscillations in terms of the ephemeris second. (http://www.leapsecond.com/history/1958-PhysRev-v1-n3-Markowitz-Hall-Essen-Parry.pdf) Cesium is even more stable than the orbit of the earth around the sun.

There are a few ways to do the calculations that they show in the paper (having to do with exactly what period they observed over and whether they corrected for some subtleties re: the moon's orbit), giving results between 9,192,631,761 and 9,192,631,780. The average was 9,192,631,770.

In 1967, this became the official definition of the SI second, replacing the ephemeris second. But the reason the number is what it is is because Newcomb analyzed observations from 1750 to 1892, and the middle of that period is 1820, and that's how fast the earth was spinning on its axis in 1820.

Q: If one day is not exactly 24 hours and is in fact 23 hours, 56 minutes, shouldn't the error add up, and shouldn't we see 12 a.m. becoming noon?

You're right that a "sidereal" day is about 23 hours, 56 minutes, 4 seconds. But this is not a day in the everyday sense.

A sidereal day is how long it takes the earth (on average) to make one rotation relative to the faraway stars and other galaxies in the sky.

If you find a star that is directly above you at midnight one night, the same star will be directly above you again at 11:56:04 p.m. the next evening.

Similarly, if you were sitting on the star Proxima Centauri looking through a powerful telescope at earth, you would see Toledo, Ohio, go by every 23 hours, 56 minutes, and 4 seconds.

However, we don't keep time by the faraway stars -- we measure time by a much closer star, the sun! And we are actually in orbit around the sun, orbiting in the same direction that the earth is spinning on its own axis. From our perspective, the sun goes a little slower in the sky because we are also orbiting around it.

How fast are we orbiting around the sun? We make one full orbit every year, or roughly 366.25 sidereal days.

So after a year, the faraway stars will have done 366.25 rotations around the earth, but the sun will only have done 365.25 rotations. We "lose" a sunset because of the complete orbit. (The extra quarter day is why we need a leap year every four years.)

So there are 365.25 "mean solar days" in 366.25 "sidereal" days. How long is a "mean solar day"? Let's do the math: One sidereal day is 23 hours, 56 minutes, 4 seconds, or 86164 seconds. Multiply this by 366.25 sidereal days in a year, and you get 31557565 seconds. Divide by 365.25 solar days, and we get that a solar day is.... 86,400 seconds. That's 24 hours exactly!

It's this "mean solar day" (24 hours) that is the normal definition of day.

If you want to do the math more exactly, a sidereal day is 86164.09054 seconds, and a tropical year is 366.242198781 sidereal days. That works out very closely.

(P.S. Unfortunately, the earth's spin has been slowing down because the moon is sucking away the earth's energy. Every time the high tide of the Atlantic Ocean slams into the east coast of North America, the earth slows its spin a little bit. The definition of the second is based on the speed the earth was spinning back in 1820, and we have slowed down since then. As a result, we occasionally have to add in a "leap" second to the world's clocks. See http://online.wsj.com/article_email/SB112258962467199210-lMyQjAxMTEyMjIyNTUyODU5Wj.html?mod=wsj_valetleft_email)

Q: Why don't we see green stars?

Stars are black bodies in thermal equilibrium (http://en.wikipedia.org/wiki/Black-body_radiation). Their spectrum depends only on their temperature, and the shape of the spectrum is described by Planck's law (http://en.wikipedia.org/wiki/Planck%27s_law).

(from http://xkcd.com/54/, showing the spectrum of the cosmic microwave background radiation)

As a result, only some colors are possible: the ones that can be formed by a black-body radiator with this shape of spectrum. The line in the CIE diagram below shows the possible colors of black-body radiation, depending on the temperature:

(from Wikipedia's http://en.wikipedia.org/wiki/File:PlanckianLocus.png)

You will see essentially the same colors from incandescent light bulbs and toaster heating elements as from a star -- a 2700K tungsten filament will radiate light that appears to the human eye with the color corresponding to 2700K on the above diagram.

The "black body" curve does not go through anything you could really call green. 

Qualitatively, for something to appear green, it essentially needs to stimulate the medium-wavelength cones more than the long- and short-wavelength cones in the human eye. Black-body radiation is too broadband to do this.

Here, the colored lines represent the sensitivities of the three kinds of cones in the human eye. The dashed line is black-body radiation from a 5400K star, obeying Planck's law. Black-body radiation is way too broad to hit the "green" cones without also hitting the "red" and "blue" ones. That's why this light appears white.

Q: What are the most iconic images from astrophysics?

Orbital decay of a binary pulsar compared with the prediction of general relativity. This won the Nobel Prize in physics in 1993.

Power spectral density of the cosmic microwave background radiation, showing perfect correspondence with a black body. The measurement was taken from the first nine minutes of data from COBE, launched in 1989.

Maps of the cosmic microwave background radiation (with and without the dipole from our own motion), as measured by COBE in its first four years. The above two graphs won the Nobel Prize in physics in 2006.

Angular power spectrum of the magnitude of the cosmic microwave background radiation, here as measured by WMAP, showing the "third peak" and giving clues to what went on in the early universe.

Q: Given that the universe is expanding and the Solar System is hurtling through space, is there any frame of reference for zero motion?

The laws of physics (Maxwell's equations, etc.) work the same in any inertial reference frame, so in that sense, no, there is no inertial reference frame that is the unique one with "zero motion." Space could just as easily be hurtling past the Solar System as the Solar System is past space!

However, one thing we can observe is the light from shortly after the Big Bang (about 300,000 years after). This "Cosmic Microwave Background Radiation" was discovered in the 1960s and has dimmed considerably over the last 14 billion years. It has the spectrum of a "black body" -- like the light you get off a hot piece of metal, like a lightbulb filament, except that this piece of metal is 2.725 Kelvins.

The COBE and WMAP satellites have observed that the light is slightly bluer in one direction in space (l = 264 degrees, b = 48 degrees) by about 3.4 milliKelvins and slightly redder in the opposite direction. We believe this is like the Doppler shift that happens when an ambulance drives by and shifts in pitch -- in other words, that the Solar System is flying through this background radiation, left over from the Big Bang, at a particular speed and direction.

We can calculate the velocity that must be:



Solving for v, we get v = 229 miles per second.

So, to sum up, in theory anybody in the universe who can measure the CMB precisely enough can agree on a "CMB rest frame" that is moving, relative to our Solar System, in the opposite direction from the galactic coordinates l = 264 degrees, b = 48 degrees, at the speed of 229 miles per second.

http://pdg.lbl.gov/2010/reviews/...