News tidbit: Water bottle light bulbs

September 24th, 2011

How do you light the inside of a windowless room? With a bottle of water, of course! Driven by the outrageous price of electricity in the Philippines, Illac Diaz developed this economical and environmentally-friendly alternative. And in just four months, more than 15,000 bottles have been installed. How does it work? Imagine cutting a hole in the roof. Light enters, but so does the rain. Now plug the hole with a bottle of water. Sure, the bottle allows light in and not the rain, but the sunlight entering the bottle refracts in the water, spreading out into the room below! See these water bottles in action here.

The Physics of Dance

September 19th, 2011

arabesque.jpgOriginating in the elaborate courts of the Italian Renaissance in the 1400s, it developed into an art form during the 17th century in France under the reign of Louis XIV. But the elegant arabesques, exhilarating grand jetés, and energetic fouettés en tournant of ballet that we know today grew out of the Romanticism of the late 1800s, when ballerinas portrayed fairy-like creatures and almost seemed capable of floating in the air.

Have you ever wondered how a dancer can seem to defy gravity while your own feet are so firmly planted on the ground? Let’s take a closer look at gravity and discover the secrets behind some of these beautiful movements.

An article about dance should make you move, right? Here’s an experiment. Stand against a wall with your heels touching the wall. Now bend over and touch your toes. Did you make it?

Why did it suddenly become so difficult to do this simple task? The problem is the location of your center of mass: the average location of all the matter in your body. When standing straight, your center of mass lies within your body just below your belly button. It is situated above your feet, so you have no trouble standing.

But your center of mass can move depending on the position of your limbs. What if your body is horizontal? In a pas de deux, a male dancer may lift a ballerina into the air. Have you ever noticed where his hands are placed? Rather than clasping her waist or her thighs, he clasps her hips. Not only do her hipbones provide support, this is the point where her body is balanced; this is the location of her center of mass. Any closer to her belly or her thighs and the balance is upset; her center of mass is no longer above him, and he won’t be able to hold her aloft.

If your body is not straight, however, your center of mass is different. Try the experiment again. What happens to your center of mass as you bend over? By moving your torso away from the wall, you move some of your mass forward. Your center of mass also moves forward to a point somewhere in front of your upper thighs, not inside your body! Continue bending forward and at some point it will have moved out beyond your toes and you risk falling over. What do you do to keep from landing face-first on the floor? Try it and see. Can you figure out why standing against the wall makes such a difference?

Dancers instinctively know that to execute a perfect turn, their center of mass needs to be over their feet. Imagine trying to execute a turn, like a pirouette, on one foot. What happens if your center of mass is not directly over your feet? You end up with a wobbly turn, or worse, falling over!

grandjete.jpgThe center of mass also helps explain those big leaps, or grands jetés, that seem to hang effortlessly in the air. After taking a few quick steps, a dancer takes a leap, one leg leading and one trailing. During the leap her head rises a certain amount. (For some numbers and more physics, check out Dr. George Gollin’s Physics of Dance website.) As soon as she starts the leap, however, she raises her legs, i.e. some mass, to be parallel to the floor, which raises her center of mass some more. During the jump, her center of mass rises more than her head, making the leap seem even higher. What is more, her center of mass moves the most at the very beginning and end of the jump; it moves very little through most of the leap, giving the impression she is hanging in the air or floating.

We are so familiar with gravity’s pull attaching us to the ground that the light airy movements in ballet take us by surprise. The movements seem much more possible, however, when we apply a little physics and see how ballet has developed to work with gravity. The result? An art form that becomes even more exquisite!

PS. Here is another experiment. Sit in a chair, with your knees at a 90° angle, your feet flat on the floor. Now stand up without moving your feet or bending forward. How did you do? Our natural instinct is to bend forward, but try it again, without bending forward! When you sit in a chair, your center of mass lies at a point above your thighs in front of your lower belly. It is impossible to stand up in the second experiment unless you move your center of mass closer to your feet, which is what happens when you bend forward.

News tidbit: Hi-res Moon photos

September 8th, 2011

As part of the Apollo program, United States astronauts (one was also a geologist) walked on the Moon six times between 1969 and 1972, the only times humans have set foot on another celestial body. Will we ever return? As the BBC describes, NASA has released high-resolution images of the Apollo landing sites, all located on the near side of the Moon. The Lunar Reconnaissance Orbiter Camera has been orbiting the Moon since 2009 at an average altitude of 31 mi (50 km) to gain information about potential future landing sites, and was able to move into an orbit bringing it just 13 mi (21 km) above the surface. Think the astronauts left the Moon in pristine condition? The pictures reveal tire tracks, astronaut boot prints, and discarded pieces of equipment.

Share your thoughts: Would you go to the Moon if you had the chance?

Catch a Falling Star

August 27th, 2011


Did you catch any? A couple of weeks ago, many eyes were turned on the sky to witness the annual Perseid meteor shower where, under the best conditions, viewers can see a meteor as often as every minute. Though meteor showers have been observed since antiquity, it wasn’t until the mid-1800s that they were recognized as astronomical events. But what are meteors and why the name “Perseid”? To understand, we need to step back 4.5 billion years, to the beginning of the Solar System…

It all began with a massive cloud of gas and dust collapsing under the force of gravity, flattening and spinning faster and faster as it got smaller. A star, the Sun, formed at the center and the gas and dust revolving in a disk around the star coalesced into objects of various sizes: the familiar eight (sorry!) planets, their moons, the minor planets and asteroids, and other smaller chunks of rock and/or ice.


While the largest objects are nearly spherical and move smoothly in their relatively circular orbits, comets are the unruly hooligans of the Solar System. These irregular chunks of rock and ice formed in the farthest reaches of the Solar System. Close encounters with more massive objects flung them into highly eccentric — very non-circular — orbits, carrying them extremely close to the Sun. Notice how oblong the orbit of Halley’s comet is, as well as how close it approaches the Sun. As a comet nears the Sun, heat from the Sun causes frozen gases to vaporize, releasing dust and debris in the process. The gases, which we see reflecting light from the Sun, surround the comet and stretch out in a tail due to the Sun’s radiation pressure and solar wind; the dust and debris remain behind in the comet’s orbital path.

This rocky debris left by the comet is just one source of meteoroids — called meteors when they hit the Earth’s atmosphere — but it offers the most eye-catching display for us here on Earth. If the orbit of a comet crosses Earth’s orbit, the Earth will travel through the stream of rocky debris left by the comet. Thus, the Perseid meteor shower occurs when the Earth passes through the debris trail of the comet Swift-Tuttle just as the Orionid meteor shower, occurring in late October, is due to debris from comet Halley.

And the name of a meteor shower? We have to be good observers and notice that all the meteors in a shower come from the same point in the sky, the radiant point, which lies in a region, or constellation, of the sky. So, the Perseid meteors seem to come from the constellation Perseus, and the Orionids from the constellation Orion.

When meteoroids hit the Earth’s upper atmosphere, molecules in the atmosphere and those stripped off the surface of the meteor become ionized — they lose electrons. When atoms recapture the electrons, light is emitted. Aside from a pretty show, the color of this ionization trail gives us clues to the meteor’s composition; most meteors are yellow or green, meaning they contain a lot of iron or copper.

But scientists often want to know specifics: how much iron or copper is in each meteor? Practically all meteors disintegrate before they reach the lower atmosphere, so it is a challenge to have a meteor in hand. However, some meteors do hit the ground — they are called meteorites — and, if recovered, offer us a glimpse of the very origins of the Solar System!

As the meteorite speeds through the atmosphere, its outer layers melt, but the interior remains as it was when the meteoroid formed. Most recovered meteorites contain a lot of iron and nickel, which were used by early civilizations to make tools. Far more common are stony meteorites, which look like… well… stones. Because of this, they are difficult to identify. But, if you find one, you will most likely be holding a chunk of a primitive asteroid! The asteroid probably collided with another hunk of interplanetary rock, forming a meteoroid that went hurtling through the Solar System, through the Earth’s atmosphere, and, after some years, wound up in your hand!

What’s more, that meteorite can give us some very useful information. For example, when it formed, it contained two isotopes of strontium: 86Sr and 87Sr, which has one extra neutron. Over a characteristic length of time, that extra neutron turned into a proton, creating a different element, rubidium (87Rb). If we compare the ratio 87Sr/86Sr to 87Rb/86Sr, we get 4.6×109 years. Sound familiar? Not only is this the age of the meteorite, but since meteorites are among the oldest objects in the Solar System, it also gives the age of the Solar System!

If you missed the Perseids or you simply weren’t aware of it, keep looking up. Your next chance is just a couple of months away. The Orionids occur in late October, and the Leonids show up in mid-November. Here’s to clear skies!

On Rainbows and Diamonds

July 17th, 2011

Yesterday a quick rainstorm came through.  Shortly after it passed, a beautiful rainbow appeared in the sky, a perfect arc that touched down somewhere this side of the distant hills. While my 2-year-old nephew thought the rainbow very pretty, he would have none of the explanation, so I offer it here to you.

In our last post, we talked about why the sky is blue, and in particular, we mentioned that light from the Sun contains “all the colors of the rainbow.” We also mentioned that the atmosphere contains water vapor, the amount of which is obviously higher just after a rainstorm.

To these two elements we add a third: the refraction of light. Light refracts, or changes direction, when it enters a different material, and the amount and direction of refraction depends on a property of the material called the index of refraction. For example, light traveling from air into water refracts less than light traveling from air into glass because the index of refraction of water is lower.  Refraction depends on the wavelength as well, with blue light refracting more than red light. This is known as dispersion, and it also depends on the material.

So given some sunlight, a raindrop, and a bit of physics, what happens? The figure below shows a raindrop. See how the colors separate when sunlight enters the raindrop? This results from refraction and dispersion. Look now at what happens when the light in the raindrop tries to get out the other side. It reflects! If light incident on this part of the raindrop is not perpendicular enough to the surface, it will reflect instead of refract; this is known as internal reflection.


So light enters the raindrop and reflects off the inside, hitting another part of the raindrop. This reflected light now refracts a second time when it leaves the raindrop (the light is more perpendicular to the surface this time). Blue light again refracts more than red light, meaning the colors spread out even more.

If you’ve looked carefully at the diagram, you’ll notice the blue light ends up on top. But rainbows don’t look like this! To observe a rainbow, you need to stand with the Sun at your back, facing the raindrops. Looking straight ahead, there is a band of raindrops where the blue light is directed at your eyes. The raindrops further up will be in a position where the green light reaches your eyes, and finally the raindrops even higher are in a position where red light reaches your eyes. So we see red on top!

What about that pot of gold? I’m sorry to say you’ll never reach it. The rainbow’s location is not fixed, but rather depends on the your position and that of the Sun. If either you or the Sun moves, so does the rainbow! In fact, the rainbow’s semicircular shape also depends on these positions. Sunlight reflects off of all the water droplets in the sky; it just happens that the reflected light that reaches your eyes comes from a position 40-42° from the line connecting the Sun and your head. (This diagram may help clarify things.) Consequently, rainbows can only be seen when the Sun is within 42° from the horizon, or if you are high off the ground.

And double rainbows? This is caused by light internally reflecting twice within the water droplet. This secondary reflection also causes the colors to be inverted, with red on the bottom and blue on the top. Between the two rainbows lies a dark band known as Alexander’s Band, after Alexander of Aphrodisias, the Ancient Greek philosopher who first described it.

And last question… Why mention diamonds in the same article? Because they sparkle for pretty much the same reasons!

“Not that I give a hoot about jewelry. Diamonds, yes. But it’s tacky to wear diamonds before you’re forty.” ~Holly Golightly, Breakfast at Tiffany’s

Diamonds have high dispersion, which separates the colors a lot giving diamonds that characteristic fire. But diamonds can’t sparkle if light doesn’t internally reflect twice and exit out the top of the diamond. This depends on the index of refraction: the higher the index of refraction, the more likely it is that light will be internally reflected in a material. Diamonds have a very high index of refraction, making internal reflection very easy. This is where the cut of the diamond becomes important. If the bottom angle of the diamond is too shallow or too deep, light will not reflect, or it will only reflect once, getting lost out the lower side of the stone, as in the figure below. The magic number for this angle, as it turns out, is about 98°, depending on the way other parts of the diamond are cut.

 Diamond cuts

The next time you’re shopping for diamonds (maybe before you’re forty), you’ll now know why your purchase should have the right cut. The things nature designs are often inspiring, but it’s always amazing how they can become truly dazzling with just a little bit of tweaking by human hands!