Category Archives: science

The flip-around thing

After seeing the film The Martian, my sister Suzanne posed a science question about it to me, one that I can imagine many other moviegoers had as well. Here’s (an edited version of) her question and (an elaborated version of) my answer. Spoilers ahead!

Q: ‎My very first thought when NASA finally realizes Watney’s still alive was, great! It’s only been 40-something days. Surely there’s a way for the Hermes crew to go back for him. And then I waited another hour before the movie caught up.

What I don’t understand is why that idea became such a big aha/eureka moment for that dude who thought of it, why the “top minds” at NASA rejected it, and why it took so long to get behind it as a plan. Why didn’t anyone think of it sooner? Why couldn’t they expedite the rescue by boosting thrusters or whatever‎ to do the flip-around thing earlier?

A: The movie was great (and very faithful to the book), but it could have done a better job of explaining why the Hermes-return solution was such a big deal.

Star Trek makes space navigation seem like steering sea vessels. Star Wars makes it seem like driving hot rods. Other movies, video games, etc. – and even Interstellar, which took pains to depict some exotic science accurately – give the impression that it’s just a matter of pointing your ship where you want to go, and going there. For better or worse, that’s the mental frame of reference that audiences bring to movies about space.

In fact space travel (given our present technology) is much more like firing a gun. The spaceship is the bullet. You get one main chance to aim correctly, and then BANG, off you go. After that there is no changing course. Tom Hanks puts it like this in Apollo 13: “We just put Sir Isaac Newton in the driver’s seat.” (Something no real astronaut would say, understanding that there is no time Sir Isaac Newton isn’t in the driver’s seat).

In fact it’s even harder than aiming a bullet because a bullet reaches its target, or misses, in fractions of a second. A spaceship bullet is aimed at something that’s months away, at a target that’s in motion, and it travels – or more precisely, falls – through a medium governed by gravity, where the sources of gravity – the Sun, the Earth, Mars, etc. – are all in motion relative to each other, creating ever-shifting “currents” tugging the spaceship this way and that.

Once the Hermes fired her engine for the return trip to Earth, that was pretty much that. It had almost no fuel left for other maneuvering. There was no “doing the flip-around thing.” It would have taken a fair bit of inspiration even to think of looking for a return-to-Mars trajectory (let alone a return-to-Mars-and-then-Earth-again one!) plus a lot of luck that one existed, plus a lot of work to actually find it, plus a lot of daring to attempt a critical resupply during the high-speed gravity-assist Earth flyby, all of which the movie depicts a little too simply.

Hopefully, the many cool science things that the movie does depict accurately will whet audiences’ appetites to learn more and thereby discover for themselves just how audacious and unlikely the rescue plan was. Meanwhile, go play with NASA’s interplanetary trajectory browser!

The nature of reality, part 3b: The speed of light

This is a followup to The nature of reality, part 3: Gravity specifics.

The speed of light, we know, is the universe’s speed limit. Nothing can move faster than that through space.

Are we missing the point? Maybe it’s not so much that that’s the top speed through space; maybe that’s the only speed through spacetime, and everything is moving at it — you, me, light, trains, turtles, mountains, everything, always. “Slower” things are moving at the speed of light more in the time direction of spacetime than in the space direction. “Faster” things are moving at the speed of light more in the space direction of spacetime than in the time direction. What we call “acceleration” is (I speculate) nothing other than changing the direction of your constant motion, more timeward or more spaceward. Non-spaceward motion (i.e., standing still) is what we experience as the ordinary passage of time.

If this is anything like right, then it supplies an intuitive foundation for thinking about all kinds of weird mysteries: why the speed of light is a constant in all reference frames (the paradox that got Einstein thinking about relativity in the first place); what’s special about acceleration; and time dilation and the physical basis of the Lorentz transformation.

The nature of reality, part 3: Gravity specifics

Reality is maddening. A deep understanding of it is elusive. If you think you understand its nature, you’re not trying hard enough.

Every now and then, however, I get a flash of insight that seems to put the nature of reality just nearly within my grasp. The feeling is brief and tantalizing, like trying to recall the details of a dream as they evaporate on waking. But it’s thrilling.

My latest one came while pondering the odd fact that there is no discernible difference between gravity and the acceleration due to motion.

When you’re sitting in a parked car, there is a force pressing your butt down into the seat. That’s gravity acting on your mass. (I’ll refrain from making comments about the mass of your butt.) When you peel out of that parking space and go from zero to sixty in 6.2 seconds, there is another force pressing your back against the seat. That’s acceleration. Science says that if you didn’t already know which force was acting on you, and the only clue you had was how it felt (not how it looks out the window, not the roar of the engine, not that you remember the Earth being beneath your feet when you got into the car, etc.), you couldn’t tell whether you were sitting still in a gravity field or accelerating through space, or some combination of both.

This turns out to be useful for sending humans on long interplanetary journeys in the future. If we invent a propulsion system that can sustain enough power continuously, then the spaceship can accelerate at 1g halfway to its destination, then turn around and decelerate (which is just accelerating in the other direction) at 1g the rest of the way. The humans on board will avoid the many health hazards of prolonged weightlessness; they’ll experience “gravity” holding them to the spaceship’s floors.

But what accounts for the fact that gravity and acceleration are the same thing? When you’re accelerating, your velocity is changing from moment to moment. And your velocity is nothing more than a measure of how your position changes from moment to moment. If your velocity is constant, you experience no acceleration. That is, you can be changing your position, but as long as it changes at a steady rate, you’re not accelerating. On the other hand, as soon as there is a change in the rate at which your position changes, the force due to acceleration appears.

  • Velocity: rate of change of position
  • Acceleration: rate of change of velocity

You can have lots of velocity and still have zero acceleration. If you plot your position over time on a graph, anything that’s a straight line means your velocity is constant and you’re not accelerating. To get acceleration, the graph needs to curve. (Any curve will do, but if the acceleration happens to be constant, then the curve is a parabola.)

Unchanging velocity; no acceleration, no force.

Velocity changing at a constant rate; produces a parabolic curve and a steady force.

Wrap your head around this

Here’s another recent insight that might help you to understand the idea of spacetime: The Big Bang happened in this very spot 13.8 billion years ago, and it’s also happening right now, 13.8 billion light-years away in every direction.

When you’re standing still on the ground and experiencing the pull of the Earth’s gravity, what’s changing to make that feel like acceleration? Not your position (with respect to the Earth). Not the rate of change of your position. But time is passing, and thanks to Dr. Einstein we know that space and time are mysteriously bundled together into something called spacetime. So even if you’re not moving through space, you’re always moving through spacetime.

But as I pointed out above, it’s not enough to be moving to experience acceleration. The rate at which you’re moving must itself be changing. When you’re standing still on the Earth, you’re moving through spacetime, yes; but the rate at which you’re moving through spacetime stays the same. So again: what’s changing that can give rise to a force like acceleration?

Standing still in space…

…is still moving through spacetime.

Well, hang on. We know (also from Einstein) that the presence of a large mass like the Earth causes spacetime to curve — whatever that means. So maybe it’s wrong to draw our spacetime axis as a straight line.

Suppose spacetime happens to curve just like this:

Standing still in curved spacetime.

Straightening the axis again forces the plot into a curve. (In fact, in this [manufactured] case it forces it into the shape of our old friend the parabola.)

Standing still in curved spacetime.

So. I’ve managed to convince myself that just standing still in a region of curved spacetime can look exactly like accelerating in a region of flat spacetime. Spacetime itself remains a difficult idea to internalize, to say nothing of it being curved, and even if I’ve managed to make one graph look like another in a hand-wavy way, still none of it makes any intuitive sense.

But I observe that moving at a constant velocity requires no energy. You need energy to change your velocity — i.e., to accelerate. And you need mass to curve spacetime. And as we know (thank you once again, Dr. Einstein), energy and mass are the same. Somehow it’s all down to the interactions between space, time, and energy. But what are they?

See what I mean? I can almost feel what real understanding would be like. It’s maddening.

[Update: followup thoughts added here.]

Have you herd?

[Cross-posted at]

Suppose there’s a disease that has a 50% chance of infecting you if you come into contact with it. Now suppose you come into contact with 10 people in one day. On average, 5 of them will be carrying the disease. Your odds of avoiding the disease are 50%×50%×50%×50%×50%, which is about 3%. In other words, you have a 97% chance of contracting it.

Now suppose you – and only you – get vaccinated. Let’s say it reduces your odds of infection, when exposed, from 50% down to 10%. Since no one else is vaccinated, when you come into contact with 10 people, it’s still the case that 5 are infected. Your odds of avoiding the disease are now 90%×90%×90%×90%×90%, or 59%. There is a 41% chance you’ll get sick. That’s a big improvement compared to 97%, but we can do a lot better.

Now suppose everyone gets vaccinated. Of the 10 people you come into contact with, on average only 1 will be infected. Your odds of getting sick are now only 10%.

That is the power of herd immunity.

Science limerick

Posted moments ago on Facebook in response to a challenge from They Might Be Giants for “science limericks”:

Is space made of strings or of foam?
Is it flat? Does it curve like a dome?
  Does time go both ways?
  Is the cosmos a phase?
I don’t know, but I still call it home

Kernel of truth

Yesterday I received a link — buried at the end of a long chain of e-mail forwards all saying variants of, “Wow, this is scary!” — to a video that depicted groups of people using stray microwaves from their cell phones to cause popcorn kernels to pop.

In the video, three or four phones are placed on a table in a ring around a few popcorn kernels, and then someone dials each of the phones to cause them to ring. Within a couple of seconds the kernels start to pop.

The sender who forwarded it to me asked if I knew whether this was for real.

My reply asked the sender to consider the power available to a cell phone versus the power available to a microwave oven. A microwave oven draws 15 amps of current from the household mains, producing hundreds of watts of focused microwave energy with the specific purpose of heating up food placed in the target area — and even so, it takes at least 30 seconds of exposure for the first kernel to pop. A cell phone, by contrast, houses a battery rated in milliamp-hours, with a typical one holding 1500 milliamp-hours of energy. This means it can draw 1 milliamp for 1500 hours, or 1500 milliamps (1.5 amps) for one hour, and so on. If a cell phone tried to draw 15 amps from such a battery, then (apart from the phone melting) the battery would be depleted in 1/10 of an hour — six minutes. Clearly cell phones do not draw 15 amps, but even if they did, they wouldn’t convert nearly as much of that energy into microwaves as microwave ovens do; and even if they did that, the microwave energy wouldn’t be focused the way it is in a microwave oven. Yet the video depicts the first kernel popping within about three seconds.

If that much microwave energy really were reaching the popcorn kernels, we’d also be seeing the other effects of powerful microwaves on objects in the immediate vicinity. For example, we’d see sparks and electrical arcing from metal objects, including the cell phones themselves. But we don’t.

Finally, why would a ringing cell phone cause popcorn to pop? To ring, a cell phone merely has to receive an “incoming-call” signal from a cell tower. The phone doesn’t begin transmitting any appreciable amount of power until after you answer it and begin speaking!

At this writing, the video in question has a supposed 11,031,929 views. When I think of all the people across the Internet who are now arranging their cell phones in rings around a handful of popcorn kernels, I despair.

Boy heaven

We did an amazing thing today.

As usual, Andrea had to drag me out of the house to it. I’m getting over a cold and all I wanted to do was catch up on blogging and work and Netflix discs, all of which sounded more interesting than driving to Point Reyes Station to see the culmination of the Giacomini Wetlands restoration project. But Andrea insisted, and I’m glad she did because she was right as usual, and it was amazing.

It’s a former marsh that was walled off from Pacific tides sixty years ago with a series of levees to create pastureland for cattle. Eight years ago the land was purchased by the National Park Service to begin a wetlands restoration project, which it turns out is a lot more complex than merely ripping out the levees. It’s taken from then until now for the project to reach its climax, which happened at high tide this morning. The public was invited to trek across the former ranch as water poured through a brand-new levee break and flooded the land for the first time in three generations.

Turnout was huge. Hundreds of nature-lovers showed up on a crisp, picture-perfect autumn morning to walk across a vast flat range of grasses and overturned dusty soil where construction machinery had been hard at work. A shallow channel was dug into the ground, making a straight line for the open water that we could see on the horizon; and when we’d walked far enough across the pasture, we came to a spot where a trickle of water was turning the dusty channel bed damp. As we watched, fingers of mucky water reached inland, inch by inch.

We stepped out of the channel onto the grass, which lay a few inches higher, as the water slowly overtook the spot where we’d been standing. Jonah and Archer tentatively placed their feet in the new muck.

A few minutes later they were notably less tentative.

All the grownups in the vicinity participated vicariously in Jonah’s and Archer’s delight at tromping through the mud, splashing in a dozen brand-new streams, pitching pebbles, ripping up tufts of grass, and conducting miniature impromptu soil-engineering projects. One onlooker commented to us, “Boy heaven.” (Lamentably, we saw almost no other children with anything approaching the liberty that we gave Jonah and Archer to explore and get absolutely filthy.)

Wherever we saw a limb of water, we could watch it reach into the low places in the land, rills of water filling one tiny depression after another. In some places the matted vegetation underfoot would grow first squishy and then splashy. Now and then a field mouse would emerge from a flooding hole and head for higher ground. Clods of dry soil would darken, crumble, then melt into thick dark mud through which Jonah and Archer gleefully trod. (We’re amazed it never sucked their shoes off.) Newly flooded sections of the plain bubbled noisily long after the last bit of earth was covered up.

When the tide began sluggishly to reverse itself, we retraced our steps through the pasture — at least, those parts of it that were still dry — returned to our cars, and reconvened a few miles down the road for a champagne celebration with the Park Service rangers and scientists for whom this was not merely an incredibly cool way to spend a Sunday morning. That it had been a lot of hard work was obvious, as was their satisfaction at its outcome.

Bullet time

I decided to apply a little physics to my KitchenAid mixer misadventure, in which I claim I was nearly killed by a hunk of metal propelled past my head by spinning mixer blades. When that projectile whizzed past my head, how much danger was I really in compared to, say, a bullet from a sniper’s rifle?

It comes down to a calculation of the kinetic energy of the projectile. Fortunately it’s very easy to approximate by making a few assumptions and by ignoring the effects of air resistance and the spray of cake batter.

The projectile was the mixer’s own removable endcap. As soon as it vibrated loose, fell into the bowl, and was struck by the spinning mixer blades, it was on a ballistic trajectory, arcing up, past my head, and then down behind me. Let’s assume that the highest point of the trajectory was about level with the top of my head, roughly 1.75 meters off the ground, and that this height was attained just as the projectile was passing me, meaning that once it did pass me, it had already started down.

We can decompose the motion of the projectile into a pair of vectors: the one pointing straight down to the floor and the one perpendicular to it, pointing horizontally past my head. The speed in that direction was constant until the endcap hit the floor. The speed in the floorward direction was increasing due to gravity.

Since we’ve assumed the endcap reached its apex as it passed my head, we know that its downward velocity at that moment was zero. We also know that the acceleration in that direction (due to gravity) is 9.8 meters per second per second. Finally we know from high school physics that:

distance = initial-velocity×time + acceleration×time2/2

and since we know initial-velocity is 0, we can rearrange this to say:

time = √distance/acceleration

And since we know “distance” is 1.75 meters and “acceleration” is 9.8 m/s2, we know that it took about 0.4 seconds for the endcap to fall from the height of my head, regardless of its motion in the horizontal direction.

In that 0.4 seconds I estimate (based on where I later found the endcap) that it covered a horizontal distance of 3 meters, giving it a speed of 7.5 meters per second.

I haven’t weighed the endcap but I’m going to guess it’s about 0.25 kilograms (around half a pound). Again, high school physics tells us that kinetic energy is:


which means the endcap, if aimed just a bit differently, would have struck me with about 7 joules of energy.

How bad would that have been, compared to a bullet? Apparently even the wimpiest guns deliver hundreds of joules to their targets, so we’re not looking at a shearing-off-the-top-of-my-head scenario here. On the other hand, I was there, and I’m not exaggerating when I say that hunk of metal could have dealt me a grievous injury at the very least. If that was what seven joules looks like, I have a whole new appreciation for the stopping power of a bullet.

How I wonder what you are

Often when I’m gazing at the night sky I will focus on a very dim star and marvel at its ability to shine steadily. No matter how long I look, and no matter whether I move a few inches to the left or right, it keeps right on shining. (It may twinkle a bit, but as you probably know, that’s due to our fluid, shifting atmosphere causing the starlight to refract slightly differently from one moment to the next, not due to anything about the star.) Photons emitted by that star hundreds of years ago poured out in such numbers that, even as they fanned out across unimaginable distances, there are still enough of them landing continuously in the tiny target of my eyes that the star remains a constant point of light.

Knowing the distances involved, it seems implausible that enough photons would be headed in my exact direction — of all the other places in the universe they could have gone! How implausible? Let’s figure it out.

We’ll start by estimating that the area of my dilated, night-sky-gazing pupils is about one square centimeter, or (to keep all measurements using the same units) one ten-thousandth of a square meter.

Thanks to Wikipedia I know that a single photon of visible light carries about 4×10-19 joules of energy which is just enough to excite a photoreceptor in my eye. How many must arrive each second for me to perceive a continuous image? I know that movies, projected at 24 frames per second, are good enough to trigger the persistence-of-vision effect. Since a distant star has far less detail than a frame of movie film, I’m guessing that it can appear steady at even fewer than 24 “frames” per second. Let’s guess 10 photons per second must arrive in my eyes to perceive a steadily shining star. 10 photons delivering 4×10-19 joules every second is 4×10-18 watts (because one watt is equal to one joule per second).

Now, how far is that star? A bit of googling reveals that a typical faintly visible star is 200 light years away (though many are much closer and many are much farther). 200 light years is 1.89×1018 meters.

From the perspective of that star, what fraction of its “sky” is taken up by my eyes? If you imagine a gigantic spherical shell centered on and surrounding that star, with a radius of 200 light years and my eyes on the inner surface, then the total area of that inner surface — the star’s “sky” — is 4×π×200light-years2, which is 503,000 square light-years, which is 4.5×1037 square meters. My pupils, one ten-thousandth of a square meter, comprise 1/2.22×1042 of that “sky.” That’s two millionths of a trillionth of a trillionth of a trillionth — not like that’s going to make my big ego feel small or anything.

So if 4×10-18 watts of visible light is delivered to 1/2.22×1042 of the star’s sky, then the total power delivered to its full sky is that first number divided by that second, which is 1.8×1024 watts, or 1.8 trillion terawatts. Is that a plausible number?

Yes it is. Our own sun has a visible-light output of 3.8×1026 watts. Which means, incidentally, that (using my guesses from above) it would be visible as a steadily shining star to a distance of 2.7×1019 meters, or about 2,900 light-years. Future criminals exiled from our galaxy will lose sight of their home star while barely a thousandth of the way to their new home in Andromeda.

U.S. Department of Mwa Ha Ha

From time to time in the popular science press I see something about generating electricity by placing enormous solar collectors in space and beaming the power as microwaves to special receivers on earth.

One such article, “‘Drilling Up’ — Some Look to Space for Energy,” appeared recently from the Associated Press. It describes a joint effort between the U.S. Department of Defense and the island nation of Palau to demonstrate the feasibility of receiving power from an orbiting satellite. The satellite will collect solar energy during its ninety-minute orbit, storing it up in order to beam it down to a receiver on Palau as it passes overhead. It will send a million watts of power during a five-minute window.

The article touts it as a forward-thinking alternative-energy project that will benefit at first the citizens of Palau and later the world. But nowhere in the article, or indeed in other articles of this ilk, are any red flags raised about placing in the Pentagon’s hands a solar death ray that can incinerate targets from orbit.

Now I don’t wish to impugn the Pentagon’s motives. I am sure their ambitions have everything to do with altruistically improving the standard of living for every person on earth and nothing to do with a lust for high-tech war toys. But if you or I built something that could store up three hundred million joules of energy and then deliver it all in a five-minute burst to any spot on earth, you could forgive the people of the world harboring a little concern.

You’d think that science writers could follow the technological implications of the things they write about. Hell, for this story all they need to do is watch some James Bond.

From Die Another Day