Terraforming Mars

While I've been here in Australia I was introduced to the board game Terraforming Mars by a friend at one of the student board game nights. It came out in 2016 and has received both a number of awards and five expansions to date. In it, two to five players take on the role of corporations (each with a unique specialty) competing to, well, terraform Mars, accomplished by raising three parameters (global temperature, oxygen level, and oceans). Many actions are accomplished by playing cards, which are randomly drawn throughout the game (and there are literally hundreds with all the expansions); choosing a winning strategy from among the cards you get is a big part of the appeal. I also like it because, while you're competing for points at the end of the game (after Mars has been completely terraformed), there's little direct competition within the game itself other than a few cards that let you steal or remove (small amounts of) resources from other players.

Now while I've enjoyed the board game a lot, I've held off on buying it so far as it's pretty pricey (and bulky) with all the expansions and I'd just have to move it anyway (though it's definitely got a place in my ideal future board game collection). I did, however, buy a digital version of it (which released in 2018) on Steam a few months ago and have been playing a lot of games against the computer. (Though both the board and digital version also have a single-player challenge where you need to terraform Mars in a certain amount of time.)

I've noticed a particular pattern recurring in games, and today I decided to see if I could show its existence. The game takes place over a number of “Generations,” within each of which players take turns performing actions until all players have passed their turn, at which point resource production happens and the next generation starts. Each player can take one action and skip the rest of their turn, two actions, or pass on taking any turns for the remainder of that generation. Actions can be many things, though the most common involve paying for and playing a card. (Many cards also allow you to take certain rare or unique actions once per generation.)

Here's a screen shot during a game in generation 4, though not the one I mention later on, showing the (rather lovely) map along with some of the tiles players have placed on it. On the bottom left you can see the resources in the game: money, steel, titanium, plants, energy, and heat. On the right are the terraforming parameters; oxygen is just over half-way, heat's about a third done, and 3 of 9 ocean tiles have been placed.

Anyway, the pattern I'd noticed is that players tend to take a bunch of actions in the very first generation, but drop off steeply in the second, before climbing back up over the rest of the game. (For reference, a five-player game might be over in seven to nine generations; a two-player game might need twelve to fourteen.) This is because each corporation has an amount of money (and potentially other resources) that it starts the game with, and the Prelude expansion from 2018 also allows players to choose two other bonus cards in the set-up phase. Much of the game is about investing in production which increases over time, but since the average player resource output is still going to be much lower on generation 2 than the initial resources available, the number of actions players can take (which are constrained by costs) generally nosedives on that second generation.

Today I decided to finally quantify this observation by recording the number of actions each player took in each generation and plotting it. I started a game with myself and four medium AI players, and proceeded to take careful notes for the entire game. And here's the results:

I've plotted each player by the color used in the game (I'm green, if you're curious) with the number of actions in a generation on the y-axis, and generation number on the x-axis. We can clearly see that every single player has a drop of one or two actions in the second generation compared to their first generation, which starts to slowly rise again over the next five generations. Cards can have very different costs, which partly explains why players had anywhere from one to seven actions in this game. Interestingly, despite being fairly middle-of-the-pack in actions (and rather distracted), I still won this game, which I suppose demonstrates the importance of quality over quantity of actions.

Here's the same game as in the above screenshot (though not the one in the plot) in generation 7. Here you can see that the terraforming parameters on the right have been raised a bit, and there are some more tiles placed on the board. The player order changes each generation since going first offers some advantages.

Anyway, this was a fun little experiment to verify a pattern I'd seen across a lot of games. I can definitely recommend the board game version of Terraforming Mars, though note that it typically takes several hours to play—it's not difficult, but there can be a lot of things to consider with all the nigh-infinite combinations of cards that players can get, so it definitely requires some free time and concentration. While the digital adaptation is serviceable, and I've been enjoying it, it's a bit limited in comparison, with only the Prelude expansion available despite being out for three years at this point. I'm really hoping that additional expansions get released soon (especially Colonies is fun and adds some interesting choices), so if you're used to playing with the expansions just be aware that they're not available digitally yet. If you're fine with that limitation (and even with just the base game and Prelude there's still a decent amount of stuff), it's a good way to get some practice in playing on your own or to play over the internet with friends. A hui hou!

Mars: Birthday #17

In the first of this month's birthdays, today I have my 17th birthday on Mars. That'll be the lowest number we see this month, since Mars orbits the Sun the slowest.

To give me something to talk about in these posts, I've decided to do something I don't normally do and post some photos of a painting in progress. I started this one in March, and it's not finished as of today, so this will be some good motivation to keep working on it. It was actually directly inspired by my previous painting, though I expect the link will not be obvious; I'll reveal it when the painting's done, and leave it to your imagination in the meantime.

Anyway, for this painting, I needed a background looking like bark, so I decided to try something new and do some plein air painting. En plein air is a French term meaning “outdoors,” and plein air painting is the act of painting outdoors, as opposed to inside a studio. While I could simply look up bark textures online, I decided I wanted to paint one from life, so I packed up some supplies and headed out to the nearest tree.

Setting up the easel and canvas next to my model.

Turns out plein air painting, especially with acrylics, is a very different beast to painting indoors. I picked a moderately sunny day, and my acrylic paint—already known for drying quickly—was drying even faster both on the palette and the canvas. I made liberal use of the spray bottle I brought with me, furiously misting everything in an attempt to keep everything damp enough to work with, but still ended up rushing to capture the texture as quickly as I could (I sketched it out roughly on the canvas first). While this generated a unique sort of pressure to the painting, I don't think it was negative, exactly; I ended up using some very fast, loose brush strokes, which gave it a somewhat freer quality than normal for me, I think. Anyway, here's a shot I got of myself with the finished product:

The Sun came out from behind the clouds after a while.

…and here's a closeup of the canvas:

Sort of looks like bark, if you squint?

As you can see, I only used the tree as a reference for the texture, not the color. As to why I chose the particular colors I did, well, that's part of the composition…which I'll reveal on my next birthday! For now, I'll leave you with the fruit of my first experiment in plein air painting, while I get back to work. A hui hou!

A Second Exhibition: Earth, Moon, and Mars Paintings

I've been incredibly busy this past month getting ready for my Mid-Candidature Review, which I passed on Thursday. (This wasn't helped by me coming down with a moderate case of the flu last week.) All of which meant that I didn't really mention here the exhibition I had some paintings in as part of the 50th anniversary of the Apollo 11 Moon landings, which was partly because I never even got to visit the gallery and see everything in person. (And yes, this means I'm now a twice-exhibited artist! Maybe I should add that to my résumé…)

Thankfully, my friend James at Swinburne visited and took some pictures for me, so you all get to see them after all. (All these pictures are courtesy of him; you can check out his website here.)

“Main Sequence”

The first one is one you've seen before, my series of stars on the main sequence. Here, though, they're arranged similarly to how they would be located on a Hertzprung-Russel diagram, from which the main sequence was first identified. This is how I'd always envisioned hanging them if I got the chance, so it was pretty cool to see.

“Tenuous Transport.” Individual panels 40×40 cm, or 40x80 cm. Acrylic, embroidery on canvas.

Now, this is an interesting one. It's a four-panel work (or tetraptych), of which I've posted the Moon painting before. The rest are new, however, and they're not all mine! This piece is a collaboration with another Swinburne student, Grace, who embroidered the outline of the Eagle (the Apollo 11 lander) on the second panel from the right. I had originally envisioned this piece as a single new panel, but while discussing it with everyone at one of our art workshops the topic of making it a multi-part collaborative effort came up, and since I already had the Moon painting it was a simple matter to paint a matching Earth painting to go with it. (Plus a few stars on a blank panel.) Grace meanwhile stitched the outline of the Eagle onto another canvas. The stitching and outline gave it a very fragile feeling, which led us to give the piece the name “Tenuous Transport” in recognition of the sheer fragility of the craft which carried the first humans to the Moon, and just how dangerous the journey was. (You definitely can't see it at this scale, but Grace also subtly highlighted some of the edges in the Moon in thread, making it an interesting mixed-media collaborative piece.)

Since it's probably not obvious at this size, the Earth painting is mostly looking at the Pacific Ocean; you can see Australia at the lower left, and the western coasts of North and South America on the right, but it's mostly water and clouds. Also now that I have it back I may go and touch up the shape of the terminator on the Earth a bit, as it doesn't quite match the Moon and it's been bugging me for a while.

“Vallis Marineris Afternoon Overlook.” 8×10 inches, acrylic on canvas.

And finally, here's a little piece I did unrelated to the Moon; instead, it's a view out over the colossal canyon Vallis Marineris on Mars. At least, that's what I intended, it never quite came together with the right perspective in my eyes, but at least the pink sky is really attractive. Much of the red color in this painting comes from iron oxide pigment, which is interesting because A) it's one of the first pigments people ever used for painting, as seen in cave paintings, and B) it's the reason for Mars' red color in the first place: iron oxide is rust. While I wouldn't call this one of my better works, it was still pretty fun to play around with some new colors I haven't really used before.

Anyway, those are some of the paintings I spent most of May, June, and the first half of July working on. Now that I've passed my Mid-Candidature Review I'm taking the next week off, which will hopefully allow me to get a lot of work done on the ones I've been working on since. A hui hou!

An Astrophysicist Reviews: The Martian

Yesterday I went to see The Martian with my friend Graham from work. Overall I had a pretty good time with it, and I liked the happy ending.  I can't really talk about what I want to without spoiling the plot, so consider the rest of this post one big spoiler warning.

If you saw a trailer for The Martian, you probably already got the gist of the movie. The Ares III mission (third in a series of five manned mission to Mars) encounters a mission-scrubbing sandstorm only twelve days into their mission. During the emergency evacuation one crew member (Mark Watney) gets lost in the sandstorm after getting hit by a flying communications antenna and is (quite reasonably) presumed dead after his suit reports a suit breach, leading the rest of the crew to abandon Mars and head back to Earth. Mark turns out to be alive, amazingly (the blood from where he got impaled having sealed the small hole in his suit), and most of the rest of the movie deals with his attempts to survive until he can be rescued. Luckily, as this was a series of planned missions, Ares IV is already set to land 3800 kilometers from his position in a few years, leading to the idea of getting there to meet it when it arrives. The rations left behind in the evacuation won't stretch that long, but a serendipitous discovery of viable potatoes among the rations leads to him growing them and giving hope that he can survive long enough to modify the rover (also left behind) to be capable of traveling to the landing site.

It takes a few months for anyone to notice he's still alive based on satellite photos of Mars, but when they do they manage to get communications up and running between NASA and Mark. NASA fast-tracks sending the scheduled pre-delivery of food for the Ares IV mission in order to get it to Mark faster, especially after a freak explosion blows up his growing habitat and destroys his potato crop, leaving him with the unenviable prospect of running out of food in a very definite amount of time.

Meanwhile, the rest of the crew of the Ares III are still on their several-month journey back to Earth in the Hermes crew vessel. An astrodynamicist at NASA realizes that the Hermes could potentially slingshot around Earth and get back to Mars fast enough to save Mark as a backup in case the food shipment doesn't make it. (Turns out the Ares IV ascent vehicle has already been landed at the proposed landing site on Mars, since it could be launched ahead of time and means the actual Ares IV mission doesn't need to bother with bringing it along; Mark could take it up and rendezvous with the Hermes as it slingshots again around Mars on its way back to Earth.) This idea is floated in a secret meeting, but is rejected for putting the rest of the crew in additional danger (not to mention several more months of spaceflight time). However, when the rocket carrying the food package explodes during launch the Ares III mission director secretly sends the crew details of the maneuver, whereupon they unanimously vote to mutiny and perform the maneuver against NASA's orders.

Ultimately, the Hermes makes it back to Mars in time for Mark to make it to the Ares IV ascent vehicle before starving, where he strips a frankly ludicrous amount of material out of the ascent vehicle in order to make it light enough to reach the speed necessary to rendezvous with the Hermes (as in, he strips out all of the manual controls leaving it controlled remotely from the Hermes, and even the windows and airlock, performing the ascent in his spacesuit with a tarp over the windows). After a climactic rescue scene Mark is saved, and in the epilogue it's shown that everyone made it back to Earth safely and Mark has taken up teaching future astronauts.

Think Apollo 13 meets Robinson Crusoe.

Now, most of the time, the science was quite good, as you would hope for a movie where almost all of the tension comes from butting up against the laws of nature. Things like burning hydrogen to get water (and causing an explosion due to unaccounted-for excess oxygen), space scenes shot in zero-g conditions (although the Hermes also has rotating sections where people can walk around normally due to centrifugal force), and a homemade bomb made of sugar mentioned as being “four times more powerful than a stick of dynamite” (which is entirely believable, given the vast amounts of energy in food; thankfully, it doesn't easily burn fast enough to explode under normal conditions). The shots of Mars were also particularly gorgeous, especially in the 3D version I saw, which worked well; the 3D was used to good effect rather than being a mere gimmick, and was never used to “in your face” type things.

As an astronomer, however, several details stuck out to me while watching. At least twice, the Martian night sky is shown with a small crescent moon hanging in space. While pretty, it's also unrealistic because Mars' two moons Phobos and Deimos are both tiny, and far too small to be seen as anything other than star-like points (they're also irregularly shaped like asteroids, so they wouldn't have a nice crescent like the Moon does here on Earth). There was also a beautiful shot of a Martian sunset…which looked suspiciously like a sunset on Earth, with a blue sky fading to red around the Sun. Interestingly, it's almost the exact opposite on Mars: the sky is normally red due to ever-present dust in the atmosphere, while fading to blue around the Sun at sunset and sunrise. The atmosphere on Mars is only about 1% as thick as Earth's at ground level, so it's usually too thin for there to be enough Rayleigh scattering to produce the blue skies here on Earth. However, at sunrise or sunset the Sun's light passes through enough of the Martian atmosphere to create a pale blue color, as seen in the picture below. (On Earth the extra atmosphere at those time scatters so much blue light out that what's left appears red or orange.)

Another thing I noticed is that the movie tries to have it both ways with regards to how thick Mars' atmosphere is. In the first few minutes of the movie, the sandstorm that kicks everything off both rips off a communication dish and takes out Mark with it, and presents a credible threat of blowing over the ascent vehicle. Yet near the end of the film as Mark is preparing to ride an Ares IV ascent vehicle that has had even its windows and airlock removed in order to lighten it, it's pointed out that the Martian atmosphere is thin enough that you could feasibly pull such a thing off due to air resistance being essentially non-existent. I'm not familiar enough with the fluid dynamics of the Martian atmosphere to say anything myself, but I've read that in reality even a fierce sandstorm on Mars would feel like a light breeze and wouldn't be able to tip over a large metal ship. The highest atmospheric density on Mars is only 0.6% that of Earth's, so I believe it. Mars' famous planet-wide sandstorms work because of the lower Martian gravity, not because the wind is so strong. And speaking of gravity…

…as a physicist, I couldn't help but notice how Mars has Earth gravity the whole time. The surface gravity on Mars is just 3.7 m/s², a mere 37.6% of Earth's 9.8 m/s². Obviously the movie was filmed on Earth (Wadi Rum in Jordan standing in for Mars), and it'd be to impossible to change something like that, so this isn't a fault of the movie in any way—it just wouldn't be possible to make it look realistic. The fact that something so minor is what I kept noticing really says something about how good the rest of the science was.

Interestingly, during the part where the crew on board the Hermes votes to mutiny and perform the maneuver to return to Mars against NASA's orders to save Mark, the commander says something to the effect of “if we do this, none of us are likely to ever fly again.” This may sound like mere dramatic oratory (although it's justified in the context), but it turns out this has actually happened: in at least two cases crews of astronauts (on Apollo 7 and Skylab 4) have mutinied while in space, and both times no one on the crew ever flew in space again, as eloquently explained in the videos below.

Overall, as I said, I found it a pretty good film, though I couldn't watch the early scene where Mark performs self-surgery to remove a bit of metal from his abdomen from where a spike on the communication array impaled him with nothing but local anesthetic (queasiness is why I'm an astronomer and not a doctor!). I laughed at the part where, in the secret meeting to explain the maneuver for the Hermes, the guy who came up with the maneuver calls it “Project Elrond” and while one of the people in the meeting is trying to figure out what “Elrond” means the normally staid and stoic director of NASA pipes up from the background to say “If this is the council of Elrond, I want my code name to be Glorfindel.” And I especially winced in sympathy at Mark's line “I ran out of ketchup seven days ago” said while eating a potato. Surely that would have to be the worst thing about being stranded on Mars: running out of ketchup. A hui hou!

Terra Nova Cognita

Planet Earth never ceases to surprise us. Within the past month we've discovered a canyon and a volcano, both of which are longer and larger than the previous record-holders in those categories.

The first record-breaker, known as the Greenland Grand Canyon, remained unknown until last month because it lies beneath Greenland's ice cap. It was discovered using ice-penetrating radar and is over 750 kilometers (466 miles) long, a bit less than twice the length of the Grand Canyon in Arizona (at 446 kilometers [277 miles] long. It's also up to 800 meters (2,600 feet) deep, and up to 10 kilometers (6 miles) wide. (Though Arizona's Grand Canyon is both deeper and wider in places.)

(The longest canyon in the world is actually the Yarlung Tsangpo Grand Canyon in Tibet, which is a bit longer than the Grand Canyon in Arizona, although I couldn't find solid numbers on how much longer. It is also the worlds deepest canyon, with a deepest point of 6,009 meters [19,714 feet].)

The second record-breaker is a volcano located on the Pacific sea floor about one-third of the way from Japan to Hawai'i. This humongous edifice goes by the name of Tamu Massif, and while it has been known since at least 1993, it was previously thought to be multiple volcanoes due to its incredible size. On it September 5th it was announced by scientists studying it that it was actually a single volcano, which made it the largest volcano on earth.

This announcement was of interest to me, since I live on the flank of what was previously thought to be the largest volcano in the world – Mauna Loa. When we say “largest,” we should be sure to define what we mean. Tamu Massif is larger in surface area than Mauna Loa, but shorter in height. Mauna Loa has a surface area of 5,000 square kilometers (about 1,900 square miles), and rises an incredible 9,170 meters from the sea floor (30,085 feet). Tamu Massif, by contrast, rises a mere 4,460 meters (14,620 feet) from the sea floor, but has a surface area of 260,000 square kilometers (100,000 square miles), approximately the size of New Mexico.

Despite its height, the summit of Tamu Massif is still 1,980 meters (6,500 feet) below the surface of the Pacific Ocean. This is because it has an incredibly gentle slope (it's also long extinct, so it's not getting any higher). Mauna Loa has slopes that don't exceed an average inclination of 12 degrees, but Tamus Massif's sides have an average inclination of no more than a single degree.

Tamu Massif has some interesting similarities with a volcano on Mars called Alba Mons. Since “Everything's Bigger on Mars” when it comes to geological features, it's no surprise that Alba Mons is larger than Tamu Massif. In terms of surface area it stretches for a good 1,000 by 1,500 kilometers (620 by 930 miles). Like Tamu Massif, it too has incredibly gentle slopes of 0.5 degrees on average.

It's not surprising that these incredible features of our world could remain hidden for so long, given their locations under ice cap and ocean. It's definitely exciting that we're starting to discover them. Who knows what else there is out there waiting to be discovered? 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.

Couriosity's Seven Minutes of Terror

In a similar vein to yesterday, here's a fascinating video about the upcoming landing of the Curiosity rover on Mars next Sunday. This landing is going to be the most complicated landing maneuver ever attempted by mankind, and it's going to be so far away that the time it takes the signal to get back to Earth is longer than the time the landing will take, should everything go smoothly. It also explains stuff a lot better than I can, so I'm going to stop talking now so you can watch the movie.

Climbing Mauna Loa

Last week I had the amazing opportunity to hike the summit of Mauna Loa with a few friends.

Mauna Loa, if you don't know, is the largest volcano on Earth, and second in the Solar System only to Olympus Mons on Mars. It is estimated to have a volume of 18,000 cubic miles of rock (75,000 km³), that is, 375 times the size of Mount Hood, enough to fill the Grand Canyon 18 times over, and more than the entire Sierra Nevada range. It achieves this great volume by being not only incredibly tall (almost 56,000 feet [17 km] from the ocean floor), but incredibly flat. The overall slope of the mountain doesn't exceed 12°, which, despite its great height, makes it rather hard to see when you're directly on it. From Hilo, Mauna Loa just looks like a big hill, while Mauna Kea (which is only 120 feet [36 m] taller than it) looks like a looming mountain. The name Mauna Loa means “Long Mountain” in Hawaiian, and as I quickly discovered, it could not be more appropriate.

We got out of Hilo a bit late, and the fact that the road from the Saddle road up to the Mauna Loa Observatories is a big pot-hole-y mess meant we didn't arrive at the 11,000 foot mark until 8:40 AM, at which point we left the car and began hiking [edit from the future: how funny that by 2017 the road would be entirely paved, and an easier drive than Mauna Kea]. Now, being the over-prepared nerd that I am I had taken the opportunity beforehand to thoroughly inspect our route on Google Earth, so that I would have at the very least a mental map in case I couldn't get reception, or the weather suddenly turned nasty and we couldn't navigate. The smooth slope of Mauna Loa actually makes it somewhat difficult to determine which way is mauka (uphill, away from the sea) or makai (downhill, seaward) in places.

Anyway, on Google Earth there was a very clearly defined route traveling up the mountain via several switch backs that petered out just below the rim of North Pit, a small secondary crater on the edge of the summit caldera, which is named Mokuʻāweoweo.  (Mokuʻāweoweo is an absolutely huge crater, 1.5 miles wide and 3 miles long. North Pit is small only in comparison, and is probably a mile in diameter.) I naturally assumed that this was the “6 mile trail” mentioned on several websites, and that it would be a fairly simple matter to just walk up the nice, gentle slope of Mauna Loa's flank.

Since no one else was showing any signs of navigation, I assumed the position (aided by the fact that I had excellent reception [and access to Google Maps] the entire way up) and bravely led the group up the fork of the trail that led up the mountain, rather than the mysterious fork that appeared to continue on around the mountain. Or, rather, I pointed the way out to the group and huffed and puffed along behind them in the thin atmosphere. Along the way I turned around long enough to snap the following picture of Mauna Loa in the early morning light:

Mauna Kea in all its glory. So pretty...

In the slightly zoomed-in image below, you can make out several observatories on the summit (I see the James Clerk Maxwell Telescope, Subaru, the Caltech Sub-millimeter Observatory, Keck I & II, the Canada-France-Hawaii Telescope, Gemini North, and the UH 88-inch telescope) and can even spot the limits of Mauna Kea's glaciers as a fairly distinct line encircling the mountain about a third of the way down from the summit.

Observatories on Mauna Kea, and the line marking the extent of glaciation.

Breathing at altitude is funny stuff. The slightest exertion leaves you breathing heavily, and heavy exertion has you gasping. By the end of the day I was beginning to worry I'd cracked every rib in my body from the force of my breathing alone. (Thankfully, that healed up in about two day. But boy, when it hurts to breathe, every day seems like an eternity.)

Anyway, we continued on our merry oxygen-deprived way for an hour. Then two. Then another. And another. Finally, after five hours of almost non-stop walking, at long last we we reached the edge of North Pit. Oh, and did I mention that the clouds came in and started dropping sleet on us (yes, sleet) about noon?

Trying to get out of the constant light sleet I clamored down the edge of North Pit, found a slight outcropping of the crater rim, and proceeded to eat the small lunch I had brought with me. It was quite exciting to be sitting on the frozen surface of a vast lava sea, knowing that the volcano had been active a mere twenty-eight years earlier, and that a vast magma chamber lurked only a little less than two miles below my feet. I was able to put together the following panorama while I was sitting there.
Edit (3/17/18): I redid the panorama using Hugin, but you can still see the original by mousing over the image.

This picture was taken in a rare five-minute period when the sun broke through the clouds. Off in the distance, just below the far wall of North Pit you can see steam rising from the floor of the crater. (Probably from rain landing on rocks heated by the sun I hasten to add, not because they were being heated by magma underneath!) Further off you can see through the break in the wall of Mokuʻāweoweo, and even see the highest part of the crater rim near the center of the image.

By this time, it was already 2 in the afternoon, the sleet was switching to rain and back again and showing no signs of letting up, and we still had to walk down, so after eating a woefully late lunch we started the trek back down. I was happy when we got low enough for the sleet to stop, until it was replaced by rain. That morning I had made the decision to wear my (lighter, non-water-proof) fleece in favor of my (heavier, water-proof) coat, so everything I had very slowly began to moisten as we walked down. That actually turned out to be a blessing in disguise, because my damp clothes kept me from overheating and kept my body temperature just about perfect the entire way down. Thankfully the rain never got heavier than a light drizzle.

Three hours after we left the summit we finally staggered back to car, whereupon we had another hour-and-a-half drive back to civilization. I haven't heard of any lasting injuries, but we were all stiff and sore for the next few days.

Mauna Loa is an absolutely fascinating mountain, especially when you compare it with its near sibling Mauna Kea. The lava on Mauna Loa is obviously much newer and fresher than on Mauna Kea, where most lava flows have been covered by either cinder, glacial deposits, or vegetation. (There are some places near Mauna Kea's summit where you can see the exposed flows, usually deeply scarred from the glaciers they erupted under.) On Mauna Loa, lava flows stand out stark and fresh. They also weather to a different color; while old lava on Mauna Kea oxidizes to a reddish-brown color, Mauna Loa's lava goes more for a straight brown. It's very neat to be driving through a patch of black lava, probably less than a hundred years old, and come across a small kīpuka of much older brown lava that didn't get covered in the middle of it. There is a lot of older lava on Mauna Loa (take a look at the picture below for some) and it's fascinating to think about what Mauna Kea must have looked like before it began its post-shield phase and covered everything with a layer of cinder. Alternatively, it's really cool to imagine Mauna Loa after it enters its post-shield phase and starts erupting cinder and cinder cones all over.

A fairly old lava flow on Mauna Loa's flank.
Note how the lava is starting to crumble and flake off.

All in all it was an incredible experience, though one I am in no hurry to replicate. In fact, after we got back and started mentioning it to others more familiar with the mountain, it turned out that we had missed the actual trail and taken the vehicle trail. (Turns out it was that mysterious fork after all.) So instead of a 12.2 mile round trip, it was probably more like 15-20. Because it took us so long to reach the summit we were in no position to actually explore or look around, so we didn't make it to either the true summit on the west side of the crater or the location of the historic Wilkes Expedition campsite on the east side. (The Wilkes Expedition was part of the U.S. Exploring Expedition to the Pacific, a push by the young United States to explore the Pacific for scientific and commercial reasons that lasted from 1838 to 1842. Fun fact: the site of Wilkes' campsite on the rim of Mokuʻāweoweo is the only physical evidence in the Pacific that remains of the entire expedition.)

Now that I know where the trail really is, I wouldn't mind going back some day (hopefully one with better weather) and trying again for the summit. Because despite the discomfort and days of soreness, there's something incredibly cool about standing on an active volcano so far removed from sea level and civilization.

I'm going to close this post by linking to a chapter from a book called Life in Hawaii by Titus Coan, an early American missionary. He describes Mauna Loa's great eruption of 1855-56 that came within a few miles of destroying Hilo. He describes ascending to over 12,000 feet to find the source of the eruption, watching it for many days, trying to cross it in full flood (!!!), and a whole bunch of other incredibly nifty observations about it. It's a long read, but I suspect that once you start you won't be able to stop reading it. Here it is: The Eruption of 1855.

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!

When worlds align...

Well, the frogs are chirping merrily away in the background, and for once there are no clouds in the sky, allowing me to see the close conjunction of Venus and the Moon, with Mars and Saturn nearby for good measure. It's a beautiful night in Hilo.

It almost makes me sad, knowing that Thursday I'll be on the airplane back home to California for a few weeks. By the time you're reading this, I may already be in the air. To be honest, I'm going to miss the lovely weather here. And the rain. I'll probably miss the rain.

In the almost 11 months I've been living here, Hawai`i has steadily grown on me, ever since I first got off the airplane. I love it here, and will be sad if or when I eventually have to move away.

But all good things tend to come to an end, and indeed, trying to hold onto a good thing too hard often ends up being counter-productive. It'll be good to see family and friends again, catch up, "talk story". And at the end of my vacation, I have the coming back to look forward to. So I guess it's not so bad after all.

Mentioning that conjunction reminded me I should try to go photograph it. As you can see below, it's quite the picturesque alignment:

Saturn, Mars, the Moon, and Venus. Click on the image for a larger view.

Visible in the full-size picture but hard to see here, Saturn lies near the top of the picture with Mars to its lower right, while just to the right of the three-day-young Moon lies Venus. And the nifty part is, the alignments just get more interesting as we head into August! Saturn, Mars, and Venus will each take turns getting close to each other over the next few weeks, and are optimally placed for evening viewing. Check them out some time, if you get a chance. There's really no way you can miss Venus, as it's the brightest thing in the sky after the Moon, and Saturn and Mars will show up as fairly bright stars to its upper left, similar to the picture...for a few days, at any rate.

See you in California!

Thoughts on astrophotography.

Things haven't been too busy around here, but they have been happening. I've just been too lazy recently to write about them. Rather than write one big block post, I'll space it out over a few days. It's taken me this long to get around to writing about it, but Saturday I went on a summit tour to Mauna Kea, during which I decided to stick around for stargazing as well. That's 10 and a half hours above 9,000 feet, which can take a bit of a toll on your energy levels.

The summit tour was nice, although once again -- as it has been 4 out of 5 of the times I've gone -- there were some scattered clouds around the summit (strangely, the one time it wasn't cloudy is when I forgot my camera, although they assure me that such cloudy days are rare up there. Apparently I am a cloud magnet). We stopped at the Very Large Baseline Array telescope on the way up to the summit, which allowed me to get this great picture of the first-quarter moon over the telescope:

Moon over VLBA.

For comparison, this telescope is 82 feet (25 m) in diameter, nearly 10 stories tall when pointed straight up, and weighs over 200 tons (I had to cut off the base so you could see the moon easily).

Stargazing in the evening went well too, although the first-quarter moon washed out most of the Milky Way, so I couldn't get a picture of it. There were a lot of people there; two different school groups, a group of Women in Engineering, plus the usual assorted tourists. Probably close to a hundred for a good part of the night.

I spent some hands-on time with one of the larger Dobsonian-mounted Newtonian telescopes, observing Saturn, Mars, the Moon (blindingly bright!), the beautiful double star Albireo (two similar brightness stars, one yellow, one blue), and the tiny but iconic Ring Nebula in Lyra. As an astronomer, I feel it's important to do some visual observing once in a while. Most of the things I observe in the telescope I have already seen in photographs, often very good ones, perhaps even by the Hubble Space Telescope. Compared to those pictures, what I see in the telescope is somewhat akin to watching a High-Definition made-for-widescreen movie on a 5-inch black-and-white screen. And yet the visual experiences are what leave me overawed and grasping for words to describe, every time. I have a special fondness for Saturn, and have seen a good many amazing pictures from the Cassini space probe currently orbiting it, but the most immediate reactions I have to it are when I'm seeing it as a tiny dot that I can just make out the rings on, with Titan and perhaps another moon or two hanging off to the side in its gravitational embrace. A picture is worth a thousand words, so they say; but a good visual observation is worth a thousand pictures any day (or night) in my book.

(of course, sometimes pictures are all you can have, which is why I will continue to keep taking them for those who don't have the privilege of seeing these things for themselves)

Next time I'll post some pictures of silverswords in bloom, along with a surprising fact I learned about them on Saturday...

New classes, new teachers...(part II)

Aloha kākou!
I am back, after a busy two days. Monday night, after posting, I went up to the Visitor Center on Mauna Kea, a trip I don't regret, but one that did cut into my studying/sleeping time. I was to busy to post last night because of homework. I nearly didn't get the chance to post tonight for the same reason. When I decided to take 21 credits this semester, I did it for two reasons: 1) I need to get credits quickly in order to graduate in a decent amount of time, especially with what I'm going for, and 2) I know that if I have too much free time, I get lazy and slack off. So I aimed to prevent that by simply not having any free time, and it may work even better than I'd planned.... If I don't post for a couple of days, that's probably what happened.

 Monday night at the Vis was very nice. Despite the cold, there were a lot of people, and I got to point out and see many beautiful sights. I especially loved seeing the Great Nebula in Orion through the 14-inch scope we have up there. There's just something about seeing something through a telescope that pictures cannot capture. I've seen more pictures than I can count of the Orion Nebula, and it doesn't show up anywhere near as much detail in the eyepiece, but experiencing the photons from it hitting my eye after thousands of years' travel through interstellar space is indescribable. I wish I could take a picture of what I saw, but it's too faint for my camera to be able to pick it up by holding it to the eyepiece.

There are other objects in the night sky, however, that are brighter, one of them being the planet Mars, which I saw Monday night through the same telescope. I managed to catch a picture of it. It's a little hard to see, but on the left you can just make out one of the polar icecaps of Mars, and there's a suggestion of a darker marking on the lower right. They weren't much easier to see through the eyepiece, but I could make them out, so I know they are real markings.

Tuesday I attended the rest of my classes, and met my new professors.  I think they will work out all right. Since I didn't take a specific 'easy' class this semester, it will be interesting to see which class turns out to be the easiest. For my Introduction to Modern Physics class, I have to do an experiment at the end of class demonstrating some effect or principle of modern physics. Toxic and flammable are both out, which unfortunately also rules out the only one I had on the top of my head, but I have plenty of time to get one worked out. I just have to pick a partner now.

It's getting late, so I need to finish up here. I hope to give a fuller exposition of how my classes are going a little later on, when I've had the chance to observe them for a while. In the mean time, I have a little something for you to do. On the right side of this blog, I've added a little poll. The reason I'm asking what level of math you're comfortable with is so that if I feel like discussing things of a mathematical nature later on, I'll know how much I need to explain for you, my readers. But that will come later...
Aloha aumoe! (good night!)