### Kepler 2: Photometry, With a Vengance

The highly successful NASA Kepler Mission was a beautiful thing, and its beauty was primarily in its simplicity. The mission is based on a 1-meter Schmidt camera in space that resides in an orbit about the Sun with a semimajor axis slightly larger than the Earth's. This "Earth-trailing" orbit allowed it to maintain a continuous gaze on a single target field near the constellations Cygnus and Lyra, just off of the Galactic plane.

Once Kepler reached its orbit, it blew away a dust shield that covered the front of the telescope and from that point onward there were very minimal moving parts. On the space telescope there is only a single instrument: a 340 megapixel CCD imager of epic proportions. There are no other instruments to swap in and out of the light path, no filters, not even a shutter. For four years Kepler measured the brightnesses (relative fluxes) of ~150,000 target stars searching for periodic eclipses of planetary companions.
 One of Kepler's infamous reaction wheels.

The Kepler telescopes only major moving parts were four "reaction wheels," which used the principle of the conservation of angular momentum to keep the telescope precisely aimed at the target field. Early in the mission, one of these wheels failed. Fortunately, only three wheels were needed, and Kepler soldiered on past its expected mission lifetime of 3.5 years and was poised to enter into a glorious extended mission, with a target list modified to include thousands of additional red dwarfs, the stars my group and I love so much. However, on the eve of the extended mission, a second reaction wheel failed, leaving Kepler without the ability to maintain precise pointing. Cue sad trombone.

However, there were rumors and stirrings that there may be a way to operate the telescope using only two reaction wheels. The space-flight and control-theory wizards at NASA Ames Research Center have been working tirelessly since Kepler's death was announced. Using creativity, grit and the power of engineering and science, the wizards have come up with a viable plan. Instead of a third reaction wheel to stabilize the telescope, they'll use radiation pressure supplied by the Sun. That's right, the Sun will be Kepler's third wheel!

Light can be thought of as a wave or particle phenomenon. Light doesn't care which, but if you think of light as discrete particles, their collision with, say, a spacecraft imparts a bit of an impulse. Not much, mind you. But there are many, many photons streaming out of the Sun, and their individual momenta adds up. And since the Kepler spacecraft has a nice house-roof-shaped ridge along its back solar panels, the spacecraft can be oriented like a rudder in the stream of photons coming from the Sun. Viola!

Now let's hope that the preliminary tests show that this is truly viable, and then let's hope that NASA has the funding and will to make K2 a reality.

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### Finding Blissful Clarity by Tuning Out

It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…