Posts Tagged ‘math’

Mercury MESSENGER Mission

Tuesday, October 14th, 2008

MESSENGER is a scientific investigation – by spacecraft – of the planet Mercury. The name comes from “MErcury Surface, Space ENvironment, Geochemistry, and Ranging,” highlighting the project’s broad range of scientific goals.

MESSENGER is the first orbital study of Mercury, and this is very cool! I’m all for the exploration of space at any cost. What makes me most interested in this mission is not that it’s the first mission of its type to Mercury, but the way the probe is arriving. I’ve swiped the image from the Mission Page, so I can show it to you here:

The MESSENGER probe follows quite a circuitous path to its destination

The MESSENGER probe follows quite a circuitous path to its destination (click for big)

What you see here, is a diagram of the trajectory the probe will take.

  1. The probe leaves Earth
  2. One year later, Earth gives it a gravity-assisted push to Venus
  3. Venus catches it and pushes it out again on a slightly different orbital path
  4. Venus catches it again and pushes it to Mercury
  5. Mercury then catches and pushes it three times, each time placing it on a slightly different path
  6. The fourth time the probe encounters Mercury, the probe is supposed to be at the right speed and vector to enter orbit

That’s pretty nuts, huh? Seeing this trajectory diagram gives me a great excuse to show you my wallpaper at work.

Crippled satellite slingshots around moon to correct its orbit

Crippled satellite slingshots around moon to correct its orbit (click for original article)

Basically, a satellite got fucked and we needed to get it back – but how? SEND IT TO THE MOON! The science behind this is obvsiouly rocket science, but it’s really not that hard. For the most part, if you had the idea to use gravity wells in sequence to get the proper vectors in order, a low-level physicist, even a B student at a community college, could bang this out in an afternoon. Of course there are other like effeciency and mass changes due to using fuel for launch and attitude controls, but the “big picture” really is as easy as solving for x.

nanos gigantum humeris insidentes

It’s hard to think of a more applicable quote than “Standing on the shoulders of giants…” here. If a relatively uneducated person (relative to a top physicist), can come up with an trajectory of a probe that uses planets as gravity-assist slingshots for proper orbital insertion, then humanity has come a long way since believing “Here be dragons.”

Of what use is a child? 
-Benjamin Franklin

That depends – what is its tensile strength?

PS: In this post, I go crazy with HTML tags.

Pizza π

Monday, August 4th, 2008

At work today, pizza was provided in the break room as the first day of Employee Appreciation Week. It was Cici’s, so it was terrible of course, but I still helped myself to a couple slices. Come on, free pizza! Why wouldn’t I pass it up?

It got me thinking though. The slices were ridiculously small, something like 20 slices to a large pie. I know Pizza Hut will allow you give special instructions for how to slice the pizza. The example they give is “cut into squares.” That’s a pretty neat service if you ask me. Why not ask for something obnoxious though? The reasons are obvious, like not wanting extra off-menu toppings (gross) on your pizza, but how about a pizza cut into 7 slices?

Anything 5 slices and under require only a little thought. Everyone knows how a 5 point division works. 6 is an easy concept, the cuts go all the way through, the difficulty is simply in getting the slices all the same size; but from my experience in receiving pizzas for delivery, this mustn’t be a hard and fast requirement either – even on the standard 8 slice pie…

7 though. That’s tricky. It’s seven cuts, all halfway through. And on large surfaces, the middle is hard to find unless you mark it. And what are you gonna mark it with? A topping? Maybe not, overshooting the middle is acceptable for difficult cuts though so I’ll let that slide. You might get lucky and get an engineering major who’s putting himself through college on this one and end up with a perfect result.

And on the maximum side, anything over 10 is ridiculous. Even on extra-large pizzas, the slices get too small after 12. You might be able to do an 11-slice pizza on that size of pizza, but with the same technical difficulties as a 7 or even a 9.

How about cutting it into pieces that aren’t slices at all? A spiral cut that’s still one piece, or a pentagon or pentagram? That could be fun…

“Avoid the noid”

Electric Companies Benefit from Software Piracy

Sunday, July 15th, 2007

Surely I can’t be the first one to note that software piracy isn’t completely cost-free, can I? I won’t go too in-depth here, but computers don’t run on fairy dust, they run on electricity. Delicious electricity. As for myself, my computer has a 650 Watt power supply and I pay 14 cents per Kilowatt-hour of electricity. This means that if I run my computer for one hour, I pay the electric company:

(650 Watts / 1000 [1 Kilowatt]) * $0.14 = 9.1 cents

Another way to conceptualize this with easier math, is if I have a 1000 Watt (1 Kilowatt) computer, and I run it for 1 hour, it costs me 14 cents. So, if I were to download a 5 GB file through unscrupulous means – which, for the most part have abysmal transfer rates unless you pay for other, faster, services (another can of worms to this line of reasoning) – for 500 hours, it would cost me about $45 versus, the $30-$35 cost of going to the store and picking it up legitimately. Piracy is more expensive than acquiring software through legitimate means to the end-user (pirate). The money just goes to a different place. I’d prefer actors or musicians getting a fraction of a penny for my purchase than the power company getting my dime.

Now, this whole argument goes out the window if you download in the background casually, and only when you would be using the computer anyway. At which point, the extra cost of piracy to you, the pirate, is zero. Understand though, that you are still using your computer to do… whatever it is you use it for, and you still pay the electric company.

You dirty pirate.