The stubby

For all those who remember when beer came in a more practical shape (Quoting Wikipedia: "Some of the expected advantages of stubby bottles are: ease of handling; less breakage; lighter in weight; less storage space; and lower center of gravity").

And of course, not wanting to advertise any specific brand here, feel free to go to this Canadian Living article to look at other brands of stubby! Or to this site - http://www.stubby.ca/ - to find out more than you ever needed to know.

I was never that much of a beer drinker, but recently came across the above ad in an old scrapbook (don't ask me why I kept a piece of newspaper for 30+ years!).

But related to the stubby, I did drink Uncle Ben's pop (soda for any American readers) when I was a teenager - always cool to be holding a 'beer' bottle and walking around downtown!

Are Rocket Booster Tests Slowing Down (or Speeding Up) the Rotation of the Earth?

Seeing the recent solid fuel rocket booster test got me to thinking about how much this might change the rotation of the Earth and thus the length of our day. What if it shortens the day?! It would be "Give us back our 11 days" all over again.

Anyway, The calculations seemed simple enough and follow for your viewing pleasure. (Note: if you find any major errors I'll just fix the blog and pretend it was right all along).

First, the change in angular momentum of the Earth is (F)(d)(t), where 'F' is the force of the rocket engine, 'd' is the distance from the axis of rotation, and 't' is time. For this blog I'm going to try and get the maximum effect, so we'll assume the engine is set parallel to the ground at the Equator (i.e. perpendicular to the radius), and facing East (or West).

The change in angular momentum = (moment of inertia)(delta omega) where 'omega' is the angular rotation of the Earth in Radians/sec.

For this calculation I'm going to assume a big rocket thruster produces roughly 10,000,000 Newtons force (the one linked to above may be slightly larger) and runs for a minute. The moment of inertia of the Earth is about 8 x 10³⁷ kg m², and the radius of the earth is roughly 6500 km. Putting this all together gives:

(8 x 10³⁷ kg m²)(delta omega) = (10,000,000 kg m/s²)(6,500,000 m)(60 s)

Doing the math:
(delta omega) = 4.9 x 10^-23 rad/sec

Seems pretty big so far - after all 4.9 is no small number. But it would be useful to see just how much the x 10^-23 affects it. (Side note, this reminds me of Avogadro's number which is 6.02 x 10²³)

So how much of an effect is this? How long will it take the Earth to slow down or speed up enough to add or subtract another second to the day?

1 second is 2(pi) / (24)(60)(60) radians
so 4.9 x 10^-23 (t) = 2(pi)/(24*60*60)
t=1.5 x 10¹⁸ seconds or roughly 4.7 x 10¹⁰ years (or approximately 10 times the age of the earth!)

Maybe not quite such a large effect!

20150316 Update: Seems that similar calculations have been done ('stopping the world' using Space Shuttle boosters) and the numbers are similar - with the caveat that it's only really valid if the Earth has no atmosphere! Oh well, it probably only works for spherical chickens in a vacuum (Big Bang Theory reference to the spherical cow metaphor).

So how cold was it in Toronto this year?

There was a lot of talk about the frigid arctic air 'hovering over Toronto' (or some such) this year, so I thought I'd check against our prairie cousin Edmonton.

It's actually quite easy to do this.

1. I went to wunderground.com (I know you can get the info from other sources, but I like the name) and looked up 'YYZ' for Toronto. I then clicked on 'Almanac for <today>', 'Custom', and entered Nov 1, 2014 to March 14, 2015 (Pi Day of course), clicked on 'Get History' then scrolled down to the bottom and clicked on 'Comma Delimited File'.
2. I then copied the data into Excel (didn't bother saving and then importing to Excel as I find it faster to just copy into Excel, then select 'Data', 'Text to Columns' and get the data in columns that way).
3. I repeated steps #1 and #2 for Edmonton and copied into a second tab in Excel
4. Finally, I created a 3rd tab that contained the same column headings and first column (date) and filled the cells with the Edmonton temperatures minus the Toronto ones. Then created a simple scatter chart (see below)

This whole exercise took less than 5 minutes - amazing what you can do with a basic source of info combined with a tool like Excel.

And the results? (Hopefully you can click on the picture below to get a slightly larger version). It looks like Edmonton was generally quite a bit colder in November/December (makes sense...it gets colder faster there) through to about Jan 12th. But after that, the graph is often in the positive range - meaning Edmonton was warmer! This is often because Edmonton's temperature is swinging to warm temperatures for a few days. Also - looking at the numbers - from Jan 13th onward Edmonton had 37 out of 60 days where the maximum temperature was warmer than Toronto's, but only 23 out of 60 days where the minimum temperature was warmer. So Edmonton still gets colder at night (it's probably all those darned cloudless days and nights :-) ).