Author: John F. Lindner

  • Barred Warped Wobbly Spiral

    John F. Lindner

    Advances in astronomy can rewrite even introductory astronomy textbooks. Although no spacecraft have yet exited our Milky Way galaxy to image it from the outside, the Gaia astrometry space telescope recently completed a dozen years of accurately measuring the positions, distances, and motions of billions of Milky Way stars from a Lissajou orbit about the…

  • Weak Prime Number Theorem

    John F. Lindner

    As a child, I was inspired by Arthur C. Clarke‘s 1956 science fiction novel The City and the Stars to search for patterns in prime numbers. Chapter 6 begins: Jeserac sat motionless within a whirlpool of numbers. The first thousand primes, expressed in the binary scale that had been used for all arithmetical operations since…

  • Fram2 Over the Poles

    John F. Lindner

    Historically, astronauts have launched roughly east to exploit Earth’s spin, as the terrestrial equator moves at nearly 1000 mph with respect to its center. But last week the Fram2 SpaceX Dragon crew launched south from the Kennedy Space Center to become the first humans to orbit Earth over its poles. The all-private, all-international, rookie crew…

  • 2D Kepler Conjecture

    John F. Lindner

    Johannes Kepler asserted in 1611 that no packing of identical balls has density greater than the hexagonal close-packed “cannonball” packing of oranges at a grocery store’s fruit stand. But the gulf between intuition and proof was so large that the latter was not achieved until the work of Thomas Hales and Samuel Ferguson in 1998.…

  • Blue Ghost Eclipse

    John F. Lindner

    Last night’s lunar eclipse, as seen from Earth, looked like a solar eclipse, as seen from Luna. Firefly Aerospace‘s NASA-funded Blue Ghost lunar lander recently became the first commercial spacecraft to successfully land on Earth’s moon Luna. Blue Ghost’s mission is designed to last a single lunar day, about two terrestrial weeks. Last night it…

  • Mach Cutoff

    John F. Lindner

    Two weeks ago, I watched live via Starlink as the Boom Supersonic XB-1 test aircraft broke the sound barrier in level flight, the first all-civilian aircraft to do so. This success promises the return of commercial supersonic flight, at least over ocean. This week, during the final test flight, I learned that no sonic boom…

  • Mount Wilson Trek

    John F. Lindner

    Nobody walks in L.A., but as a Caltech grad student without a car in the mid 1980s, I once walked from my dorm room up Mount Wilson and touched the enclosure of the famous 100-inch (2.54-meter) Hooker telescope, for 32 years, the world’s largest, where Hubble discovered that the Andromeda “nebula” was actually a galaxy…

  • Outer Planet Cloud Colors

    John F. Lindner

    From my teens to my twenties, from junior high school to graduate school to young professor, I excitingly followed the first reconnaissance of the outer solar system by the Pioneer and Voyager spacecraft. But the exploration isn’t over. For the last decade, the Hubble Space Telescope has been systematically observing the colors and dynamics of…

  • Sum of Reciprocals

    John F. Lindner

    The sum of the reciprocals of the natural numbers diverges, but slowly, like the logarithm of the number of terms. The sum of the reciprocals of the prime numbers also diverges, but even more slowly, like the logarithm of the logarithm of the number of terms, as the primes are sparse in the naturals! Here…

  • There and Back Again

    John F. Lindner

    I awoke yesterday at dawn in a log cabin in Vermont. Fortunately, the wifi was good. Each successive test of the SpaceX Superheavy Starship has been a significant improvement over the previous one, and test five was no exception, with both the booster and the ship demonstrating soft pinpoint landings — except this time, the…

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