ALCon, the Astronomical League Conference, was to have taken place this year from July 15 to 18 (Wednesday to Saturday), but, like so much else, it has had to be cancelled – for the first time since it began in the 1950s. There won’t be an ALCon till August 4-7, 2021, at Albuquerque, New Mexico.
Nevertheless, you could celebrate a virtual ALCon by looking out at a sky still ornamented by Comet NEOWISE in the northwest and the great planets in the southeast.
See the end note about enlarging illustrations.
It’s now the day after Jupiter’s opposition, but opposition is an event of the soft-edged kind: the planet is essentially as large, bright, and high in the midnight sky for a number of days before and after.
I want to look again at the spider-like diagram of Jupiter’s 12-year cycle of oppositions, shown a few days ago.
This is a heliocentric picture – Sun stationary, in the middle. But there can be a geocentric version – Earth stationary instead.
Jupiter’s path, relative to Earth, forms inward, backward loops, each centered on the date of opposition. The arrows are at the ends of the years. Each pink part of the path is in the morning sky; the yellow part is in the evening sky, from opposition onward to the next conjunction behind the Sun.
This was suggested by the geocentric diagram for Venus on page 31 of my new Venus book.
This is the “pentagram of Venus,” caused by Venus’s cycle of 8 Earth-years or 5 Venus-apparition-pairs. It looks more compact, complex, maze-like than the Jupiter 12-year picture because the orbit is smaller and the paths for the years overlap.
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ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format. You may be able to enlarge them on your monitor. One way: right-click, and choose “View image”, then enlarge. Or choose “Copy image”, then put it on your desktop, then open it. On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers). Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.
Sometimes I make improvements or corrections to a post after positing it. If you click on the title, rather than on ‘Read more’, I think you are sure to see the latest version.
This weblog maintains its right to be about astronomy or anything under the sun.
A thoroughly enjoyable post, I absolutely love the diagrams. As we’ve talked about before, I love thinking about the motions of celestial bodies relative to each other and your geocentric Jupiter plot is one I’d never pictured. Thank you for taking the time to create these and share them – I could look at a book full of them and never get bored of it.
Once again your charts proved most useful. This time to help see NeoWise in the evening sky last night. Thank you for prepring and sharing them, Guy.
These rosette diagrams make it easy to see how Hipparchus, Ptolemy, and many others inferred that the planets move along deferents and epicycles as they orbit the Earth. Even Copernicus needed epicycles to make circular orbits around the Sun synchronize with observations. Then along came Kepler to simplify the math with elliptical heliocentric orbits, and Newton to explain those orbits with the same physical laws that describe an apple falling from a tree or a cannonball landing on a target. And then Einstein, bringing it full circle, realized that spacetime doesn’t have any one unique center, or rather that every point is the center of a uniquely described universe.
I would say that Kepler simplified the model but not the math – an ellipse looks smooth (like an egg) and a circle festooned with epicycles messy (like a coronavirus), but the math behind the elliptical orbit is literally infinite (Kepler’s Equation!).
Your last phrase: “every point is the center of a uniquely described universe.” Is that really a property of relativity? If so, it’s an insight I hadn’t known of before.
Thanks for the clarification about the math of ellipses vs. circles. That’s an interesting distinction, that a smooth model has complicated math. Come to think of it, a huge reason why deferents and epicycles were used for millennia is that you could calculate the position of a planet at any time using manageably simple formulae.
I don’t understand the actual math of special relativity at all, so I can’t defend my impression that every point is the center of a uniquely described universe. Maybe that’s just a colorful oversimplification. But when you think about frames of reference, clocks running at different speeds depending on how fast they’re accelerating, and distances shrinking as an object’s speed approaches the speed of light, it seems like a reasonable picture. In his book “From Eternity to Here”, Sean Carroll describes the unique light cone of every point in spacetime, with our pasts and futures delimited by a unique cone in four-dimensional spacetime. That made an impression on me.
I’ve just started reading Carlo Rovelli’s “The Order of Time” which addresses similar concepts. So far I’m enjoying it, and I think I understand most of what I’ve read so far on a conceptual level. The mathematical formulae in the end notes are all Greek to me.
Cloudy today but I had a beautiful view of the comet 2 nights ago, it’s naked and I think the brightest since the Holmes Comet although I did see one a few years ago but it was via a monocular and wasn’t naked eye.Neowise is superior to the Holmes Comet in that it has a tail,2x, like a comet should.i viewed it naked eye, Zeiss mini quick 5×10 monocular and Viking 10×42 monocular to even better it had noculuicent clouds under it!