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If you asked Kepler, “Why do your laws work the way they do? What causes planets to move in these sorts of orbits?” Kepler would tell you that, “God is a mathematician, and so am I!”

Though Kepler’s celestial mechanics equations worked for predicting the position of Mars and other bodies, Kepler was not able to explain why planets moved the way they do around the sun without invoking a higher power.  As a geometer, Kepler tried to understand the behavior of the solar system in terms of areas, ratios, and other geometrical principles; it wasn’t until Newton came along that there was a more elegant mathematical understanding and derivation of celestial mechanics and the laws of motion: calculus and the inverse square relation for gravity.

In 2011, hundreds of years after Kepler’s life, a telescope named after this German astronomer is in orbit around Earth to look for… other Earths around other stars. Last week a bonanza of candidate Earth-like planets was announced; astronomers everywhere cannot contain their excitement at the prospect of planets like home in the habitable zones around other stars.

Kepler’s ideas were revolutionary for his time, and it’s appropriate that a revolution in Egypt occurred almost simultaneously with the release of Kepler mission results.  (I’d like to add that Jack Lissauer of the Kepler team is perhaps one of the nicest guys in astronomy; I’m really glad that someone like him is involved in this project.)

The Kepler team isn’t content to just release mountains of data on potentially habitable terrestrial planets; they also have a t-shirt available with a Carl Sagan quote:

For small creatures such as we the vastness is bearable only through love.

The shirt features a variable star light curve in the shape of a heart, which is appropriate, as asteroid light curves were my first astronomical crush.

If you’re looking for more interplanetary affection in time Valentine’s Day, NASA’s Stardust-NExT mission will be encountering comet Tempel 1 on Monday. Stardust-NExT originally sampled another comet, Wild 2, on Independence Day in 2004; Tempel 1 will be the second comet imaged by this mission. Ooh la la.

Much love to all heavenly bodies in this solar system and beyond.

I was drawn to how they’re pointing in different directions, and the blueness of the water. Way to go, Richard!

I’m off to Massachusetts for four months to finish my master’s thesis.  Here’s to more sailing on that coast!

print -depsc -painters file.eps

Now that you have a vector image containing your colormap information, it’s time to display your figure. On some systems, your PS/PDF renderer will insert some crisscrossing white lines while rendering your vectorized image. However, you can usually turn off anti-aliasing on your viewer and you should be to witness your glorious figures sans white crosshatching (again, thanks to MATLAB Central).

Sure, I could probably tackle these problems in Adobe Illustrator or Inkscape, but I like having things work properly on the first go when it comes to creating figures and otherwise minimizing the number of non-automated steps in my image-creation workflow.

(PS: a draft of my thesis is available here.)

Our model splits Earth’s mantle into 1000 concentric shells, then solidifies the shells layer by layer from the bottom up (because the adiabatic temperature profile and the solidus intersect at the bottom of the mantle).  Assuming that once a layer has solidified, the rest of the mantle evenly mixes to have the same composition means you can just think about this problem two layers at a time: the layer you’re solidifying (with pre-solidification composition measured in mass percentage liquid_n and mass mass_n), and the layer just above that.  The above layer will have the same composition as the rest of the mantle (liquid_n+1), which means you can just concentrate (ha) on those two layers without having to worry about the mass of the rest of the mantle.

We’re also keeping track of the composition (solid) and mass (mass (solid)_n) of what fractionates (solidifies) out of the liquid, as well as the volumes of each shells (vol).

With all these parameters in mind, we can calculate the composition of the next layer of liquid (and by proxy, the rest of the mantle) after solidification liquid_n+1:

This equation assumes that mixing of the remaining liquids post-solidification in the magma ocean occurs on small timescales compared to that of the solidification process, producing a homogenous liquid mantle.  The magma ocean is assumed to have a bulk silicate mantle of melted material with a composition from Hart and Zindler (1986) and Bertka and Fei (1997), with average chondritic trace elements from Anders and Grevesse (1989). For solidified minerals, mineral phase behavior is based on experimental results (Elkins-Tanton et al., 2003; Trønnes and Frost, 2002; Bertka and Fei, 1997).

Why bother with going to all this trouble for mass balance?  The previous equation for calculating the composition of the next liquid layer (and thus the remainder of the mantle’s magma ocean) would make some of the mass percentages in that layer go to zero, or worse, negative, meaning that the rest of your model was being fed rather bad values.  Now, after much digging and wrangling through MATLAB’s debugging mode (not to mention initially blaming some nuances of clinopyroxene and magnesiowüstite’s density behavior at various temperatures and pressures ), it looks like the problem might have been in how the composition of the next liquid layer was calculated, or at least the problem has shifted to other points in the model.  Although the liquid composition is no longer getting assigned negative values, there’s no certainty that the values being written into it are reasonable, much less physically sane.

Regardless: thank you, generous and insightful housemate!  Next on deck: what common mantle rock-forming minerals have densities greater than 4,000 kg m^-3?  What happens to the last 0.03% of the mantle that doesn’t solidify?  What’s the viscosity and density of mantle material below the magma ocean and above the core?  How do you explain that melting starts where the adiabat intersects the solidus?  Stick with us next time for As The Earth Solidifies (And Overturns)!

On Saturday morning after the Inverness Yacht Club’s October board meeting, Ned Congdon and I intended to find out empirically if a sail to Point Reyes Station from the Inverness Yacht Club was possible. A small armada began rigging two Flying Scots to navigate the narrow channels of Papermill Creek to Point Reyes Station. In the blue Club Scot were my friend Zach from Pasadena, my housemate Emily, staff commodore Mark, and me; in Ned’s boat was his sailing partner Steve and Ned’s son Aaron. Ned has been sailing into Point Reyes Station to grab lunch at Café Reyes for years, so we figured it’d be a grand opportunity to join him and learn a thing or two about sailing south through the narrow channels, as well as to verify for ourselves if such a trip could be accomplished. Our crew grabbed a spinnaker and set off toward Papermill Creek in the last bits of the rising tide and light winds, Ned hot on our heels as we turned south for Point Reyes Station.

Heading south and preparing the spinnaker

Ned behind, chute up

Eventually, we let Ned pass us since he knew the entrance to the channel.  We tried to keep up with him without a spinnaker, then decided it was time to hoist the kite.  Alas, the pin on our pole broke, so we were faced with a dilemma: be left in Ned’s wake, or pop the chute without a pole?  Mark decided to go with the latter, so we gurgled down the bay, chasing Ned with our spinnaker flying poleless high above our boat.

Rigging the spinnaker

Content crew

Three Peaks

The wind was blowing perfectly for our sail into the channel cut by the creek and we had an effortless downwind cruise toward White House Pool.  Motorists stopped on the side of Sir Francis Drake to watch and a coupled leaned out of the window of their house to video the two 18’ boats navigate a channel maybe 60’ wide.  Several kayakers seemed confused that sailboats were encroaching on their territory.

Thistledown scattered over the creek’s surface in the small puffs of breeze. It felt exceptionally like autumn as we drifted alongside the verdant shrubs and golden grasses of the former cow pastures. We tied up at the Green Bridge without encountering any powerlines or other deterrents to our forward progress. Thus, it has been established that it is possible to sail into town without incident. We set off to find oysters and wait for the tide to turn..  You can find the route we took to Point Reyes Station here.

Thistledown scattering over the water

Tule rushes

Stowing sails

Tied up at the Green Bridge

Admiral Ned posing with the armada

When we did leave Point Reyes, we had some difficulty tacking out of the narrow portion of the creek in the flaky wind, and Ned got mixed up with some willows growing on the bank.  The eastern channel proved to be rather narrow, so we put Zach on the tiller, Mark on the jib and main sheets, and me on the centerboard line as if it was controlling a third sail.  Emily’s job was to make sure nothing jammed as we hauled the board up and down during countless tacks across Papermill Creek.

Steering along the creek

Ned’s boat sailing down the channel to the bay

The ebb was so strong at this point that the creeks rushing into the channel looked like raging rivers.  We saw a family swimming through the rapids through a gap in a railroad levy.  At this point, we were focusing on navigating the channel and not getting stuck on the ground, rather than how our admiral was doing.  When we looked behind us, we saw the nose of his boat stuck in the mud.

A few tacks later Mark asked, “Where’s Ned?”  We scanned the southern horizon as we fought weatherhelm to return to the club in the strengthening wind, and I spotted the white hull of the other Scot.  “Ned’s capsized.”  “Well, there’s nothing we can do for him until we get a motorboat at the club and go back for him,” responded Mark.

We sailed on, anxious, glancing south under the sails, eager for visual updates.  “He’s back upright!”  “He’s capsized again.”  “He’s up again, but his sails are down.”  We lowered our centerboard as far as we dared in the dropping tide and raced to the club.  Mark and Zach launched the Whaler to rescue Admiral Ned, while Emily and I took our Scot out of the water and watched the rescue efforts.

The Whaler returned with Ned’s Scot in tow, containing a very broken centerboard and tiller, as well as a damp ego or three. While I was grateful for the chance to see part of Tomales Bay that I’ve never explored by boat and to prove that one can indeed sail into Point Reyes Station, we were glad that everyone had been wearing personal flotation devices, numerous people were aware of our sail plans, and that several folks in the vicinity knew how to operate a safety boat. As winter approaches, let your friends know where you’re going, pack your foul weather gear, your lifejackets, and your radios. Happy sailing!

Broken centerboard and tiller

Another casualty was my camera: as there was nothing I could eat at Café Reyes aside from butternut squash soup, the effects of protein deprivation hit rather hard and I wound up falling off the dock with my beloved Canon Digital Rebel 300D. We’ll see if it works after drying out for a week. The rest of its last photos are here.  Zach and Jim also took a few shots.

Community Boating holds a race off the Longfellow Bridge

Not quite sailboat related, but still entertaining.

Her dress matches the coral-print fabric in the store

The Charles River as seen from the Anderson Bridge

Sunflowers at the Copley Square market

Reflected light on Destiny

Sailing on Destiny

View through the bimini

Marge on the stern

Fireboat plume

Steering Destiny

Kaycee snoozing

Sound structure

More here.

Eugene ordered entirely in Chinese, resulting in some dishes that I’d never seen before (chicken with candied pecans and vegetables in a flour shell?). After mandating that all of our students speak in English all summer, it was fascinating to watch our pupils’ expressions as someone carried on a conversation in a language they could not understand at all.

The final night in the dorms, Anna and I decided to create a feast of our remaining foods. We had both stoves in two apartments going, and wound up with Moroccan lentils, corn fritters, garlic Swiss chard, polenta, pasta sauce, pasta, sauteed onions, sauteed mushrooms, and fresh dates with quiona for desert. Yum!

The next morning, I woke up early and made omelets for my fellow instructors who were also awake and packing. We managed to get everything out of the dorms on time, then we packed up the vans and dropped off at the MEET office armloads of linens and kitchen supplies. Thank you MEET for giving us things to sleep on and cook with (though not at the same time!).

I spent the next three days near Jerusalem visiting with the parents of a friend from MIT. First off, it’s incredible that you can pick up any one of seven cell phone carriers from three different territories/countries.

Despite it being a very hot August, the grape arbors, and loquat, olive, and pomegranate trees were very verdant and some were burgeoning with fruit.

The chili peppers were also beginning to ripen.

The figs here are incredible. As soon as they begin to split their skin, you know they are ripe. Oh, to have a fig.

We visited one home that had an early copy of the Communist Manifesto in Arabic.

I then went to Mishmar Ayalon to stay with my cousins on a moshav, a small agricultural community with a little less of a socialist streak than the kibbutzim: land is owned individually, and not everyone is involved with agriculture. They too had a fig tree which was readily climbable. Oh, glorious figs. (Their passion fruit tree was just starting to mature, resulting in slightly tart fruit.)

My cousin then took me to Mini Israel, which is like a model village but has miniature versions of major landmarks of the region. Some favorites included the Baha’i Gardens, complete with the staircases and red-roofed houses of the surrounding German Quarter of Haifa.

The gardener is a nephew of my cousin, and had studied in Holland how to grow bonsai trees. When the nephew tried to introduce the Dutch techniques to the Middle East, the trees wound up growing too big due to the abundance of sunlight! He was eventually successful in growing tiny plants at Mini Israel: a tiny pomegranate tree had perfectly small fruits and flowers.

The Basilica of the Annunciation had the architectural details down, but didn’t have the wonderful murals and mosaics of the original.

The Dome of the Rock was very impressive, and even had a small Mount of Olives behind it.

At the Western Wall (Kotel), you could leave notes and someone would transport them to the actual wall.

There was even a small version of the ruins at Caesarea.

MEET did a great job of showing us the area from north to south in six weeks, and it was wonderful to see a concise summary of our travels in one place.

And so ends my updates about MEET. I loved exploring the Middle East both gastronomically and geographically, but I especially loved teaching the brilliant, creative, and very adult students that compose the program. Thank you to everyone who made this summer incredible!

The northern beach had a sign admonishing us to not swim in the clear green Mediterranean water.

In the evening, we drove up to the town of Zikhron Ya’akov and wandered off in search of dinner. We came across a pub called “The Hobbit”, complete with wizard decorations and not very low ceilings. The drink menu was in English, but the food one was in Hebrew, which made ordering somewhat difficult. We managed to get pretty good burgers and enjoyed listening to 1990s rock in the dark room of the pub.

The next morning, Mor and I went to the restaurant in search of the breakfast provided by the hotel. I’m always timid about kosher dairy meals, but this was perhaps one of the best I’ve had: scrambled eggs; halva; fresh, stewed, and dried fruits; olives; and pickled fish. The 12 types of labane, yogurt, and cheese didn’t really appeal, but I was incredibly pleased with the food selection.

Later, some of us decided to explore beyond the resort beach. A small knoll stood to the north end of the cove, where we could see ruins from an ancient fortress. Excavations in the area have apparently found items left by Napoleon’s armada, and a group of archeologists were hard at work (not pictured) recovering relics and old pottery shards. When you have a site that’s been inhabited for roughly 4,000 years, you’re pretty likely to find all sorts of artifacts!

Where the rocks meet the water, pools had been carved into the stones. Was this part of an ancient palace or fortress?

Timid exploration of the rocks yielded to jumping into the deep pools, mostly protected from the waves.

After splashing around, it became apparent that the pools were deep enough to accommodate jumping, so Ben climbed a rocky knob and sprang into the water.

Kathleen followed suit.

We spent the rest of the morning jumping off the rocks and exploring the small grottoes of the area.

Reluctantly, we loaded up the vans and headed back to Jerusalem.

We’d originally intentioned to leave last Tuesday morning for Eilat, but because of the rocket attacks, MEET cancelled our reservations and we were on our own for finding a “relaxing” activity for the instructors and staff. While Talya opted to find us bungalows at the beach for Wednesday night, several of us in the dorms were developing cabin fever and were itching to head to do something now and not wait another day. After three days of writing student evaluations, filling out surveys, and documenting the summer for the next generation of MEET instructors, the prospect of spending another day in Jerusalem was not very exciting.

In the spirit of last summer’s rather ad-hoc trip to Death Valley (seat of the pants planned and executed), all the instructors piled into the vans on about an hour’s notice and headed for the Dead Sea sometime on that Tuesday afternoon. Where exactly we’d go, or if we’d spend the night anywhere were undetermined. Yela!

Because of the State Department’s travel restrictions for the area, which MIT applies to folks traveling with MIT money/on MIT business, we weren’t able to take the direct route to the lowest point on earth, which takes a little over an hour and looks something like this:

Even though we wouldn’t have to pass through checkpoints, if MIT says we can’t enter the West Bank, we can’t enter the West Bank. Instead, we had to go all the way out of Jerusalem to the west towards Tel Aviv, turn south, pass through Be’er Sheva and Arad, then take a long (three hour), winding mountain road:

The highways to the desert start off along agricultural fields, but the expanses of corn and grapevines quickly give way to arid desert and Bedouin villages. In contrast to the lush green campus of Hebrew University and the tree-lined streets of Tel Aviv, these villages lack sanitary services, sidewalks, or any sort of infrastructure. Trash collects along the highways and in depressions in the towns. Houses are built out of corrugated metal and wood scraps. This is not the route the tour buses take.

After navigating the twisty desert road past markers indicating how far in meters we were below sea level, we arrived at the inland seashore, opened the van doors, and almost fainted due to the heat.

Where the dry, barren mountains meet the Dead Sea are a cluster of hotels and shops selling Dead Sea mud and other skin treatments. I’d rather not know what their bills are for air conditioning and fresh water.

Ignoring the stores, we changed into our bathing suits and stepped into the intensely (magnesium) salty water. Maybe the sea would be cooler than the air? No such luck; it was probably 105˚F outside, and the water couldn’t have been much colder. Despite the lack of temperature differential, we had a lovely time effortlessly bobbing in the water.

Like the rest of the region, the Dead Sea is home to numerous feral cats and kittens, picking through trashcans, climbing trees, and generally looking forlorn in the darkness.

Around nine at night, one van of sane, boring people opted to return to Jerusalem, while a group of seven intrepid instructors remained in the Judean Desert, hoping to climb Mount Masada at sunrise. The Magnificent (or Stupid) Seven set out in search of food for the next morning. Heading up Route 90, we passed Masada and eventually reached Ein Gedi where the beachside convenience store was still open around 10 pm. Despite being disgustingly hot for 10 pm, Ein Gedi was rather alive: feral cats were eating pita bread out of trash cans and a bonfire was roaring near the edge of the parking lot.

We retraced our drive back to Masada and prepared to sleep in the “campground”, a generous term applied to a broad, flat parking area carved out of gravel, sand, and small rocks. Picnic tables? Grills? Nah; just rocks. Spreading our towels on the desert floor, we admired the stars, listened to a group of French pilgrims party at an adjacent campsite, and eventually drifted off into fitful sleep, interrupted by gravel and pebbles poking into our backs.

Sometime in the middle of the night, I hear a very very strange noise: somewhere between clearing one’s throat and squeegeeing a bathtub. I turned over, unable to place the sound, focusing instead on how absurdly warm it was—without blankets, we were still baking in the desert night. Whatever that sound had been, it was not worse than the nocturnal heat keeping us awake.

At 4 am, we woke up and began repacking ourselves into the van. I started the van and turned around from the parking spot, waiting to flip on the lights until we were pointing away from the French pilgrims. Once the high beams were on I found that the windshield was covered in streaks of dust so thick that I could hardly see outside. There’d been no wind at night; what had happened to cover the windshield? Eugene and Jenny had attempted to sleep on the roof of the van, but Eugene’d given up sometime before we awoke and slid off the roof via the window, hence the odd sound and dusty streaks. Mysteries solved.

We parked at Masada and unloaded in the predawn stillness. Michaela was so pleased that she had trouble containing her glee at being up before sunrise.

After paying 25 NIS to enter the park, we began the 350 meter vertical ascent up the side of the mountain along the Snake Path. Winding over two kilometers along a sheer cliff, the Snake Path was a secret route taken by rebels to avoid the Roman legions laying siege to the rebels’ mountain stronghold.

Eventually, the sky began to lighten and we could make out the cables for the cable car against the eastern sky. Even before sunrise, we’d worked up significant sweats in the relentless heat.

Clouds drifted over the waning gibbous moon.

The path seemed like it’d never end.

Finally, we ascended the summit.

The sun rose over the mountains of Jordan, a bright magenta orb ascending rapidly over silhouetted peaks.

We headed to the northern end of the mountain to see the ruins of King Herod’s formerly luxurious palace, but were deterred by the hordes of tour groups swarming the mountaintop.

One tour guide dressed in a white toga and a huge floppy blond wig was leading a group of British students around Masada. I stepped aside to allow his group pass me on a staircase and said “boker tov” (good morning) to him. Without missing a beat, he brightly turned to his group and stated, “And here’s a rebel! You can even practice your Hebrew with her.” I think I uttered something along the lines of “toda” (thank you), smiled, and went on my way.

Turning south, we left the crowds and went to the other end of the plateau, which was mostly deserted except for us.

Our next destination was a staircase leading into the mountain. We descended the stairs into a giant water cistern carved by King Herod’s workers.

Carved into the living rock and sealed with eight layers of plaster and large enough to hold thousands of cubic meters of water, this cistern was part of a complex network of water diversion and storage chambers. As Masada gets only a few millimeters of rain a year, it was important in ancient times to gather as much water as possible during the winter rains in order to last during the dry months.

Ascending out of the cistern, we headed for the southern point of the rhomboid known as Masada. The southern lookout point was too windy to experience the echoing cliffs, so we turned around and three of us descended along the Snake Path, burning hot even at 8 am. The remaining four took the cable car down the mountain.

We were treated to some beautiful views of the Dead Sea and the surrounding valleys, filled with rills and wadis.

After drinking several liters of water, iced tea, and Gatorade, we loaded into the sandy and salty van and headed off for points west. I took the first driving shift, and after a few minutes I glanced in the rearview mirror to see that all my passengers had passed out. We stopped at some nameless desert town, purchased “lunch”, switched drivers, and continued off to the coast. For going from having no plan to climbing Masada 16 hours later at dawn, I’d say we did pretty well.