dimension analysis, scientific notation, and fun facts.
Monty Python comedy group has helped fill the world with laughter, and for that I am grateful. But there was also a moment of artistic magnificence when they gave the world an inroad to knowledge. In the middle of the the movie, “The Meaning of Life” Eric Idle performs the Galaxy Song. Copied from montypython.net
(spoken)
Whenever life gets you down, Mrs. Brown,
And things seem hard or tough,
And people are stupid, obnoxious or daft,
(sung)
And you feel that you've had quite eno-o-o-o-o-ough,
Just remember that you're standing on a planet that's evolving
And revolving at 900 miles an hour.
It's orbiting at 19 miles a second, so it's reckoned,
The sun that is the source of all our power.
Now the sun, and you and me, and all the stars that we can see,
Are moving at a million miles a day,
In the outer spiral arm, at 40,000 miles an hour,
Of a galaxy we call the Milky Way.
Our galaxy itself contains a hundred billion stars;
It's a hundred thousand light-years side to side;
It bulges in the middle sixteen thousand light-years thick,
But out by us it's just three thousand light-years wide.
We're thirty thousand light-years from Galactic Central Point,
We go 'round every two hundred million years;
And our galaxy itself is one of millions of billions
In this amazing and expanding universe.
(waltz)
Our universe itself keeps on expanding and expanding,
In all of the directions it can whiz;
As fast as it can go, at the speed of light, you know,
Twelve million miles a minute and that's the fastest speed there is.
So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth;
And pray that there's intelligent life somewhere out in space,
'Cause there's bugger all down here on Earth!
Whenever life gets you down, Mrs. Brown,
And things seem hard or tough,
And people are stupid, obnoxious or daft,
(sung)
And you feel that you've had quite eno-o-o-o-o-ough,
Just remember that you're standing on a planet that's evolving
And revolving at 900 miles an hour.
It's orbiting at 19 miles a second, so it's reckoned,
The sun that is the source of all our power.
Now the sun, and you and me, and all the stars that we can see,
Are moving at a million miles a day,
In the outer spiral arm, at 40,000 miles an hour,
Of a galaxy we call the Milky Way.
Our galaxy itself contains a hundred billion stars;
It's a hundred thousand light-years side to side;
It bulges in the middle sixteen thousand light-years thick,
But out by us it's just three thousand light-years wide.
We're thirty thousand light-years from Galactic Central Point,
We go 'round every two hundred million years;
And our galaxy itself is one of millions of billions
In this amazing and expanding universe.
(waltz)
Our universe itself keeps on expanding and expanding,
In all of the directions it can whiz;
As fast as it can go, at the speed of light, you know,
Twelve million miles a minute and that's the fastest speed there is.
So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth;
And pray that there's intelligent life somewhere out in space,
'Cause there's bugger all down here on Earth!
Isaac Asimov once wrote that he loved big numbers. Many people I meet today say that they do not like math, but let’s not let that dissuade us. There is a great challenge we are faced with here. Check these numbers and see if they are correct. Then convert them to standard international units using scientific notation. Then watch the youtube video of the Galaxy Song with deeper appreciation.
Earth rotation: 900 miles an hour, is this figure correct? Well Earth’s radius is 3960 miles. The circumference of a circle is 2 x π x radius, and each rotation takes 24 hours.
2 r=24881 miles/24 hours=1037 mi/hr
Well that’s about right near the equator. As you proceed North or South from the equator the radius of the path you travel on your daily rotation gets smaller so at some latitude on Earth you are revolving at 900 miles an hour. Try to determine what that latitude is for extra credit. The number gets smaller as you near the pole until when you get there you are just spinning slowly around and not traveling with each daily rotation. Now let us convert 900 miles an hour to standard international (SI) units:
9x10^2 mi/hr x 1.609x10^3 mi/hr x 3600 s =
4.02x10^2 m/s
With paper and pencil (and calculator) in hand check all their numbers and convert them to SI units. Stephen Hawking did, you can do it too. I noticed he corrected five of Eric Idle’s numbers and he missed one incorrect number. Both versions of the Galaxy Song are available for your enjoyment on youtube. Using scientific notation we should have:
9.0x10^2 mi/hr = 4.02x10^2 m/s
Now check the rest:
19 miles a second____________________________ m/s
A million miles a day__________________________ m/s
40,000 miles an hour__________________________ m/s
One hundred billion stars________________ pure number
One hundred thousand light years_____________ meters
Six thousand light years_____________________ meters
Three thousand light years___________________ meters
Thirty thousand light years___________________ meters
Two hundred million years__________________ seconds
Millions of billions = 106109= ___________ pure number
Twelve million miles a minute____________________ m/s
I sing this song to myself often using Stephen’s numbers. Except I say ten million miles a day for the Sun and you and me and all the stars that we can see. We are orbiting around the Milky Way galaxy this fast due to the gravitational attraction from the supermassive black hole in the constellation Sagittarius. Orbital velocity can be figured in meters per second with the simple formula:
v(orb)=sqrt(GM/R)
G is Newton’s constant G=6.674x10^-11 m^3/(kg s^2)
M is the mass of one hundred billion stars
M=2x10^30 kg x 10^11
R is the distance to the center we are orbiting, 30,000 light years. R=3x10^4 LY x 9.46x10^15 m/LY=__________meters.
This velocity can be rounded off to 200,000 meters per second. It agrees with Stephen’s number, 400.000 miles an hour, to one significant figure. So go through and check all these numbers and see if they are correct. Wikipedia is a helpful reference for this type of exercise where possible errors are of little impact. What we really want is to get a mastery of using scientific notation and dimensional analysis, so that we can be confident of the facts we are using and communicating with others. Besides, Stephen and Monty Python have created a masterpiece and everyone should go to youtube and see it.
