Celestial conjunctions and telluric temblors

Two nights ago was the closest approach of Venus and Jupiter in a conjunction, and despite the very rainy weather this summer the sky was actually clear enough just after sunset for me to get a few photos. Not entirely clear, mind you, but I think the ragged clouds drifting across the sky add to its effect.

Venus and Jupiter in conjunction. Captured with my Pixel 7 Pro.

Venus is the brighter of the two bright lights on the right, with Jupiter on the right. After the Sun and Moon Venus and Jupiter are the third- and fourth-brightest objects in the sky, so their conjunction is particularly impressive. Above and to the left of them you can faintly see Messier 44, the Beehive Cluster in Cancer.

Last night we also had an earthquake just as I was dropping off to sleep of about magnitude 4.7, with an epicenter about 23 km to the east. I realize now that I haven't mentioned the larger earthquake (magnitude 6.0) which happened back on May 22nd over on the western side of the island. (The largest earthquake I've felt since the magnitude-6.2 tremor I felt within a month of moving back to Hilo in 2021.) Both of these earthquakes felt pretty long; it's always hard to estimate time during an earthquake, but I've lived through enough that I feel pretty confident that these were on the longer side of ones I've experienced. Neither produced any damage here thankfully, though the larger one did some damage on the western side of Hawaiʻi island.

According to the USGS the large one was fairly deep, at 22.6 km; deep enough that it likely wasn't volcano-related, but was instead due to the ocean crust buckling and adjusting to the weight of the island. Last night's was also pretty deep, at 39.2 km, so I wonder if it's simply the crust adjusting on this side in response. As I like to say, life's never boring when you live on a volcano in the middle of the Pacific ocean! A hui hou!

Rocks in Space: Finding Asteroids in the Solar System

I came across a neat video on YouTube the other day, showing visually the discovery of all the asteroids found since 1970 up to the present.

In this video the Sun is at the center, with the inner planets (and occasionally Jupiter) seen rotating around it from a position above the plane of the solar system (so looking down on the Earth's North Pole). The planets aren't labeled, but it's easy to count outwards from the Sun to find Earth. At the start of the video in 1970 all of the 4,422 asteroids known at that point are marked with tiny dots. (It's best to watch on the highest resolution you can, otherwise they're hard to see.) As time unfolds, asteroid discoveries are marked with bright white dots, before fading to a fainter color. Yellow and red dots (I'm guessing) are asteroids that come close to Earth, or Near-Earth Objects (NEOs).

Later in the video you might notice asteroids in the same orbit as Jupiter. These are known as the Trojan asteroids. These asteroids orbit the Sun in roughly the same orbit as Jupiter, but 60° either ahead or behind of it. The name comes from the fact that early on the first few discovered were given names from the Trojan War (starting with 588 Achilles), and it was proposed to continue with the naming scheme and give them all such names. The naming scheme even extends to location: asteroids ahead of Jupiter are given names from the Greek side of the war, while those trailing it are given names from the Trojan side. (Though amusingly, there are two out-of-place names from before this particular convention was adopted: Patroclus is found among the Trojans, and Hektor among the Greeks.)

The term Trojan asteroid originally referred to just the asteroids in the orbit of Jupiter, but when other asteroids sharing similar orbits with other planets were found the term expanded to encompass them as well. Currently Trojan asteroids are known for Earth (1), Mars (7), Jupiter (6,000+), Uranus (1), and Neptune (13).

As for why Trojan asteroids are generally found around 60° in front of or behind the planets they share an orbit with, that has to do with gravity, the three-body problem, and Lagrange points, and really deserves a blog post to itself sometime.

And finally, while watching these nifty visualizations, just keep in mind the fact that sizes are not to scale. In reality, while it looks like the asteroid belt is a swirling maelstrom of space debris, there are typically millions of miles (or kilometers!) between any two asteroids. There may be a lot of rocks out there, but there's an even larger volume of space to hold them. A hui hou!

Science Clock Series: Part XI

Today's number comes from astronomy and is given by:

\[\approx\ \text{diameter of ♃(in \(\beta\); \(\oplus=1\beta\)}\] This is a slightly roundabout way of saying "approximately the diameter of Jupiter in Earth-diameters." Let's look at it a little more closely:

First of all, what in the world is ♃ supposed to be? Or \(\oplus\)? To answer those questions we need to go back in time. About 2,000 years in fact, give or take. You see, one thing that I've learned from idly inspecting ancient writing, whether written, inscribed, or etched, is that ancient people liked to abbreviate.

Although it surprised me at first, this is entirely reasonable when you think about it; we do it all the time in everyday life, especially with the proliferation of instant messaging. Ancient peoples had to write everything by hand, which in my opinion is very dull and tiresome. You start looking for ways to reduce the amount you have to write, and before you know it you've got abbreviations all over the place.

Anyway, writing goes back a long time, but for much of history it was limited to a thin slice of the most educated in society. The study of astronomy also goes back a long time, and was one of the most common subjects for that educated elite to study, given its importance to pre-Industrial societies in helping to determine things like the proper time to plant and harvest crops in order to ensure everyone didn't starve over the winter.

Put those fact together, and people have been writing about astronomy for a very long time. Some of the oldest writings we find have been discovered to be about astronomy. Since it was so important, and given that most people like to save time and effort when writing, ancient astronomers in the Hellenistic period around the time of Christ came up with a set of symbols to refer to the "planets."

Note that the word "planets" in this context refers to the seven "planets" of the Ptolemaic (and originally Aristotelian) heliocentric system: the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn.These are the objects which, if you're familiar with the night sky, appear to move across it against the background of the fixed stars. Anyway, ancient astronomers came up with symbols for them that were used up through the Renaissance period. In fact, their use was so common that when astronomers such as William Herschel started discovering new planets astronomers rapidly came up with new symbols for them too. Anyway, here's a table with the symbols for the Sun, and the eight planets discovered before 1900:
\begin{align*}
\text{Sun}&\dots☉\\
\text{Mercury}&\dots☿\\
\text{Venus}&\dots♀\\
\text{Earth}&\dots\oplus\\
\text{Mars}&\dots♂\\
\text{Jupiter}&\dots♃\\
\text{Saturn}&\dots♄\\
\text{Uranus}&\dots♅\\
\text{Neptune}&\dots♆
\end{align*}You may be familiar with the symbols for Mars and Venus, as they have come to stand for “male” and “female” respectively in modern usage. Other than that, the only symbols commonly used in astronomy any more are the ones for the Sun and Earth. It's standard practice in astronomical journals for the symbols \(\text{R}_☉\), \(\text{M}_☉\), and \(\text{L}_☉\) to stand for the mass, radius, and luminosity of the Sun, respectively (and similarly for the Earth using the symbol for Earth).

It might give you some indication just how little known these symbols are today if I told you that right up until I looked them up to write this post I thought the symbol for Jupiter on my clock stood for Neptune!

Now that I know it stands for Jupiter, we can look at what the clock actually says: approximately the diameter of Jupiter in terms of “beta”, where “Earth” = 1 “beta.” I actually looked up beta to make sure there wasn't some special use for it that I wasn't aware of and couldn't find anything, so I'm not entirely sure what the point of introducing it only to immediately define it as one Earth was. Anyway, if we then check with the diameters of both Earth and Jupiter, we find that Jupiter does indeed have a diameter about 10.9377 times greater than Earth's.

So there you have it. And I realize this post isn't actually as short as I promised last time, though hopefully it was still interesting. There's a lot related to the astronomical symbols that I didn't cover, such as the fact that several were created for the first nineteen asteroids discovered before people realized that creating unique symbols for every asteroid would be effectively impossible and gave up (given that we now know of over a hundred thousand asteroids and suspect there may be ten times that number in the solar system, we can see that this was a good decision!).

Anyway, check back for the final post in this series, with a number from meteorology! Click here to jump directly to it.

Moons and Months

It's probably not a big surprise to most of you to learn that the words for "moon" and "month" are related in English (and some other languages as well). Our Moon's orbital period of 27 days, 7 hours, and 41.1 minutes comes very close to the number of days you get when you divide the Earth's orbital period by twelve, and makes a nice natural division of time.

But have you ever thought about the moons of other planets? For example Mars' two moons, Phobos and Deimos, orbit their parent planet in just 7 hours 40 minutes and 30.3 hours respectively. Many of Jupiter and Saturn's close-in moons likewise orbit in less than an Earth day. In fact, there are dozens of moons with a shorter orbital period than our Moon.

On the flip side of the scale, there are also dozens of moons with longer orbital periods than our Moon. Jupiter and Saturn both also have lots of small, irregular moons that orbit far from their parent body, which can take months or even years to complete one orbit. Saturn's moon Phoebe, for instance, takes 550.3 days to make a complete circuit, nearly two Earth years. Prior to last week, I knew of a few Jovian moons with orbital periods measured in days in the 600's and 700's. Given Jupiter's humongous mass, you'd expect that it would be able to hold onto satellites further out than other planets, which would have correspondingly long orbital periods.

So you can imagine my surprise when I, on a whim, looked up the satellite with the longest orbital period and discovered it belonged to...Neptune?? And not just by a few days or even a few months – we're talking years here.

In fact, it turns out the four longest orbital-period moons all belong to Neptune. The two inner ones, Sao and Laomedia, have orbital periods of 7.97 and 8.68 years respectively. The two outer ones, Psamathe and Neso, take 24.84 and 26.67 years to orbit Neptune once, respectively.

I found this revelation absolutely mind-boggling. Neither of these moons has completed an orbit since I've been born. They have longer orbital periods than the first five inner planets. They orbit Neptune at a mean distance of around 48-49 billion kilometers (about 30 million miles), which is nearly a third of the distance from the Earth to Sun. At its furthest point, Neso can be further from Neptune than Mercury ever gets from the Sun!

If you wondered, like me, how Neptune and not Jupiter can have the furthest-out and longest-orbiting satellites, it has to do with something called the Hill sphere (named after 19th-century American astronomer and mathematician George William Hill). The Hill sphere is basically the region of space in which an object's gravitational pull dominates the attraction from other objects in the region. For a moon to remain in orbit about a planet, it must remain entirely inside the planet's Hill sphere, or it will eventually be pulled loose by the gravitational perturbations of other planets. This limits how long of an orbital period a moon (or other satellite) can have before it is no longer stably bound to its parent planet. For instance, the mathematics suggests that it is impossible for the Earth to have a satellite with an orbital period of longer than about seven months.

To get to the point, a planet's Hill sphere depends both on its mass, and its distance from the Sun (and other massive sources of gravitational perturbation). Jupiter, of course, is many times more massive than Neptune (and all the other planets combined), but Neptune is several times further from the Sun. Add in the inverse-square nature of gravity, and Neptune manages to eke out a victory in the "largest planetary Hill sphere" competition. (Interestingly, of the four outer planets, Jupiter has the smallest Hill sphere; it increases slightly but steadily in size from Jupiter through Saturn and Uranus on to Neptune. Turns out increased distance from the Sun is more important than decreasing mass.) Neso and Psamathe are orbiting nearly at the outer limit of Neptune's Hill sphere, so they are likely to remain the moons with the longest orbital periods for the foreseeable future.

Of course, they were only discovered in 2002 and 2003, respectively, so who knows what else could be out there! It's an exciting time for us lovers of planetary science and Solar System dynamics.

Anyway, I hope you found that as interesting as I did. If you're interested in other comparisons between the moons of the Solar System, this page on Wikipedia has a nice table that you can sort by various categories.

Our Star

Have you stopped to ponder just how mind-blowingly huge the Sun is lately?

Last week while volunteering up at the Vis I took a picture of the Sun through the solar telescope on a whim. I noticed a large sunspot group on it, but didn't think anything else of it until this week when I learned that said sunspot group (called Active Region 1339) is one of the larger ones on record. I'd also heard somewhere along the line that it was larger than Earth, so I decided to do some visual comparing of my own. After seeing how Earth and Jupiter looked against the Sun, I decided to go all the way and add the rest of the planets. This image is the result. It shows the 8 planets of our Solar System against the Sun with AR 1339, all of them correctly sized relative to each other. (The distances between the planets are not to scale, due to the way I set up the picture.)

Our Solar System.

Look at this image, and let it sink in for bit. The Sun accounts for a whopping 99.86% of all matter in the Solar System. It's big. For fun, see how many other sunspots you can spot in this picture that are larger than Earth.

Edit (11/25/11): One other thing I like about this picture that I forgot to mention the first time is the sense of security it gives, when you really think about it. Stable orbits, despite their ubiquity in nature, are still nothing to take for granted, and it's sort of comforting seeing just how huge the Sun is compared to the Earth, and just how firmly we're caught in its gravitational embrace.

“Tremble before Him, all the Earth; indeed, the world is firmly established, it will not be moved. Let the heavens be glad, and let the Earth rejoice” -- 1 Chronicles 16:30-31a

Celestial Choreography.

Since I'm going up to Mauna Kea tonight, I thought I'd put up some pictures I took the last time I was there. The first one is very cool, because it shows one of the phases of Venus. I don't recall ever having seen these before, so it was an awesome experience for me. Seeing such phases is one way to tell that Venus orbits closer to the Sun than we do.

Crescent Venus.

North is roughly off to the right in the picture. Note the chromatic aberration present in the image, visible as a slight separation between the most red and most blue parts of the image.

The second picture is of Jupiter, the behemoth of the solar system.

  

North is up in this picture. You can clearly the North Equatorial Belt near the top of the planet. The corresponding South Equatorial Belt has been missing for several months now. It will no doubt return as it always has sometime in the next few years, but for now you get to see the planet in a little more lop-sided version.

While checking up on Jupiter, I learned a rather funny fact about the Trojan asteroids. The Trojan asteroids are two groups of asteroids that are caught by gravity at Jupiter's L₄ and L₅ Lagrange points. This means they orbit the Sun roughly 60 degrees ahead of and behind Jupiter in its orbit. I had never known why they were called the Trojan asteroids before, but it turns out it's because the first one discovered was called Achilles, and by convention every one discovered since (all 4,076 of them) have been named after figures in the Trojan War from the Iliad. In fact, it's even more structured than that; the asteroids orbiting ahead of Jupiter are named after people in the Greek camp, while those following Jupiter are named after people in the Trojan camp (although this rule was suggested after they'd found a few, so there are two exceptions: Patroclus is found in the Trojan camp, and Hektor, the largest of them, in the Greek camp).

As an interesting aside, the word trojan has now entered the astronomical lexicon to refer to any body trapped 60 degrees ahead or or behind another in its orbit. Thus, there are other trojan asteroids (note the lowercase spelling); several associated with Mars, and a few with Neptune. There are even 4 known trojan moons, all in orbit around Saturn, which is where three moons share the same orbit, one large one in the middle with two smaller flanking ones behind and before.

A hui hou!