Yesterday, I was minding my own business when a captain idea loomed on my horizon with a little nudge from my shipmate JamBerry. My allusion to Fibonacci numbers in my maiden blogpost inspired her to share something cool about that series and Earth's relationship with Venus. Here is how it began.
JamBerry 022218ZJAN14 saw this just now and thought of your math blog . . . [Link to a really cool graphic]
Me 022308ZJAN14 Oh, man! I love this. Off to research this graphic.
I am not ready to share yet. It blew my mind, but I am a skeptic because some stuff floating around the Internet is full of errors. I will divulge what I have know mathematically. You can find three Fibonacci numbers in the relative orbits of Venus and Earth.
I easily confirmed two of the numbers (8 and 13) before bedtime. I researched the other number for about three hours before giving up. Trying to sleep with a captain idea in your head is as much fun as trying to sleep with a rock in your stomach. It took me about an hour in the morning to clinch the third one (5).
The first factoid is this: Earth orbits around the sun almost exactly 8 times in the same time it takes for Venus to orbit the sun 13 times. By almost exactly, I mean when rounded to the hundredths place. Both 8 and 13 are Fibonacci numbers.
The first step in verifying anything is looking up facts from a reliable source like NASA: Venus orbits the sun in 224.701 days while Earth takes 365.256.
Given that information alone, I demonstrated that 8 earth cycles is the same as 13 earth cycles by setting up a spreadsheet. It took about five minutes to verify the claim. Can you do it?
It's okay if you're struggling. There is a way to figure this out if you're willing to venture out into space on the mathship Rarefied.
Grab your math notebook (perhaps, a fresh cup of coffee) and watch this animation of the orbit of the inner planets. Earth is the blue ball with the moon in orbit. Venus is the yellow ball. Do you see the date in the upper right corner of the screen? Click it and type 11-1-2014 (11 Jan 14). Why? The sun, Venus, and Earth fall on the same line (collinear) with Venus in the middle. That will make counting orbits easier. Below is a screen shot I took before I started the animation.
Are you ready to start the animation? There is a motion box in the upper left. The neat thing is that you can back up the animation in time or go forward. The future interest me the most, so I clicked the rightmost arrow.
Did it work? Mine did. I felt a little giddy when the date rolled around to 11-1-2022. A nearly perfect alignment of the sun, Venus, and Earth.
Tomorrow, I will share my numbers if you want to compare notes.
29 days and a wake-up until the winner of the potholder giveaway is announced. What giveaway? Read on for more details.
P.S. Did you notice how I slipped in that math term you might have forgotten from high school geometry? I hope you will think about the sun, Venus, and Earth the next time you run across the word collinear.