jueves, 5 de octubre de 2023

MILKY WAY SONG - ANALYSIS


(Annotated by S. C. Smith)

Whenever life gets you down Mrs. Brown, 

and things seem hard or tough, 

and people are stupid, obnoxious or daft

and you feel that you've had quite enough...

Just remember that you're standing on a planet that's evolving
And revolving at 900 miles an hour

Speed of revolution should actually be measured in terms of angular velocity, since the actual speed varies for different points on the Earth. The angular velocity of the Earth's revolution is 1 rotation per day. The radius of the Earth, $R\approx 6378 \mbox{km}\approx 3827 \mbox{mi}$. The circumference of the Earth is thus $2\pi R\approx 40054\mbox{km}\approx 24032\mbox{mi}$. A point on the equator therefore travels a distance of about 24,000 mi in 24 hr (1 day) is thus traveling at a speed of  1000 mi/hr. Speeds are lower at other locations, and a point on the poles has a speed of 0 mi/hr.
That's orbiting at 19 miles a second,
So it's reckoned
The orbit of the Earth has a radius of $\sim 1.5\times 10^{11}\mbox{m}\approx 9.3\times 10^7\mbox{mi}$, which is defined to be 1 astronomical unit (AU). The Earth thus travels a distance of $2\pi R \approx 5.84\times 10^8\mbox{mi}$ in $3.16\times 10^7\mbox{sec}$ (1 year) at an average speed of  18.5 mi/sec.
A sun that is the source of all our power

The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at 40,000 miles an hour
Of the galaxy we call the Milky Way

In fact, the speed is closer to 3 times that number, if you count only the rotational motion of the galaxy, and approximately 20 times that number if you count the motion of our galaxy with repect to the cosmic background radiation of the universe.

Our galaxy itself contains a hundred billion stars
It's 100,000 light years side to side

A light year is the distance light travels in one year. $1 \mbox{ ly}\approx 9.46\times 10^{15}\mbox{m}\approx 5.9\times 10^{12}\mbox{mi}$.
It bulges in the middle, 16,000 light years thick
But out by us it's just 3,000 light years wide

We're 30,000 light years from galactic central point

While this number is somewhat uncertain, ranging from 23000 ly to 32000 ly, the currently accepted value is approximately 28000 ly.
We go round every two hundred million years
Current estimates put the length of the galactic year at 225 million years.
And our galaxy is only one of millions of billions
In this amazing and expanding universe

The universe itself keeps on expanding and expanding

The universe is known to be expanding because all distant galaxies are seen to be receding from us, with a velocity proportional to the distance from us.
In all of the directions it can whiz
As fast as it can go, the speed of light you know
The observable universe expands at the speed of light. The actual physical universe may expand at some other velocity.
12 million miles a minute and that's the fastest speed there is
The speed of light is $\sim2.99\times 10^8\mbox{m/s}\approx186,000 \mbox{mi/s}\approx 11.2 \mbox{million mi/min}$. According to known physical laws, it is impossible for anything to travel faster than the speed of light (relative to local space).

So remember when you're feeling very small and insecure
How amazingly unlikely is your birth
And pray that there's intelligent life somewhere up in space
Because there's bugger all down here on Earth


 Eric Idle, Monty Python player extraordinaire, wrote the Galaxy Song for the movie The Meaning of Life. I was quite curious to see how it has withstood 20 years of astronomical leaps in our understanding of the universe. My references can be found at http://www.softwarerepair.com/astro/ReferencesforGalaxySong.htm.

Just remember that you're standing on a planet that's evolving
While still controversial in some areas, evolution seems pretty well established.

And revolving at nine hundred miles an hour,
The speed of the earth's revolution is once per day (duh) but at the equator the circumference of the earth is 25,000 miles so that makes the speed just over 1,000 miles per hour. However, by the time you get as far north as the UK (Eric Idle's country) the speed is actually less than 700 miles per hour. The 900 figure might be good enough for our purposes.

That's orbiting at nineteen miles a second, so it's reckoned,
The earth orbits the sun at 29km/second and there is roughly a 3:2 ratio between kilometers and miles so 19 miles per second is pretty close.

A sun that is the source of all our power.
This may be a bit of hyperbole. The sun is responsible for all wind and solar power and because our weather depends on the sun we would include hydroelectric power as well. Oil and coal formed as a result of sun-driven processes on earth so that's okay. But this particular sun did not create uranium so it could be argued that it doesn't supply all of our power. IMHO.

The sun and you and me and all the stars that we can see
Are moving at a million miles a day

The sun (and therefore the earth and at least all the stars that you can see with the naked eye) are moving through the galaxy at 225km/sec. This comes out to more than 6 million miles per day.

In an outer spiral arm, at forty thousand miles an hour,
We are indeed in an outer spiral arm of the galaxy. If we were moving at a million miles per day that would come out to 40,000 miles an hour. If the number is closer to 6 million miles per day that makes it close to 250,000 MPH.

Of the galaxy we call the 'Milky Way'.
Our galaxy itself contains a hundred billion stars.

While there have been some estimates that are a bit higher than 100 billion stars, this is still a pretty good estimate.

It's a hundred thousand light years side to side.
Give or take 20,000 light years, this is close to the current estimate.

It bulges in the middle, sixteen thousand light years thick,
Estimates vary quite a bit but 10-30 thousand light years is at least one estimate for the middle of the galaxy

But out by us, it's just three thousand light years wide.
And in the outer arms it is anywhere from 1 to 10 thousand light years wide.

We're thirty thousand light years from galactic central point.
A very good estimate.

We go 'round every two hundred million years,
Rounding down to the nearest hundred million, this will do nicely.

And our galaxy is only one of millions of billions
Millions of billions would be quite a lot. Some estimates are in excess of 1 trillion galaxies but that's only thousands of billions. But we aren't done counting yet.

In this amazing and expanding universe.
And probably expanding at a faster rate than before.

The universe itself keeps on expanding and expanding
In all of the directions it can whiz

We have pretty solid proof of that these days

As fast as it can go, at the speed of light, you know,
But matter cannot generally move at the speed of light so the speed of the expansion is somewhat less. On the other hand, there was a time in the early universe where it seems it did expand at a speed greater than the speed of light.

Twelve million miles a minute, and that's the fastest speed there is.
The speed of light is about 186,000 miles per second or just a bit shy of 12 million miles a minute. There are claims for things that can go faster but it is still speculation.

So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth,

The human genome project has found 30,000 genes. It would take only 33 genes to make every living person unique.

And pray that there's intelligent life somewhere up in space,
Hence my membership in Team SETI.

'Cause there's bugger all down here on Earth.
An unassailable truth.

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