Posted on March 14th, 2014 by george.
Q: Is it possible for humans to exist on a planet at the L1 Lagrange point of a gas giant orbiting a star?
A: It’s definitely possible, but it’s not likely to be a stable orbit over the lifetime of a solar system. In fact, no Lagrange point is inherently stable except in special circumstances. Most of the time they require station keeping to counteract gravitational perturbations from other planets. Orbits around L4 and L5 last the longest, which is why you see so many Trojan asteroids leading and trailing Jupiter. L4 and L5 can be stable for billions of years if the body in the Lagrange point is 25 times less massive than the primary. Earth is 318 times less massive than Jupiter, so Earth could be a Jupiter trojan long term without interference. But the L1 point is not as stable as L4 and L5. And since there’s no such thing as station keeping for a planet, your planet would only stay in the L1 point for something on the order of millions, not billions, of years. This may sound like a long time, but it’s the blink of an eye compared to the necessary timescales for evolution, geology, and solar system lifespan. Intelligent life would not have time to evolve on a planet in L1 before it drifted out to wander the solar system. So you’ll need to explain the presence of humans there. A primitive species could have been dropped off by an intelligent race. Otherwise life would have had to evolve in a different orbit (likely a stable one to set the stage for life), and then once humans existed, the planet somehow migrated to this L1.
The problem is it’s difficult to destabilize a planet in a circular orbit, get it to a Lagrange point, then make it stay there. You would need to conjure a very unlikely scenario. Say, for instance, that another star passed nearby the Oort cloud of this hypothetical solar system and perturbed several planet-sized frozen bodies hanging out in the boonies. One massive interloper comes zipping in from the Oort cloud and whizzes by your planet, kicking it out to where it starts interacting with the gas giant. But that Oort cloud planet wasn’t the only one kicked loose, and another one comes careening through the inner solar system at the precise speed and trajectory such that when your planet reaches the gas giant L1, it whizzes by your planet and robs it of the exact amount of energy to stabilize its orbit in L1. This is a one-in-a-quadrillion shot (I made up those odds), but it is strictly possible. It also avoids the need for an impact. Impacts are often what would cause a planet to move around, spin up, form moons, and stabilize in a different orbit. The only other origins I can think of are: 1) if your planet starts out as a binary planet, the binary system is perturbed to L1, and another perturbation kicks off the twin, leaving your planet alone and quasi-stable at L1 and 2) a hyper-advanced alien race has the ability to move planets in their orbits without disturbing them, and does this to your planet just for fun.
Long story short if you want your humans to evolve on this planet they won’t be able to survive an impact-based restructuring of their orbit to L1. Most of the time an impact large enough to change orbital parameters will result in partial to total destruction of the original planet. Even if a collision could move the planet to L1 without destroying it, the impact would likely turn the entire surface of the planet into molten lava. So you’ll need to explain the migration with momentum transfers. This may sound fanciful, but keep in mind we know this happens for capturing moons. Our Moon is the result of a giant impact, as is Pluto’s moon Charon. Phobos and Deimos may be asteroids captured into Martian orbit, or may be the result of a giant impact. There is evidence that many small moons of Jupiter and Saturn are captured asteroids or Kuiper Belt Objects, and we are all but certain that Neptune’s moon Triton is a captured KBO. Triton is in a retrograde orbit, meaning it spins the opposite way around Neptune from the direction Neptune is spinning and from the direction Neptune is moving around the Sun. There is no way to explain a retrograde moon except capture, even though capture is very difficult to piece together gravitationally. Scientists are still studying how Triton was stabilized in its current orbit, whether it ejected a moon of its own, suffered an impact near Neptune, grazed Neptune’s atmosphere, or circularized due to tidal dissipation.
So your planet is possible, though it will only remain at L1 for a few million years at best. Based on our discovery of super-Earths you could make it much bigger than Earth and have all your humans be super strong. Or you could leave it the same size and avoid having to answer questions about all the hydrogen in its super-thick atmosphere. If you give your planet a 24-hour rotation period it will have the same day/night cycle as Earth, and if you give it the same axial tilt it should enjoy the same seasons. If the planet evolved in one part of a habitable zone and migrated to this L1 in another part of the zone (we’ll leave alone the stability of such an orbit so close to the L1 of a gas giant), your humans will have had to weather unfathomable climate change, either from a frozen planet to a steamy jungle/dry desert or vice versa, with snowball periods if the migration doesn’t start and end in a single orbit. It’s probably easier to go from warm to cold since you don’t have to pass the gas giant in the process and risk ejection from the solar system. If you make it a super-Earth it may be difficult to explain away the radiation from the gas giant. You might try claiming that the magnetic field is much stronger that Earth’s because the molten iron core is larger (if this planet happened to enjoy a core donation similar to the one Theia gave Earth). The problem is that the higher gravity of a super-Earth may preclude the interior differentiation that powers Earth’s magnetic-field-generating dynamo. Or you could just invoke magnesium oxide and say, “Trust me, it has a magnetic field strong enough to withstand gas giant radiation.” If this were the case, you could get amazingly intense aurorae on this planet, perhaps visible at much lower latitudes than we see them on Earth.
The phase of the gas giant would never change; it would always appear full at night, would always reach its zenith at midnight, and would never be visible at the same time the sun was visible. If the planet ends up following a Lissajous orbit around L1, you could see some interesting effects: the shadow of your planet might fall on the gas giant from time to time and trace different paths across its face. You may be aligned so perfectly that you’re in perpetual transit, your shadow a permanent beauty mark on the face of the gas giant.
It’s a very interesting idea. It just takes some explaining and your planet won’t stay there very long. But we’ve evolved from hunter gatherers to spacewalkers in only 50,000 years, so your humans could definitely go through their formative stages and reach Type II status before the planet was kicked out of L1.
Posted on March 10th, 2014 by george.
Got the following question from my friend Sean and thought I’d repost my answer here for those of you looking for a relatively simple explanation of Lagrange points.
Hypothetically, lets say there are two bodies of equal mass. We’ll assume they’re identical in every respect (size, density, etc). We’ll also assume that the distance between them is always constant. It seems reasonable that exactly half way in-between them their gravitational pull would be negated by the opposite mass. Therefore, if an object were to fly precisely in-between them at that point, it would not be affected by either’s gravitation pull. To the best of your knowledge is this presumption true? And if so, is there a term to describe such a zone of gravitational equilibrium? Or would an object be caught in between?
Your intuition is correct. Such a spot in space is known as a libration point. Where it gets interesting is when you mix in orbital mechanics. God doesn’t reach down with two giant hands and hold two spheres motionless in space. The laws of gravitation tend to put everything into motion, always accelerating unless balanced by another force. On Earth, our bodies want desperately to accelerate toward the center, but the surface of the Earth provides a force that exactly balances that gravitational pull and holds us in one place. The only way two massive bodies can maintain a constant distance between each other is to orbit one another in a shared circular orbit (as opposed to an elliptical orbit, where the distance would be constantly changing).
This is the simplest case, called a two-body system. Each object wants to accelerate directly toward the other, but each also has a large amount of momentum directed ninety degrees away from the other body. The centripetal (outward) acceleration due to that momentum exactly balances the gravitational pull between the two objects. So as the sphere moves forward, instead of traveling in a straight line (which it would do if the other body were not there) it gets pulled a little toward its companion. Simultaneously, the companion traveling in the opposite direction gets pulled a little toward the original sphere. Add each increment of forward and lateral motion as you march forward in time step by step, and eventually the two bodies trace a path about a common central point called a barycenter. Here’s how two identical bodies can travel in non-circular orbits around a common barycenter:
This is what it looks like when the masses are different.
The barycenter of the Earth-Sun system is inside the Sun itself because the Sun is so much more massive. It starts to look like the maps of the solar system you’re accustomed to seeing.
Even though the planet is small, you can see that it still causes its central star to wobble. This is one of the methods we use to find planets around other stars. When a planet is large and close to its sun, we can see the wobble with our current telescopes.
In the special case of symmetric bodies in a circular orbit, the barycenter (center of mass) is a libration point. If you placed a third body there, it would not accelerate toward either of the original two spheres. This is not because it is unaffected by the gravitational pull of either primary body, but because those two pulls balance equally.
Now here’s where it gets fun. The gravitational forces and the centripetal acceleration don’t just balance between the two bodies. When you invoke Kepler’s equations of motion and Newton’s law of gravitation and solve for the points in space where the gravitational pull due to both bodies matches the centripetal force needed to orbit in lockstep with them, you arrive at FIVE libration points. Euler discovered the first three that exist in a straight line traced between the two main bodies, but Lagrange discovered four and five, so they named the libration points of a three-body system after him. The one in the center of two identical bodies is the easiest to conceive of, since equal forces pull in opposite directions. This is called the L1 point. As soon as you consider a system with bodies of different masses, however, the barycenter and the L1 point part ways; the former moves toward the heavier body, and the latter marches closer to the lighter one. But there are also points on the outside of the two bodies where all the forces balance.
Let’s switch to a Sun/Earth model so it’s easier to understand. The further you orbit from a central body (the Sun in this case), the slower your orbital speed (but the higher your orbital potential energy). If you aligned a Sun-orbiting satellite with Earth at a much greater distance from the Sun and let it go, the Earth would start outpacing it on the way around the Sun. For example, Mars does not co-rotate with Earth. It follows Kepler’s laws and orbits with a period of about 1.9 Earth years. This is not to say the Earth does not exert gravitational forces on Mars. It most definitely does. The Sun, all the planets, every asteroid and all objects in the solar system (and, to an unmeasurable degree, the universe) feel the Earth’s gravitational pull. The reason the Sun dominates this neighborhood is because it is the most massive. Remember, too, that the Sun is in orbit around the center of the Milky Way galaxy. The reason we don’t orbit the galaxy directly is because we are so close to the Sun relative to the galactic center. Long story short the Earth-generated forces felt on Mars are not as large as the pull of the Sun, and Earth is so far from Mars (even at closest approach) that the overall effect on Mars is tiny over the age of the solar system.
Now if you move the Sun-orbiting satellite close enough to the Earth, its gravitational pull eventually gets strong enough that it drags the satellite along behind it, even though the satellite is still orbiting the Sun in a higher orbit, and should be orbiting more slowly than the Earth. This is L2. For reference, it is outside of the Moon’s orbital distance. Move the satellite too close to Earth, though, and it will orbit Earth instead of the Sun.
L3 is a little harder to grasp because it’s all the way on the other side of the Sun from the Earth. But it’s still in a higher orbit than Earth, so it should be going slower. Once again, however, Earth pulls the satellite along and causes it to orbit at Earth speed in its higher orbit where it should have a longer period and be outpaced by Earth. This is in spite of the fact that Earth is two astronomical units (186 million miles) away and the force due to Earth’s gravity traces a line through the Sun itself! If the Earth were the only planet orbiting the Sun, L3 would be a stable libration point, meaning if the satellite drifted the forces would conspire to bring it back (as long as you ignore solar radiation pressure, the fact that the Earth is not a perfect sphere and that the Sun is squashed, among other perturbing effects). Maintaining your position near a Lagrange point (or in any desired orbit) is called “station keeping”. But remember how the Earth is on the other side of the Sun from L3? And remember that Venus exists? In real life the Earth-Sun L3 point is unstable, because the gravitational pull of Venus is much larger than Earth’s pull on a fictional satellite at L3, no matter where Venus is in its faster-moving orbit. Venus will quickly destabilize a satellite at L3.
L4 and L5 are wacky and hard to conceive, which is why Euler missed them and Lagrange got all the points named after him when he discovered four and five. These two are at the point where the distance between the satellite and the Sun and the satellite and Earth are equal to the Earth-Sun distance, forming an equilateral triangle. The forces once again balance and the satellite is held in a higher orbit while still rotating around the Sun at Earth speed. The best way I know to think about L4 and L5 is that the presence of the Earth and its small gravitational pull causes the satellite to orbit the Earth-Sun barycenter, not the center of the Sun. It’s not as easy to understand as the case where the satellite is “pulled along” as in L2 and L3, but if you stare at this diagram long enough, you’ll see that the presence of the Earth is effectively shortening the radial distance between the satellite and the center. As we know from Kepler, shorter radial distance equals faster orbital speed, so the satellite orbits as fast as Earth even though it’s further from the Sun. This diagram shows the Earth and the Moon, but the physics is the same.
Here are all the Lagrange points together. Haw haw haw haw.
Bonus: you can orbit a Lagrange point in what’s called a “halo orbit”. There’s nothing there for you to revolve around, of course, but your momentum and the gravitational forces of the other two bodies balance perfectly to conspire to make it seem as if there is. NASA’s multi-billion dollar James Webb Space Telescope plans to use a halo orbit around the Earth-Sun L2.
Bonus bonus: JWST looks like an imperial star destroyer.
Posted on November 26th, 2013 by george.
Rafa had a rough night and Lorenia has had a cold since yesterday, so I stayed at the house this morning and watched the little guy so she could get some rest. On the way in to work I texted a few coworkers and took their orders for takeout since our food options at work are very limited, and the closest independent restaurant is a twenty minute drive one way. After leaving the restaurant I was headed north on Courtenay in the left lane, doing about 50 in a 45, when I suddenly found myself screaming at the top of my lungs. “WHAT THE **** ARE YOU DOING YOU SON OF A *****! ******* IT!” I realized I was at a dead stop in the left lane, my view out the windshield completely blocked by a stationary, mid-90s black sedan (maybe a Buick). I took stock. My neck, right thumb, and throat were all sore. Ah, I was still honking. And the primal screaming explained the throat. I played back the last few moments in my head to try to figure out what had happened.
Ok, so I’m cruising along, listening to Elliott Smith. My eyes are on the road ahead. The next light is green, as is the one after that. There’s a tall truck in the right lane merging over into the right turn lane to make a right turn into a parking lot. Ah, now I remember. Just past the nose of the truck I spotted a black sedan pulling out. At this point he was in my peripheral vision, close to the A-pillar. Things slow down. Surely he’s turning right? No. He’s pulling out blind into five lanes of traffic at lunchtime. I cannot recall sending the signal to my right foot to brake, my left foot to engage the clutch, or my right hand to take the transmission out of fifth and then move to the horn, because it was instinct. I do remember threshold braking from 50 to zero. I didn’t realize the sedan was stopping in the middle of the road, just that I needed to avoid where he was at that moment, and I had cars to my right moving with me and to my left stopped in the suicide lane. The only option was to stop. At a distance of about two cars lengths my brain somehow realized I wasn’t going to stop in time, and overrode the threshold braking in a panic. I distinctly remember the feeling in my right foot as the ABS pulsed the brakes. One piece of technology saved me from another: stopping short and missing the other car kept the airbag from deploying. The split-second recall was done, and now I realized the driver was still sitting in front of me. I was still honking. He couldn’t move because not only had he pulled out into traffic blind, he had neglected the fact that the center lane was full. Once the traffic moved, he slowly pulled into the suicide lane. I stopped honking. When he had to swing wide to drive around me, I realized just how close I’d come: I was angled slightly to the right in my lane so that my left front bumper could miss his driver side door. I looked at his license plate in my side mirror as I pulled away, dumbfounded that he hadn’t waved or shrugged or offered the least bit of contrition. I managed to catch that it was a Florida plate, but I wasn’t in a state of mind to memorize it. Besides, what legal recourse is there for an almost-accident when I’m the only angry witness? Florida driver. He doesn’t even have the excuse of being from out of town. Even now I cannot fathom what would possess someone to pull into traffic blind. Was he drunk? High? He wasn’t elderly.
I looked down and was amazed. The restaurant had packed our four lunches tightly into a cardboard box, and I’d put it in the passenger foot well. All the sushi was pushed up against the front side of the clear container, but none of the soup, salads or curries had escaped. Lunch had survived.
Within ten seconds of pulling away I hear Lorenia’s ring tone. “How did you know to call me?” I asked. “I felt like throwing up, but not because I’m sick,” she replied. I recounted the story to her, thankful that I managed to save a car that I couldn’t replace for the amount of money insurance would pay out.
Brake check: successful. Old man reflexes: still good. I just wish my neck wasn’t so sore.
Posted on October 21st, 2013 by george.
O SON OF MAN! Should prosperity befall thee, rejoice not, and should abasement come upon thee, grieve not, for both shall pass away and be no more.
So this is it
The view from the top
A sink full of dishes and the midnight oil
This is the life of the richest of the rich
Wealthier than 99.82% of all humans
7.1 billion people lower on the totem pole
In an hour I make 78 times what a laborer in Indonesia earns
The average Zimbabwean would work 57 years to see what I net in a year
In one minute and 28 seconds I make enough to buy a Coke
While a worker in Ghana toils 9 hours to feed that vending machine
In one month I earn enough to pay the salaries of 221 doctors in Kazakhstan
Even if you work one 40-hour minimum wage job in the US
Earning only $15,000 a year
You are still richer than 93% of the people on Earth
This is not good enough
How can someone so rich be so unsatisfied?
Because this is not justice
This is not fair
It is not enough for me that I am happy and content
And let’s be honest, what right would anyone in my position have to feel slighted?
I cannot in good conscience enjoy my wealth
Knowing an unfair system brought me here
Say what you will about my work ethic
No matter how hard I’ve worked I don’t deserve this
When others who are different than me can’t earn it too
None of us chooses where we’re born
What our gender will be
The color of our skin
Our home country
Whether we face malnourishment as a child
There is no bootstrapping your way out of hunger
Or lack of education
Or lack of sanitation
Or lack of stable government
Or a war zone
Women cannot be emancipated
Until they are considered equal
In the mind of every man
Us at the top?
We make the rules
This is the way we’ve set it up
Only we have the power to change this
We invented the system
We benefit from it
But this is not a zero-sum game
There is not a fixed amount of wealth and privilege to go around
And “screw you if you weren’t lucky enough to be born a white male in the US like me”
There is enough potential within this species for every last one of us to enjoy the life I do
So much more
Worlds you cannot fathom
A limitless future in this limitless universe
We can create wealth
We can create opportunity
We can create equality
We can accelerate the pace of the advancement of civilization
If only we recognize our shared humanity
That it was mere chance that put my soul in this lofty material position
And before fate snatches it away
I can seize this chance to champion the rights of all of us
The rights to have our basic needs met
To enjoy health
To live under the canopy of justice
To benefit from an education that stimulates us, inspires us, and draws out our gifts
So that we can give back to the society that funded it
Before we were old enough to pay our own way
We hold these truths to be self-evident
So glaringly obvious that they do not require explanation
That all men were created equal
Men in the 1776 sense of the word
Back when they used to use “men” to mean “humans”, male and female
Not just the ones born in the United States
Are you listening, Americans?
“But those are other countries!”
“We can’t tell them what to do!”
Except when we bomb them?
Or drone them?
Or invade them?
Or impose tariffs on them?
Or surveil them?
Or establish puppet governments in them?
What if we stopped meddling and started leading?
What if we cleaned up our own house before trashing theirs?
What if we set an example?
What if we trusted them until they gave us a reason not to?
What if we stopped acting only in our own interest, and started acting in everyone’s interest, knowing that it would benefit us even more in the long run?
What if we forgave the past?
What if we lived up to the principles we claim to cherish?
Do not tell me this is not possible
This is inevitable
This, today, is not fair
I am not happy
Until all of us are happy
We created the current system
We can make a better one
Be generous in prosperity, and thankful in adversity. Be worthy of the trust of thy neighbor, and look upon him with a bright and friendly face. Be a treasure to the poor, an admonisher to the rich, an answerer of the cry of the needy, a preserver of the sanctity of thy pledge.
Posted on October 10th, 2013 by george.
This morning on the way to school I merged onto the highway headed west, only about a mile from the house. I quickly came to a stop for the traffic ahead. I could see lights flashing. The squad car on the ramp in front of me had raced ahead to block the left lane. He was the second officer at the scene. As I crawled past the accident, I saw about four cars stopped, then a blue street bike on its side in the left lane. The rider had come to rest a couple dozen yards in front of the bike. Their shoes didn’t make it as far. A man furiously waved me past, probably upset by rubberneckers, but I couldn’t go any faster due to the car in front of me. He seemed angrier than justifiable by the situation, which made me think he might have been responsible for the accident. I caught a brief glimpse of the rider’s sock feet. They were lying face up on the pavement, knees bent, feet flat. This and the fact that the bike was still in one piece gave me hope that they were still alive. The rest of the rider’s body was obscured by people giving assistance, but the dainty legs gave me the impression it was a woman. As traffic regained speed I looked in the rearview mirror. Turns out there had been a fire truck right behind me, lights off and no siren. Perhaps that explained the furious man.
About ten minutes later I merged onto another highway headed northwest. Within seconds I saw a black-clad figure on the opposite side of the road, walking slowly against traffic and struggling to shoulder a backpack. I pulled a quick U-turn and rolled my window down.
“Where you headed?”
He got in with some difficulty, refusing to remove his mostly empty backpack.
“George. Nice to meet you.”
We shook hands.
“Where in Orlando are you going?”
“I can get you as far as Alafaya and Colonial. After that I head north to UCF.”
“That’s fine. Been walking a long time.”
“Where you coming from?”
“Cocoa. Don’t nobody stop no more.”
After a few minutes I noticed he hadn’t buckled his seatbelt. He was sitting so rigidly, gripping the door handle, I thought it best not to ask.
“Got any water?”
“No, sorry. But I can get you some.”
We rode in silence for five minutes, Sigur Ros playing softly on the stereo. I made a quick move around a dump truck. He mumbled something I couldn’t understand. I asked him to repeat it. He did, but it was still unintelligible. I thought I made out a word that sounded like “power.” I turned the volume up, thinking he wanted more power from the speakers. He didn’t say anything. In hindsight, I think he was complimenting the power of the car, because his next question was,
“Is that a radar detector?”
“Yep. It’s saved me a lot of tickets. I used to get about one ticket per year. Haven’t gotten any more since I got it.”
He laughed. I turned north on Alafaya and pulled into the Race Trac.
“You hungry? Would you like a sandwich or something?”
“Yeah, a sandwich be good.”
The low fuel light had come on during the trip, but if I took the time to pump gas I’d be late to class. I ran in and grabbed two bottles of water, a turkey sandwich and an egg salad sandwich, some honey roasted peanuts and a bag of chips. I returned to the car, bag in hand, and opened the passenger door. It took Nate about ten full seconds to get out of the seat. I had to take his bag and help him out. I handed him the food and asked if he could use some cash. I gave him what I had in my wallet, then pointed him in the direction of downtown. He said thank you a couple dozen times.
His difficult egress and the hobble in his step made me wonder what we’re doing in the United States. Why we do we keep driving when we see hitchhikers? Why is driving the only option? Why do we cross the street to avoid someone without a home? Why do we shut down the government for having the audacity to make people PAY for health insurance? God forbid we actually help those in need with universal health care. I fear that disdain for the poor is largely a result of ignorance. If you’ve always been affluent and never faced true hardship, or racism, or institutional bias, it might be easy to assume everyone with less money than you is shiftless and lazy. My question is: why would you make that assumption without knowing a single detail about their lives? Furthermore, why don’t you ever bother to get to know them? I gave Nate a ride because that’s what I hope someone would have done for me. Because he’s not just a homeless guy walking fifty miles. He is my fellow human being. He is my brother. I might have helped him out for one part of one day of his life, but I’m still failing him. We all are.
After lunch I was walking across the parking lot toward the nearest crosswalk to head back to campus. A big white Ford SUV with a creaking suspension had been idling in the middle of the lane, and slowly pulled forward into a parking spot near where I was walking. A guy cried out of the window,
I turned around.
“Hey man, you want to buy a home theater? Surround sound?”
I looked at him, then looked at my skateboard, as if to say, “How do you expect me to carry it?”
“I don’t have a car.”
“Well, do you want to go get your car? I just got these two systems and I need to get rid of them today. I’ll give you a good deal. Real cheap. They’re worth like $2,000. Come on, man.”
At this point I had seen enough red flags.
“Ok man. Have a good one.”
I kept walking, crossed the street, then noticed they had left the parking lot and were coming up behind me. I was relieved when they kept going, and memorized their plate as they creaked by. They drove aimlessly through nearby lots. I looked up the Orlando Sheriff’s non-emergency line and dialed it. They were still in sight after I navigated the automated menus and reached the laconic dispatcher.
“I’d like to report some potentially stolen goods.”
“Potentially stolen? What do you mean?”
“Two guys just tried to sell me some stereo equipment out of the back of their SUV.”
I gave her a description of the vehicle. She was surprised when I rattled off the plate number. They were still in sight on Alafaya at the intersection south of University. She was annoyed that I didn’t know the name of that cross street. I was about to hang up when she asked if I could describe the driver.
“I didn’t see the driver, just the passenger.”
“Was he black or Hispanic?”
“He was white.”
“Ok, I’ll notify the deputies in the area.”
A few minutes later I was on campus, ready to cross the main loop, a road named Gemini. There’s a crosswalk that isn’t near traffic lights and relies upon drivers to yield to pedestrians. In Florida, this is also known as a joke. Having been nearly hit here the last few times I dared to cross, I have taken Lorenia’s advice and started hopping off my skateboard and carrying it across. I caught a gap between traffic pulses and started across. The tall shrubs in the median block pedestrians from the view of oncoming traffic, so I was careful to start across the third and fourth lanes when I was sure no cars were within 100 yards, in spite of the fact that I had the right of way. Right of way means nothing here, because people either don’t know or refuse to follow pedestrian laws. Even though the majority of traffic was stopped at a red light, one car from a cross street had managed to turn left and was approaching as I crossed. Rather than slow down, he sped up. Rather than switch lanes, he maintained course. I could feel the rush of wind as he became the third car in as many days to purposefully miss me by inches. Maybe next time I’ll learn my lesson and wait until there are no cars. That way he can go even faster on his way to the next red light.
On the way home I merged from one highway to another near where I had picked up Nate. Once again, I quickly came to a stop. In the distance were blue flashing lights. I could tell they were on the left side of the highway, so I moved right and turned on my flashers to warn oncoming traffic. As is typical of Florida drivers, the next five cars simply swerved left and maintained full speed. I watched several near misses under panic braking. I can only assume they thought I was using my hazards because I was disabled. But then why wasn’t I pulling over to the shoulder?
I spent the next mile or so comfortably ensconced between two semi trucks, feathering the clutch and creeping along at the average speed. People in control of 40 tons of vehicle tend to drive more sensibly. They know from experience that they need more time to stop, and because they can see over the rooftops of cars, they know they won’t get anywhere by lurching forward and slamming on the brakes, even if their trucks were capable of that. We cruised along and watched the yahoos in the left lane waste fuel and wear down their brake pads while getting no further ahead than we were.
Eventually we reached the accident, and it was indeed on the left. An SUV had rolled over and the front of the roof had caved down to the steering wheel. Two lucky guys were standing next to it, seemingly uninjured. I was thankful that I didn’t have to see another body on the ground.
Posted on September 8th, 2013 by george.
Ok kids, this is time sensitive, so as soon as you read this you need to go outside if you’re going to catch it. The Moon moves fast enough in its orbit around the Earth that it won’t be this easy tomorrow. Today, Sunday September 8th, 2013, is a special day: you can see the planet Venus with your naked eye during the daytime. Seeing Venus (or other planets) during the daytime isn’t anything special for people with automated telescopes or Google Sky Maps, binoculars and a LOT of patience. But today there’s a trick: Venus and the Moon are in a conjunction (meaning they appear very close to each other in the sky). So if you can find the dim sliver of a crescent Moon in the daytime sky, you can find Venus. If you’re in North America, the Sun should already be in the western half of the sky. Right now, on the east coast, as of 5pm EST, you’re looking for the crescent Moon about halfway between the Sun and due south, and about halfway between the horizon and directly overhead. Even if you’re in a cloud-free area, it’s probably going to be hard to spot. But don’t give up! Keep looking, this is worth it. There’s no shame in using Google Sky Maps on your smartphone to lead you there. If you haven’t downloaded the app, this is a good time. As soon as you find the Moon, look directly above it about one Moon-width away. See that tiny white dot? That’s Venus! Congratulations! You have seen another planet with your naked eye DURING THE DAYTIME. Show your friends, this is a rare thing. But hurry, there are only a few hours left! If you wait until after sunset, the Moon and Venus will still be close together, and you’ll see just how bright Venus is: bright enough to overcome the scattered sunlight of a daytime sky on Earth.
Posted on March 13th, 2013 by george.
Our family had the privilege of spending this past weekend on Isla Holbox, a barely-inhabited island off the northern coast of the Yucatan peninsula, famous for its lack of cars, kite surfing, whale shark diving, and some of the most remote and luxurious seclusion one can find in the 21st century. As we walked back to our palm-thatched palapa on Saturday night under a sky filled with more stars than can be seen anywhere in Florida, I found myself fantasizing, as anyone in that situation would, about picking up roots and moving to that idyllic paradise awash in sand and turquoise. The more I thought about it, though, the more I realized how little I would have to offer. Not just in terms of my toddler-level Spanish, but in what I could possibly do for a living. Repair bikes and golf carts? I’d already seen local residents doing it themselves on the side of the unpaved road. Captain a powerboat for sightseeing or whale shark encounters? Men with years of experience in the local waters and an uncanny ability to locate picturesque wildlife can wait days for a customer. Give scuba lessons? This is not Cancun. The kind of people who know enough to know about the existence of Holbox and who put in the effort required to get there are the kind who arrive prepared to dive or uninterested in doing so. I have no experience as a cook and there are already plenty of great restaurants. Hotels range from resort to boutique to spa to hostel to campsite, so there’s no niche to be found, and I have no starting capital. Can’t grow much beyond coconut and a few tropical fruits, and there are fishermen galore. What the heck would I do? For my day job I consult on spacecraft avionics (spacecraft are not exactly abundant) and at school I study the science of planets, much of which is based on celestial observations that rely upon billions of dollars in telescopes (many of them taxpayer-funded) and an army of tens of thousands of highly educated scientists and engineers. My research requires thousands of dollars worth of equipment in a multi-million-dollar building at the second largest university in the wealthiest country in the world. I say this not to boast, but merely to reflect upon the level of infrastructure required just for me to do my job. During that walk on Holbox, I joked about setting up an observatory on the island, considering that it’s the clearest sky I’ve ever seen from sea level. But who would run it? Who would refine and analyze the data? Why place it there, in a location so remote that building it would be twice as expensive as it would near a city, when a mountaintop location would allow for much better observations and ultimately better science? Holbox deserves to remain as it is. Sleepy, wild, secret.
Today we hopped back on the first world treadmill with our arrival in Orlando. Thankfully we had the buffer of Cancun in between, or the contrast might have been too shocking. There were more people in the security line at the airport today than there were on the entire island this past weekend. We arrived to wide highways with smooth pavement, bright signage, street lights, access ramps and shiny new cars to fill all the lanes. The pace of life here is dizzying compared to days spent on a sandbar fifty yards from shore and breezy nights in slowly swaying hammocks. I listened to the patois of our jovial driver as we rode from the airport to the parking facility, and wondered how often he reflected on life in the States versus the life he left behind. As we exited the overnight parking lot, Rafael, whose bowels were undoubtedly loosened by the low pressure at cruising altitude, decided to gift us with a levee-breaching evacuation. We pulled over in the employee parking lot so we could use the office restroom to change his diaper. Lorenia sent me back out to the car for a change of clothes. I sat down in the back seat to rifle through his diaper bag, leaving the door ajar, with the keys in my pocket. As I bent over at the waist, the key fob locked the doors. I pulled the keys out and unlocked the doors again. Finding no clothes, I stepped out to return inside and ask if she wanted me to unpack the fifty-pound suitcase buried in the trunk for a new onesie. As the door shut, the horn honked. My heart sank. There, on the rear seat, was the key fob, which had fallen off my lap as I got out. I can only guess that the car locked itself a second time after enough time passed with no new doors opened. It has probably been more than a decade since I’ve locked the keys in the car, and I felt like an absolute idiot. I’d already missed a day in the lab, and now I was going to miss my afternoon class waiting for an expensive locksmith. I ran back inside to tell Lorenia, and we just so happened to catch our driver as he was leaving work. He called over to the mechanic, who was at our car within five minutes with two plastic wedges, and inflatable bag that looked like a blood pressure cuff and a long hooked rod. Two minutes later the door was open, alarm blaring, and we thanked him profusely and got on our way. Side note: while it may be difficult to start a modern car without a key, it is absurdly easy to get inside without breaking anything, as long as you have the right tools. Thanks to the kind and unassuming mechanic, I made it to my class on time, and enjoyed an hour-long videoconference with the astrobiology discipline scientist at NASA headquarters, discussing the last few decades of unmanned spacecraft exploration of our solar system and the likelihood that we’ll find life beyond Earth.
Here, then, is concrete, empirical, quantifiable evidence that we are absolutely reliant upon one another to maintain our civilization. It’s easy to lose sight of meaning in your life, because you never get to witness the causal repercussions of what you believe are simple, banal, boring actions. That mechanic will likely never know how he enabled my life, but he goes to work and does his job every day anyway. Kindness and service are acts of faith; we do what we can and trust in the benefits we never see. My pursuits, my profession, my purpose, and my life would all be utterly impossible if it were not for the daily effort of the entire human race, and the sum total of all the efforts of our ancestors to get us to this point. That is what makes us all family; not where we are born or who our relatives are or what language we speak or the job we do or the per capita GDP of our country of citizenship. How we treat others, what we do to help, the contributions we make that have no immediately evident effect: these are the acts that enable all of the pinnacles of human achievement, from science to art to literature and everything in between. All we have to do is be the mechanic.
Posted on February 4th, 2012 by george.
My friend Sean asked me a question yesterday, and the answer is not only something I’m learning about in school this semester, but something I’d like to share here.
Q: So, what’s the deal with planets and galaxies? I have always presumed that planets orbited on roughly the same plane around the sun. Is this true, or do they travel about diverse axes from each other? Additionally, I have always presumed that galaxies are spinning away from a central point, on roughly the same plane, in the cosmos. Is that accurate or are they shooting in a more linear fashion away from each other?
A: Your presumption about the planets is correct. The eight planets in our solar system orbit in roughly the same plane (within a few degrees). It’s called the ecliptic.
One of the strikes against Pluto as a planet is that its orbit is tilted 17 degrees from the plane the major planets orbit in.
A galaxy, on the other hand, is totally different than the solar system. The former is characterized by distributed mass, while the latter has point masses (mass concentrations in the form of planets). Yes, gravity is still the force at work in both systems, but there are so many stars per unit volume of a galaxy that their mass is effectively distributed along a density curve, like the atoms in a frisbee. And let’s not even get started on dark matter, which makes galaxies rotate faster than they would if stars were the only matter present.
There is no center of the universe (that’s a difficult one to explain, but I can try to cover it later if you’re curious). Galaxies interact with each other gravitationally, they cluster together, and they collide with each other. All the while, spacetime itself is expanding (but that too is another story). Their interactions are not collisions in the traditional sense, though, because individual stars almost never impact each other. It’s like two clouds of smoke full of embers passing through each other. Yes, their dust and gas is heated and collides and forms stars, but it’s not like two cars crashing. It’s also a crash that takes millions of years to happen, so you can put that slo-mo camera away.
It takes our Sun 250 million years to make one orbit around the galactic center. Considering the Sun is only 4.57 billion years old, that means for its entire life, and the entire life of the solar system, it has made only about 20-25 galactic orbits. So in galactic years, the Sun is only a twenty-something. And from what we know about stellar evolution, it’s only going to live into its forties before becoming a red giant, then devolving into a white dwarf that will live to a ripe old age of who knows how many billion years. All that doesn’t matter for the Earth, though, because the Sun is getting about 10% brighter every billion years (which is probably why life didn’t arise here until about a billion years ago). That means that in about four more galactic years, it’ll be too hot on Earth’s surface for liquid water to exist. So we’ll have to be gone to other planets long before our oceans boil, and four billion years before the Sun swallows the Earth as a red giant. Who knows, maybe we’ll terraform Mars by then and it will be warm enough to walk around outside.
Furthermore, the Sun doesn’t orbit the galaxy like a planet orbits a star. Yes, planetary orbits evolve, but over millions of years, not from one orbit to the next, and they may be elliptic, but they stay in one plane. Because all the mass in the galaxy is widely distributed and the Sun is constantly interacting with nearby stars, the Sun does not travel in a plane around the galactic center. It oscillates up and down in the galactic disk about three times per orbit. So imagine it tracing the surface of a kruller donut with only a few flutes.
So now to your actual question: the galactic structure of the universe is achingly beautiful. It looks like round and spiral pearls made of hundreds of billions of stars, and all those pearls are strung out like cobwebs around vast stretches of empty space. If you consider how long it takes for the Sun to orbit the galaxy, just imagine how long it would take for galaxies to orbit some fictional center of the universe; one orbit would be many times longer than the age of the universe. Astronomers and cosmologists term these large scale structures of the universe walls, filaments, and voids. So you can imagine it as a frothy soup of soap bubbles of different sizes where inside the bubbles are large voids of nothing, and between the bubbles are superclusters of galaxies.
Our Milky Way is part of a local galactic group of 54 galaxies, which is itself part of a mind-boggling huge group of galaxies called the Virgo Supercluster. But the Virgo Supercluster is just one of several “nearby” superclusters, which are themselves only one TINY region of the universe that we can ever see due to the finite speed of light and the amount of time since the big bang.
If you have the patience for the large image to load, this graphic should give you a good idea of the different structures at different scales within our glorious, illimitable universe.
Posted on May 25th, 2011 by george.
Contrary to what you may have seen in movies like Apollo 13, life in the Launch Control Center is not terribly glamorous. Sure, we get the occasional visit from the first family, Nobel-prize winning physicist, or other celebrity or dignitary. And the chief administrator of NASA is there almost every time.
But they just smile and wave at the crowd after MECO (Main Engine CutOff, when the vehicle is safely in orbit), or make a statement about how proud of us they are or how we’re the greatest launch team in the world (Russia, Japan, China, Europe, India and private companies notwithstanding).
For the most part, though, our task is tedious: monitor every single system on the vehicle as the tanks are filled, the fuel cells powered on, the auxiliary power units spun up, the hydraulics pressurized, the inertial measurement units calibrated, and so on. In general it takes more than ten thousand people about half a year to recover, safe, refurbish, repair, test, upgrade, checkout, assemble, integrate, rollout, load, retest and otherwise prepare a space shuttle for launch. The 72-hour countdown is relatively brief when compared to the processing flow, and the launch itself, at just over eight minutes, is shorter still. For the engineers who witnessed Challenger, though, who are intimately familiar with the incredible danger involved in the controlled explosion we call rocketry, those nerve-racking moments can last a lifetime. That’s why one of my colleagues, Sunshine Menendez (not his real name, but sarcastically indicative of his demeanor), characterizes our job as “six months of boredom followed by nine minutes of sheer terror.”
Don’t get me wrong, it’s a delicate ballet, and I could list hundreds of maddeningly complex components that must be in perfect working order and playing nice with each other before the candle is lit. But when things go as planned, it can feel like the countdown takes forever (understandable, given that it’s three days long). Then, toward the end, things get very tense. By the time the final minute rolls around, it’s quieter than an empty library. No one even coughs. The computer takes over at T-minus 31 seconds, the main engines light at T-minus six seconds and come up to full thrust, and then within milliseconds of T-zero the SRBs are lit (by another rocket, inside them!), the explosive hold-down bolts are shattered, and she’s away. We all look to the huge windows at the front of the room, not exactly sure where the shuttle will pop up, since we can’t see her on the pad. Then there she is, screaming by, lighting up the sky whether it’s day or night.
Blink and you’ll miss it. If you’re all the way in the back of the room, like we are at the Flight Controls console, you get to see the orbiter for a grand total of three seconds. Then we watch it on TV like everyone else, while continuing to monitor our respective systems (even though Houston takes over as soon as the stack clears the tower). After MECO we pose for photos, then it’s downstairs to enjoy some well-deserved beans.
Back when STS-134 was the final scheduled flight, I was proud that I’d be a part of the ultimate launch team, and that my vehicle, Endeavour, would have the honor of being the last to fly. Even though Atlantis is now the orbiter that gets the curtain call, I’m not upset. For the crowning space shuttle mission, I get to be a tourist just like everyone else, watching the clouds of steam rise from the pad when the SSMEs are lit, witnessing the alacrity with which the vehicle leaps from the pad, and, barring the kind of cloud cover we had for the penultimate launch, following the spacecraft from the ground all the way into the heavens. Just like the rest of the million people who travel to Cape Canaveral from around the world, I will wait in eager anticipation of the moment when the crackling vibrations from those fiendishly hot nozzles whip through the air to my ears, catching up with the spectacle of light and reverberating through every organ in my body.
I might even leave the camera at home.
Posted on April 13th, 2011 by george.
I posted this on Facebook yesterday and got such a response I decided to crosspost it here. The following is my response to a question Patrick asked me yesterday.
Patrick: If my body temp is 98.7, then why does 82 degrees feel hot? Wouldn’t it have to be hotter than me (which is hard, I know) for it to feel hot to me?
George: We were just discussing this on Sunday. Your *core* body temperature is 98.6 degrees F on average…that’s why you have to measure it on the inside of your body: mouth, ear, rectum, etc. Put a good thermometer to the surface of your skin, though, and you won’t measure 98.6. Your skin surface temperature is lower than 98.6. It can be anywhere from 70 to 90 degrees F, depending on the person. And it varies all over your body. For instance, extremities like fingertips, which are long, skinny, and surrounded by air, are naturally going to be much colder than large, flat surfaces like your chest, or warm crevices like your armpit. But I’m getting ahead of myself.
The nerves in your skin that tell you if you’re feeling hot or cold do so by measuring heat flux. Flux is just a fancy word for transfer. Heat is not something you can hold; you can hold temperature, that is, the random motion of your atoms. But heat is by definition only a transfer of energy. Your body obeys this law of physics. You touch a hot stove, and heat is transferred TO your body, which is much colder. Your nerves measure the influx of heat energy, send a signal spike to your brain, and your reflexes pull your hand back before you know what happened. When you hold onto an ice cube, your hand transfers heat from your body TO the ice. Your nerves measure the outflux of heat, realize it points outward instead of inward, and tell you that the ice feels COLD. Your nerves can only measure change in temperature, not absolute temperature.
This is why you can become accustomed to a particular temperature. It’s like the examples of the frog in a pot of water on the stove…turn the temperature up slowly, and he’ll never notice when it finally boils. Sit in a hot tub long enough, your blood vessels dilate in order to increase surface area which allows larger heat flux from the water to the regulated blood temperature, and you “get used to it.” Jump in the pool, though, and the heat flux is very large for the first few seconds. The pool may be 85 degrees, but it FEELS cold, because your now-hotter body is rapidly rejecting heat to the water. Give it a few minutes, though, your blood vessels constrict to reduce heat transfer, your brain saturates with the “cold” signal from your nerves and starts ignoring them, and now you’re “used to” the temperature of the pool water.
Add to this fact that your body is always using the chemicals in the food you eat to power your cells, and a byproduct of this power generation is heat, which your body uses partially to heat itself, but must reject the excess to the air via convection, or to whatever you touch via conduction. It’s difficult to get rid of much energy at all through radiation, the least effective method of heat transfer. We have this problem on the space shuttle, which is why there are giant radiators on the inside of the payload bay doors. Nonetheless, your body does radiate a little. This is why you show up on infrared night vision goggles as a bright green blur: you produce much more radiative energy than a tree. Remember: you’re a warm-blooded mammal.
Conduction, or bringing into contact two solids, surface to surface, is by far the most efficient method of heat transfer. The second best is convection, in which you transfer heat between a solid and a fluid, or between two fluids. The least efficient is, as mentioned before, radiation. This is why you get hypothermia in water much more quickly than you do in air, even if they’re at the same temperature! Think about it. Would you rather stand in 72 degree air for an hour without moving, or 72 degree water? Obviously air is a better insulator, and allows you to retain more body heat. The REASON it’s a better insulator is microscopic: the distance between the molecules, called “mean free path” (just the average distance they travel before they bump into each other), is MUCH larger for air molecules than for water. Water molecules are, in fact, so tightly packed together that they’re actually *further apart* in solid water. But that’s another story. Because water molecules are so close together, there are more of them available per square inch of your skin to rob your body of heat. So the amount of heat transfer from your body to 72-degree water is much higher than from your body to 72-degree air. This is why you can get hypothermia in water that is well above freezing. It’s also why you’re so hungry after going swimming: your body has been burning extra calories just to keep you warm in the water.
Your metabolic rate controls how much heat you need to reject. It varies from moment to moment and person to person. This is why two people can be in the same room and one feels hot while the other feels cold. One person needs to reject more heat, but the air isn’t cold enough relative to their skin temperature for efficient heat transfer to take place. This person feels hot. The other person’s metabolism is such that their body wants to retain heat to keep their core temperature in a stable operating range, but that same air is cool enough relative to THEIR skin surface temperature that it absorbs more heat than their body wants to give up. This person feels cold. If the rate of heat transfer available with a given air-to-skin temperature gradient balances with the amount of heat your body wants to reject, you feel like Goldilocks: just right, neither hot nor cold.
Topics related to this discussion are exercise, which increases body temperature; sweat, which through evaporation absorbs large amounts of body heat to provide the latent heat for the phase transition (liquid water to water vapor); circulation, which is of paramount importance in regulating localized body temperature (see also cold feet, frostbite, hypothermia); and blankets which insulate your body, i.e. reduce the rate of outward heat flux, and allow you to stay all toasty when the air is cold by not allowing your body to lose heat to the cold air. As every school kid knows, whales have a lot of blubber because they spend so much time in frigid water. Blubber is just fat. Fat is a great insulator. We all have it, to varying degrees, and it’s a very good thing (not just for heat retention but also quite necessary for cushioning internal organs and protecting muscle as well as vital energy storage). Some people have more fat, some less. A person with low body fat is usually going to feel cold at room temperature, but quite comfortable at the beach, in the sun, or in the tropics. A person with high body fat feels hot at room temp because they’re walking around with several blankets wrapped around them, and their body has to work extremely hard to push heat through all that insulation in order to regulate their core temperature.
So, to sum up, even though your core temperature might be 98.7, you felt hot when the air was 82 degrees because the temperature of the surface of your skin was less than 82 degrees, so heat was flowing from the air into your body, and your nerves told you as much.
Patrick: You just blew my mind. And Paolo’s. And soon, Johanna’s.
George: Hahaha ok good. Always happy to help.