Shuttles Come Nose-to-Nose

NASA's space shuttles Endeavour and Atlantis switched locations today at Kennedy Space Center in Florida, and in the process came "nose-to-nose" for the last time in front of Orbiter Processing Facility 3.

Endeavour was moved from Orbiter Processing Facility 2 to the Vehicle Assembly Building where it will be housed temporarily until its targeted departure from Kennedy atop the Shuttle Carrier Aircraft in mid-September. After a stop at the Los Angeles International Airport, Endeavour will move in mid-October to the California Science Center for permanent public display.

Now in the processing facility after leaving the Vehicle Assembly Building, shuttle Atlantis will undergo preparations for its move to the Kennedy Space Center Visitor Complex in November, with a grand opening planned for July 2013.

From Pedro A. Pisa in Scripta Mathematica, September 1954 — this identity:

1234 + 2484 + 3674 = 1254 + 2444 + 3694

… remains valid when the digits in each term are permuted in the same way:

1234 + 2484 + 3674 = 1254 + 2444 + 3694 
1243 + 2448 + 3647 = 1245 + 2444 + 3649 
1324 + 2844 + 3764 = 1524 + 2444 + 3964 
1342 + 2844 + 3746 = 1542 + 2444 + 3946 
1423 + 2448 + 3467 = 1425 + 2444 + 3469 
1432 + 2484 + 3476 = 1452 + 2444 + 3496 
2134 + 4284 + 6374 = 2154 + 4244 + 6394 
2143 + 4248 + 6347 = 2145 + 4244 + 6349 
2314 + 4824 + 6734 = 2514 + 4424 + 6934 
2341 + 4842 + 6743 = 2541 + 4442 + 6943 
2413 + 4428 + 6437 = 2415 + 4424 + 6439 
2431 + 4482 + 6473 = 2451 + 4442 + 6493 
3124 + 8244 + 7364 = 5124 + 4244 + 9364 
3142 + 8244 + 7346 = 5142 + 4244 + 9346 
3214 + 8424 + 7634 = 5214 + 4424 + 9634 
3241 + 8442 + 7643 = 5241 + 4442 + 9643 
3412 + 8424 + 7436 = 5412 + 4424 + 9436 
3421 + 8442 + 7463 = 5421 + 4442 + 9463 
4123 + 4248 + 4367 = 4125 + 4244 + 4369 
4132 + 4284 + 4376 = 4152 + 4244 + 4396 
4213 + 4428 + 4637 = 4215 + 4424 + 4639 
4231 + 4482 + 4673 = 4251 + 4442 + 4693 
4312 + 4824 + 4736 = 4512 + 4424 + 4936 
4321 + 4842 + 4763 = 4521 + 4442 + 4963

And everything above holds true if each term is squared.

Probability

Imagine two concentric roulette wheels, each divided into 100 sectors. Choose 50 sectors at random on each wheel, paint them black, and paint the rest white. Prove that we can now position the wheels so that at least 50 of the aligned sectors match.

Ans:

Follow a sector on the inner wheel through a complete revolution: That sector will find exactly 50 matches. The same is true for each of the 100 sectors on the wheel; altogether, as the wheel turns through 100 positions, there will be 100 × 50 = 5,000 matches. This means that the average number of matches per position is 50, so there must be at least one position with 50 matches.

The Hustle and Bustle of Our Solar System

This diagram illustrates the differences between orbits of a typical near-Earth asteroid (blue) and a potentially hazardous asteroid, or PHA (orange). PHAs are a subset of the near-Earth asteroids (NEAs) and have the closest orbits to Earth's orbit, coming within 5 million miles (about 8 million kilometers). They also are large enough to survive passage through Earth's atmosphere and cause damage on a regional, or greater, scale.

Our yellow sun sits at the center of the crowd, while the orbits of the planets Mercury, Venus and Mars are shown in grey. Earth's orbit stands out in green between Venus and Mars. As the diagram indicates, the PHAs tend to have more Earth-like orbits than the rest of the NEAs. The asteroid orbits are simulations of what a typical object's path around the sun might look like.

The dots in the background are based on data from NASA's NEOWISE, the asteroid-hunting portion of the Wide-field Infrared Survey Explorer (WISE) mission, which scanned the whole sky twice in infrared light before entering hibernation mode in 2011. The blue and orange dots represent a simulation of the population of near-Earth asteroids and PHAs, respectively, which are larger than 330 feet (100 meters).

NEOWISE has provided the best overall look at the PHA population yet, refining estimates of their numbers, sizes, types of orbits and potential hazards. The NEOWISE team estimates that about 20 to 30 percent of the PHAs thought to exist have actually been discovered as may 2012, the date of this image.

Image Credit: NASA/JPL-Caltech