only 1 human being on the entire Internet tried to answer this PizzaQ, you're all expelled!
Click this for original PizzaQ.
used allercalc and mostly openoffice sheet.
plz let me know if I got it right.
a = semimajor axis
b = semiminor axis
dist btwn ctr and focus
e = eccentricity
Phi = arcsin(e) = 0.016710997
E(e) = (I used allercalc here)
Units are Fz. Or Frongoz
FORMULAS ONLY BELOW
e*a=dist btwn ctr and focus
E(e) is the complete elliptic integral of the second kind for the eccentricity e = sin ? (tables are usually given in terms of ? instead of e). E(0) = ?/2, and E(1) = 1, corresponding to the limits of a circle, b = a, and a straight line, b = 0.
Modular angle = alpha,
Eccentricity ^ 2 = (a2*a2-b2*b2)/(a2*a2)
Alpha = arcsin k
k = .016710219230
let me just come right out and say I'm not definitively solving this problem this time either, just sharing where I'm at.
how about Ramanujan's formula approximation of 939,885,629.4 Fz?
hmmm. solving the complete elliptic interval of the 2nd kind (ellipticE function) seems too tricky, in light of my current inability to comprehend the concept of the elliptic modulus or the modular angle.
939,885,629.2 Fz. is the eerily similar alternate answer I come up with when I use pi/2 instead of whatever phi really is in allercalc's ellipticE function. I've figured out that phi is supposed to refer to the angle at which a hypothetical circle is positioned relative to the x-y plane to make the present ellipse, but exactly calculating it is something my searches have not answered. It's not just the golden ratio, 1.61803399, right?
I can proudly say I didn't consult with anyone to get these answers, except of course google, wikipedia, answers.com, and probably half a dozen other sites.
Attention all Space Cadets. Listen up, this is the Commandant speaking:
The entire graduating class of 2010 is hereby Expelled, and this will go on your permanent records.
Except you, Anonymous.
Your answer differs from mine by a distance of less than one frongo. That's close enough to stick your head out of a window of your sexy spacecraft and see your Space Lobster trap, if the flashers are still working.
Have you ever eaten Space Lobster? Raumus homardus, and the sweetest, tenderest damn thing you ever dipped into melted butter. And they are PRICEY!
Around 1660 the Puritan authorities on the Atlantic coast of Massachusetts forbad citizens from feeding their slaves and servants (Atlantic) lobsters more than twice a week. In them days, you could take an hour's walk down the beach and fill a bushel basket with the squiggly little suckers. They were considered trash food; they're forbidden by Kosher law, and the Puritans were trying to re-establish a New Jerusalem.
Vleeptron's got the Ministry of Food & Beverages working on the problem, but so far the bad news seems to be that Space Lobster is just as forbidden, by exactly the same Entity, for largely the same reasons, as Atlantic and Mediterranean Lobster.
Okay, back to the Length of the Orbit of Planet Yobbo.
Anonymous has gotten reallllllllllllly intimate with the Ellipse. I hope he had a good time. I hope he had a lot of aspirin in the medicine chest.
Me, I was lucky, I found a way where I only had to throw a and b at the Ellipse, and then flee. Me and the Ellipse did not get nearly so intimate.
If you are experiencing intimate math problems, this is about the best place, this guy has all the answers:
but if you want to read all the gossip and smut about the lives of all the hot mathematicians through history
Which mathematician was licked all over his body for a week? These guys know. I know. And we know why he was licked all over his body. Do you? 1 slice.
I got this infinite series by Colin Maclaurin 1742 -- certainly a worthy ancestor of Ramanujan, who must have thrilled to it when he found it as a schoolboy -- which claims to get the answer on the nose to any decimal precision your little heart desires.
You win the 3 damn slices of Pizza! And Vleeptron is troubled to report that Anonymous lives so nearby that Vleeptron may finally actually have to fork over the pizza.
The life of a Space Lobster must be a very cold and harsh life. I don't know how they survive, particulary being as tasty as they are. I had one the last time I was in Ciudad Vleeptron, gently grilled in EVOO, maybe a little fresh garlic and parsley, but nothing to challenge the natural taste. On the juke box, Caruso was singing "Vesta la Giubba" and I had a glass of Chianti. I was wearing a Toronto Maple Leafs toque and those running shoes with red LEDs blinking in the heels, like parking flashers.
We'll try to find some new recruits to take the place of all of you who Washed Out. This is a sad day for the Vleeptron Space Academy, a sad, sad day. The VSW only just opened a few years ago, they make a lot of jokes about us down in Poortown and over on Hoon. The Board of Inquiry determined that the loss of the vessel was Not Our Fault.
btw we previously hinted that 1 frongo = 1 kilometer. By an even more amazing coincidence, the semimajor and semiminor axes of Yobbo are exactly the same as those of Earth, the third massive sphere out from Sol.
Maclaurin says if you crank the handle on his equation just 4 times (in Nerd: the infinite series converges very rapidly), you soon find that every year, Earth travels
T = 4
C = 939885629.430007 km
C = 939885629.430007 km
... that's the Circumference of its orbital ellipse. Close enough to find your lobster trap.
btw Vleeptron certainly didn't do this by hand. Our prime contractor, Central American Rockwell, handed the job over to Yankee Magnetic Software ("Solving things you never even knew were problems!"), and they whipped Maclaurin's equation out in the world's finest high-level programming language, Microsoft QuickBasic. (Microsoft no longer sells or supports QB. That really bites.) We just arbitarily asked for that much precision, and we plum got it.
I think this Maclaurin guy was very smart, check this out:
However, Maclaurin had to defend a thesis in a public examination for the award of this degree (which is not the case today), and he chose On the power of gravity as his topic. The thesis, which developed Newton's theories, was written by a 14 year old boy at a time when such advanced ideas would only be familiar to a small number of the leading mathematicians.
I'm sure he and Ramanujan would have had much to talk about. "Much can be done with a Scotsman, if he be caught young," Dr. Johnson said.