When will the Earth fall into the Sun?

The time I spent making this poster could have been spent doing research.

Since December 2012 is coming up, I thought I'd help the Mayans out with a look at a possible end of the world scenario. (I know, it's not Earth Day yet, but we at the Virtuosi can only go so long without fantasizing about wanton destruction.) As the Earth zips around the Sun, it moves through the heliosphere, which is a collection of charged particles emitted by the Sun. Like any other fluid, this will exert drag on the Earth, slowly causing it to spiral into the Sun. Eventually, it will burn in a blaze of glory, in a bad-action-movie combination of Sunshine meets Armageddon.

Creating an Earth

A while ago I decided I wanted to create something that looks like the surface of a planet, complete with continents & oceans and all. Since I've only been on a small handful of planets, I decided that I'd approximate this by creating something like the Earth on the computer (without cheating and just copying the real Earth). 

Where should I start? Well, let's see what the facts we know about the Earth tell us about how to create a new planet on the computer.

A Curious Footprint

Lasers!  Credit: JPL/Caltech

In less than two days, NASA's Mars Science Laboratory (MSL) / Curiosity rover will begin its harrowing descent to the Martian surface.  If everything goes according to the kind-of-crazy-what-the-heck-is-a-sky-crane plan, this process will be referred to as "landing" (otherwise, more crashy/explodey gerunds will no doubt be used).

The MSL mission is run through NASA's Jet Propulsion Laboratory where, by coincidence, I happen to be at the moment.  Now, I'm not working on this project, so I don't have a lot to add that isn't available elsewhere.  BUT I do feel an authority-by-proximity kind of fallacy kicking in, so how about a post why not?

A Homemade Viscometer I

Stirring a bowl of honey is much more difficult than stirring a bowl of water. But why? The mass density of the honey is about the same as that of water, so we aren't moving more material. If we were to write out Newton's equation, ma would be about the same, but yet we still need to put in much more force. Why? And can we measure it?

Batman, Helicopters, and Center of Mass

A couple weeks ago, I came home after a long day at work looking for a break.  I thought to myself, “What’s more fun than physics? Batman*.”  I sat down to play the latest Batman videogame, in which Batman’s current objective was to use his grappling hook to jump onto an enemy helicopter to steal an electronic MacGuffin.  As awesome as this was, it occurred to me that something was very wrong about the way the helicopter moved while Batman zipped through the air.

See if you can spot it too. (Watch for about 5 seconds after the video starts.  Ignore the commentary.  Note: The grunting noises are the sounds that Batman makes if you shoot him with bullets.)

What occurred to me was this: If the helicopter’s rotors provided enough lift to balance the force of gravity, wouldn’t Batman’s sudden additional weight cause the helicopter to fall out of the sky?  Also, to get lifted up into the air, the helicopter must be pulling up on Batman: shouldn’t Batman also be pulling down on the helicopter?  By how much should we expect to see the helicopter’s altitude change?

Tales from the Transit of Venus

Sad Old Sun

Today is the transit of Venus, which, aside from being a totally rad astronomical event, is also the perfect excuse to tell my favorite story of an unlucky Frenchman (I have many).

This is by no means new and, if you've ever taken an astronomy course, you've probably already heard it.  It is perhaps the closest thing Astronomy has to a ghost story, told though the glow of a flashlight on moonless nights to scare the children.

This is the story of Guillaume Le Gentil, a dude that just couldn't catch a break.

How Cold is the Ground II

Images from Wikipedia

Last week (ok, it was a little more than a few days ago....) I used dimensional analysis to figure out how the ground's temperature changes with time. But although dimensional analysis can give us information about the length scales in the problem, it doesn't tell us what the solution looks like. From dimensional analysis, we don't even know what the solution does at large times and distances. (Although we can usually see the asymptotic behavior directly from the equation.) So let's go ahead and solve the the heat equation exactly:
\[
\frac {\partial T}{\partial t} = a \frac {\partial ^2 T}{\partial x^2} \quad (1)
\]

How Cold is the Ground?

It snowed in Ithaca a few weeks ago. Which sucked. But fortunately, it had been warm for the previous few days, and the ground was still warm so the snow melted fast. Aside from letting me enjoy the absurd arguments against global warming that snow in April birthed, this got me thinking: How cold is the ground throughout the year? At night vs. during the day? And the corollary: How cold is my basement? If I dig a deeper basement, can I save on heating and cooling? (I'm very cheap.)

End of the Earth VII: The Big Freeze

http://tinyurl.com/7rdj996

It is traditional here at The Virtuosi to plot the destruction of the earth. We also are making secret plans for our volcano lair and death ray. However, since it is earth day, we will only share with you the plans for the total doom of the earth, not the cybernetically enhanced guard dogs we're building for our moon base. The plan I reveal today is elegant in its simplicity. I intend to alter the orbit of the earth enough to cause the earth to freeze, thus ending life as we know it.

Earth Day 2012: Escape to the Moon

It is now Earth Day 2012, and, according to the Mayan predictions, The Virtuosi will destroy the earth. In a futile attempt to fight my own mortality, I decided to send something to the Moon. It seems, for a poor graduate student trying to get to the Moon, the most difficult part is the Earth holding me back. So first I'll focus on escaping the Earth's gravitational potential well, and if that's possible, then I'll worry about more technical problems, such as actually hitting the moon. Moreover, in honor of the destructive spirit of The Virtuosi near Earth Day, I'll try to do this in the most Wiley-Coyote-esque way possible.

Money for (almost) Nothing

Five Hundred Mega Dollars, to be precise.
(Image from Wikipedia)

I am not typically interested in lotteries.  They seem silly and I am seriously beginning to question their usefulness in bringing about a good harvest.  But this morning I read in the news that the Mega Millions lottery currently has a world record jackpot up for grabs.  In fact, the jackpot is so big...

Tonight Show Audience:  HOW BIG IS IT?

It is so big that I decided to do a little bit of analysis on the expected returns.  Zing!

Pi storage

Let me share my worst "best idea ever" moment.  Sometime during my undergraduate I thought I had solved all the world's problems.

You see, on this fateful day, my hard drive was full. I hate it when my hard drive fills up, it means I have to go and get rid of some of my stuff.  I hate getting rid of my stuff.  But what can someone do?

And then it hit me, I had the bright idea:

What if we didn't have to store things, what if we could just compute files whenever we wanted them back?

Sounds like an awesome idea, right?  I know.  But how could we compute our files?  Well, as you may know pi is conjectured to be a normal number, meaning its digits are probably random.  We also know that it is irrational, meaning pi never ends....

Calculator Pi

There is a very fast converging algorithm for computing pi that you can do on a desktop calculator.

• Set x = 3
• Now set x = x + sin(x)
• Repeat

This converges ridiculously fast, after 1 step you get 4 digits right, after 2 steps you get 11 correct, in general we find:

A Clarification

As there seems to be some confusion among my fellow Virtuosi, I wanted to point out that Pi day occurs on July 22nd or, in the year 4159, on January 3rd.

Today is in fact Seventh Power Day.

Pi-rithmetic

Fun fact:  pi squared is very close to 10.  How close?  Well, Wolfram Alpha tells me that it is only about 1% off.

I first realized this fact when looking at my slide rule, pictured to the left (click to embiggen), just another reason why slide rules are awesome.

It turns out I use this fact all of the time.  How's that you ask?  Well, I use this fast to enable me to do very quick mental arithmetic.

Moving Pi-ctures

My TV celebrates without me.

Today, as I'm sure you're aware, is Pi Day - a day for the festive consumption of pies and quiet self-reflection.  In the spirit of the holiday, I'd like to present a point for discussion:

Everyone has a great talent for at least one thing.

That this is true for at least some people is seen through even a cursory glance at a history book:  George Washington was really good at leading revolutions, Michelangelo was an outstanding ceiling painter [1], and Batman was the best at solving complex riddles (especially in English, pero especialmente en español).

But I'm certain that this holds for everyone.  What's your talent? Mine, as those of you who read this blog should know very well by now, is certainly not doing physics.  Nope, my talent is watching TV.  Seriously guys, I watch TV like a boss [2].  In light of this talent, I thought I would describe a few instances in which I have seen pi represented (for better or for worse) in TV and movies.

A Very Small Slice of Pi

Rhubarb pie (Source: Wikipedia)

Some people know a suspiciously large number of the digits of pi.  Perhaps you have met one of these people.  They can typically be found hiding behind bushes and under the counters at pastry shops, just... waiting.

At the slightest hint of a mention of pi, they will jump out and start reciting the digits like there's a prize at the end.  After rattling off numbers for a few minutes they abruptly come to an end, grin like an idiot, and walk away.  It is an unpleasant encounter.

The sheer uselessness of this kind of thing has always bothered me, so I'd like to set a preliminary upper bound on the number of digits of pi that could ever possibly potentially kind of be useful (maybe).  For those following along at home, now would be a good time to put on your numerology hats.

Primes in Pi

Recently, I've been concerned with the fact that I don't know many large primes.  Why?  I don't know.  This has led to a search for easy to remember prime numbers.  I've found a few goods ones, namely

• 867-5309  - Jenny's number
•  the digit 1 - 1031 times, in the style of the picture to above, and the largest known repunit prime
• 1987 (my birth year), 2011 (last year), 1999 (the party year)

But then I remembered that I already know 50 digits of pi, memorized one boring day in grade school, so this got me wondering whether there were any primes among the digits of pi

Lo an behold, I wrote a little script, and found a few:

Found one, with 1 digits, is: 3 Found one, with 2 digits, is: 31 Found one, with 6 digits, is: 314159 Found a rounded one with 12 digits, is: 314159265359 Found one, with 38 digits, is: 31415926535897932384626433832795028841

I think it's usual for most science geeks to know pi to at least 3.14159, if you're one of those people, now you know a 6 digit prime! for free!

F-91 Revisited

Farmer Uncle Sam...with a rifle.
(Image Credit: Wikipedia)

Today was a sunny exception to the grey overcast rule of weather in Ithaca.  I should be overjoyed by this anomaly, spending the day outside flying a kite or playing frisbee with a border collie in a bandanna.

Unfortunately, today was also the beginning of Daylight Savings Time (DST) - my least favorite day of the year.  For my colleagues unfamiliar with this temporal travesty (I'm looking at you Arizona), let me briefly explain DST.  

Once a year, the time lords steal a single hour from us and place it in an escrow account for future disbursement, presumably in some elaborate scheme to gain the favor of hat-throwing farmer-clock hybrids (see image left).  The details are a bit murky, but the net result is that today I had one less hour to do my very favorite thing in the whole wide world - sleep.

It also means that I have to set my watch, so I figured I'd check in and see how well my previous model for time-loss in my watch has held up.

Proofiness: A look into how mathematics relates to American political life

Dearest readers,

This is my first post on The Virtuosi, so I thought I’d take a moment to introduce myself.  I’m a first year physics graduate student at Cornell, recently joined after 2 years working as an engineer first at a private firm and then at a national lab.  I myself have had lots of fun following the exploits of my estimable colleagues here on The Virtuosi, and I thought I could bring a new angle to the content here.   I would like to use this space to discuss how science interacts with everyday life in a cultural sense. How does science appear in popular culture?   How do political or social issues relate back to science? Those sorts of questions.  (I understand that there are plenty of other resources elsewhere that offer far more intelligent insight into these matters than I can, but in the very least this will give people a chance point them out to me as they yell at me in the forum below.)

Enough intro, here begins my very first blog post:

Being interested in how science is communicated to the public, I am an avid reader of popular science.   While academic types sometimes dismiss this kind of writing as shallow or otherwise uninteresting, I think science writers perform a very important function serving as a way to convey information about conceptually challenging topics to a general audience.   At their best, I find that these books serve as examples for how I can communicate my own ideas better, and in addition challenge my understanding of how science relates back to society in general.

Time Keeps On Slippin'

This is picture of a watch.  (Source: Wikipedia)

A couple of months ago, the Virtuosi Action Team (VAT) assembled for lunch and the discussion quickly and unexpectedly turned to watches.  As Nic and Alemi argued over the finer parts of fancy-dancy watch ownership, I looked down at my watch:  the lowly Casio F-91W.  Though it certainly isn't fancy, it is inexpensive, durable, and could potentially win me an all-expense paid trip to the Caribbean.

But how good of a watch is it?  To find out, I decided to time it against the official U.S. time for a couple of months.  Incidentally, about half-way in I found out that Chad over at Uncertain Principles had done essentially the same thing already.  No matter, science is still fun even if you aren't the first person to do it.  So here's my "new-to-me" analysis.

The Stars Fell on Abe and Frederick

The 1833 Leonids (Source: Wikipedia)

Word on the street is there's a meteor shower set for late Tuesday night, peaking at 2 am EST on January 4th [1].  The meteors in question are the Quadrantids, which often go unnoticed for two good reasons.  Reason the first:  apparently [2], they are usually pretty awful.  Unlike the "good" meteor showers, the Quadrantids are bright and pretty for only a few hours (instead of a few days). This means that a lot of the time, we just miss them.  Reason the second: they have a lame name [3]. But this year, they should be pretty good if the weather is right.

Now, there's lots of neat physics to talk about with meteors, but that's not why I bring it up. This has all just been flimsy pretext so I could share a historical anecdote about a meteor shower. Trickery, indeed.  Those who feel cheated are free to leave now with heads held high.

Those still around (Hi, Mom!) will hear about the night in 1833 when the stars fell on Alabama (and the rest of the country, too).

How Long Will a Bootprint Last on the Moon?

Buzz Aldrin's bootprint (source: Wikipedia)

A couple of months ago, I stumbled across a bunch of pictures of Apollo landing sites taken by one of the cameras onboard the Lunar Reconnaissance Orbiter. The images have a resolution high enough that you can resolve features on the surface down to about a meter. Looking at the Apollo 17 landing site, you can see the trails of both astronauts and a moon buggy. It's pretty cool.

It also got me thinking about how long the landing sites would be preserved. More specifically, I want to know how long Buzz Aldrin's right bootprint (shown, incidentally, to the left) will last on the Moon.  Since the Moon has no atmosphere, the wind and rain that would weather away a similar bootprint here on Earth are not present and it seems as though the print would last a really long time. But how long? Let's try to quantify it [1].