All posts by David L. Kaufman

9. How to Think Like a Scientist – Astro Scale

Astronomy scale distances
Illustrators and designers have struggled with the best way to represent the Solar System graphically.

Imagine holding an automobile in your hand. It’s easy, just pick up a matchbox car. Matchbox cars have lots of features of a real car, just shrunk down. Scientists call this a “scale model.” Model because it is not a real car, and scale because all the parts are shrunk down by the same amount. A Matchbox car is scaled by about 1:64, meaning a real car is 64 times bigger than the toy.

thunderbird_matchboxA Barbie doll is also a scale model, but it can’t fit in the matchbox car because it is scaled differently. Barbie dolls are scaled by about 1:6. A real girl is about 6 times bigger than the doll. Barbie is over 10 times bigger than the matchbox car. For Barbie to drive a Matchbox car, the car would have to be about the size of a football, or she would have to be shrunk down to the size of penny.

Thinking like a scientist means trying to describe reality to make future predictions. A very effective way to do this is by using models. They help scientists understand things that are too humungously big (or small) or too freakazoidically far away to make sense of. But remember, for a model to make sense all objects in the model must be at the same scale. Barbies and Matchbox cars are both scale models, just not to the same scale.

Models are often mathematical, but can also be made of die-cast metal and plastic. The more accurate the model and the more closely it describes reality, the better. Some toy cars just roll. Others have working doors and make noise.

Definitely Not to Scale: Here is a real picture of a basketball and a real picture of a pea. Presented together, the pictures suggest something that anyone who has played basketball and eaten their vegetables knows to be untrue -- that they are roughly the same size. You'll notice that in scientific pictures, a ruler or some other object of known size is often included in the frame. Otherwise, it's very hard to know from a photograph how big something really is.
Definitely Not to Scale: Here is a real picture of a basketball and a real picture of a pea. Presented together, the pictures suggest something that anyone who has played basketball and eaten their vegetables knows to be untrue — that they are roughly the same size. You’ll notice that in scientific pictures, a ruler or some other object of known size is often included in the frame. Otherwise, it’s very hard to know from a photograph how big something really is. But of course, a ruler wouldn’t help much with objects of planetary size.

Consider our solar system: Our nearest star, the Sun, is big. Really big. 865,000 miles wide. 110 times wider than the Earth. But what does that mean? Let’s build a model.

Imagine the Sun was scaled down to the size of a basketball, how big would the Earth be? The size of a baseball? Of a golf ball? No. More like the size of a pea. A basketball and a pea.

To Scale, Sort of: In this picture, our basketball and our pea are presented in proper size relative to one another. Case closed? Not quite. Since this article is talking about models and has been discussing the earth and the sun in terms of peas and basketballs, this picture suggests that this is how the earth and sun would look together. It is, sort of, but for the model to work the pea would need to be much, much further away from the basketball, 94 times as far away, in fact. Many of the Solar System maps you see on posters show the planets and sun much closer together than they really are, even when the relative size differences are factored in.
To Scale, Sort of: In this picture, our basketball and our pea are presented in proper size relative to one another. Case closed? Not quite. Since this article is talking about models and has been discussing the earth and the sun in terms of peas and basketballs, this picture suggests that this is how the earth and sun would look together. It is, sort of, but for the model to work the pea would need to be much, much further away from the basketball, 94 times as far away, in fact. Many of the Solar System maps you see on posters show the planets and sun much closer together than they really are, even when the size differences are factored in.

The Sun is far away from us, 93 million miles away. But what does that mean? If the Sun was a basketball in the hoop of one basket at a basketball court, the Earth would be a pea at the other basket 94 feet away.

If we keep going, a quarter-mile away from the basketball Sun is a golf ball named Jupiter. A half-mile mile away is a pingpong ball called Saturn. Three-quarters of a miles away is a walnut named Neptune. The NASA spaceship Voyager 1 (the furthest out manmade object ever) is a speck of dust about a mile away from the basketball.

Perfect: We've created the most accurate picture yet! Only problem, it may be the world's most boring poster. (The yellow arrow helps you find the pea in this expansive field of blue. It's there - we promise). There is a reason they call it space.
Perfect: We’ve created the most accurate picture yet! Only problem, it may be the world’s most boring poster. (The yellow arrow helps you find the pea in this expansive field of blue. It’s there – we promise). There is a reason they call it space.
So the Sun is really big and far away But the other stars are so much farther away I can barely describe it. The Sun is just one of many stars in our Milky Way galaxy. One of the next closest stars is Alpha Centari over 26 trillion miles (4 light years away). But what does that mean? Let’s expand the model.

Suppose the Sun was a basketball was at Disneyworld, Orlando Florida, at the Space Mountain ride. At that scale, Alpha Centari would be another basketball at Space Mountain in Disneyland in Pasedena, California 2,500 miles away! And that’s just the closest star. Other stars in our galaxy are much farther away.

To make sense of them, we would have to change the scale of our model again. Shrink the Sun down to the size of a pea. Earth is the size of a poppy seed. Alpha Centauri is now a pea only a mile away still in Orlando Florida. Other stars in our Milky Way galaxy are peas in California. And that’s just our galaxy.

The next closest galaxy to the Milky Way is Andromeda. The Andromeda galaxy is 2 million light years away. What does that mean? We need another scale!

Stars are really far away. Musician George Hrab explained it best in his classic song, “Far.”

“I sense all the explosions going off inside your brain
As your mind gets blown by what I just did explain
Sorry if my words might drive you all insane
But that’s what happens when precision is your middle name

This stuff is far, [it’s really far] this stuff is far far far away
We’re talkin’ far, [like über far] you can’t get there by car in a day”


Talking Like a Scientist: Magnitude
Scientists have an easy tool to help make sense of really big numbers and make comparisons.. When looking at any two numbers, scientists count the number of digits in each number. For instance, with Barbie’s scale factor (the number of times it is shrunk), 64 has two digits a 6 and a 4. If two scale factors have the same number of digits (like 64 and 11), then scientists say they are of the same order of magnitude. If one scale has 2 digits and the other has 1 digits (like 64 and 6), the 64 is considered to be an order of magnitude smaller. Barbie dolls are an order of magnitude larger than a matchbox car.

Venus is closer to the Sun than Earth, but they are the same order of magnitude away. Andromeda is 6 orders of magnitude farther away from Earth than Alpha Centari.


References:

http://en.wikipedia.org/wiki/Matchbox_(brand)

http://www.eharm.net/night_sky_guide/distance_and_time/distance_and_time.html

Song, “Far” by George Hrab from the album Trebuchet.

Song “The Sun is a Mass of Incandescent Gas” – by They Might Be Giants, from the album Severe Tire Damage.

365DaysofAstronomy.org

Brave New Worlds and Goldilocks

In this photograph, taken by an astronaut on board the International Space Station, Venus is seen moving in front of, or transiting, the sun. Although the planet is small in comparison to the sun, it blocks part of the light reaching the earth. Using very sensitive instruments, scientists can now measure the very slight dimming that occurs when an exoplanet blocks part of the light from a distant star it orbits. (Photo: NASA)
In this photograph, taken by an astronaut on board the International Space Station, Venus is seen moving in front of, or transiting, the sun. Although the planet is small in comparison to the sun, it blocks part of the light reaching the earth. Using very sensitive instruments, scientists can now measure the very slight dimming that occurs when an exoplanet blocks part of the light from a distant star it orbits. (Photo: NASA)
Do we know if there are planets orbiting other stars? Until about 20 years ago, the answer would have been “NO!” Most astronomers believed that there were probably planets going around other stars, but that it was not possible to find them. Planets are just so small compared to stars and the stars are so far away.

Then, in the 1990s, some really smart scientists thought up some crazy ideas to detect planets orbiting distant stars.

The simplest one became known as the Transit Method. When Mercury or Venus travel across the disc of the Sun (known as transiting the Sun), the amount of sunlight hitting the Earth goes down.

Think about a light bulb burning and a fly buzzing around it. While you look at the bulb as the fly buzzes by, the amount of light you see from the bulb is slightly less than when the fly is gone. It’s a very small amount, but the bulb does in fact become dimmer.

Now what if we could measure the brightness of a distant star incredibly accurately, and see if it dims? And what the star dims and brightens on a regular basis (like once a year)?

If that’s the case, it might be caused by a planet orbiting the star.

Let me pause and be the science grammar policeman. Technically, as poor Pluto learned, there are only 8 planets; a planet is now defined as a celestial body that, among other things, orbits our Sun. So if we’re talking about worlds orbiting some other star, they cannot be called planets. Astronomers call them exoplanets. “Exo” means “outside,” so exoplanet means a planet orbiting a star outside our solar system.

Using the Transit Method and other ingenious methods, astronomers started finding exoplanets, lots of them. It takes a long time to be sure. It takes multiple observations by multiple teams using multiple methods before an exoplanet is confirmed.

Now, hundreds of exoplanets have been confirmed. Thousands more listed as probable but haven’t been confirmed yet. The number keeps growing.

The artist's concept depicts NASA's Kepler mission's smallest habitable zone planet. Seen in the foreground is Kepler-62f, a super-Earth-size planet in the habitable zone of a star smaller and cooler than the sun, located about 1,200 light-years from Earth in the constellation Lyra. Kepler-62f orbits it's host star every 267 days and is roughly 40 percent larger than Earth in size. The size of Kepler-62f is known, but its mass and composition are not. However, based on previous exoplanet discoveries of similar size that are rocky, scientists are able to determine its mass by association. Much like our solar system, Kepler-62 is home to two habitable zone worlds. The small shining object seen to the right of Kepler-62f is Kepler-62e. Orbiting on the inner edge of the habitable zone, Kepler-62e is roughly 60 percent larger than Earth. (Image credit: NASA Ames/JPL-Caltech/Tim Pyle)
The artist’s concept depicts NASA’s Kepler mission’s smallest habitable zone planet. Seen in the foreground is Kepler-62f, a super-Earth-size planet in the habitable zone of a star smaller and cooler than the sun, located about 1,200 light-years from Earth in the constellation Lyra. Kepler-62f orbits it’s host star every 267 days and is roughly 40 percent larger than Earth in size. The size of Kepler-62f is known, but its mass and composition are not. However, based on previous exoplanet discoveries of similar size that are rocky, scientists are able to determine its mass by association. Much like our solar system, Kepler-62 is home to two habitable zone worlds. The small shining object seen to the right of Kepler-62f is Kepler-62e. Orbiting on the inner edge of the habitable zone, Kepler-62e is roughly 60 percent larger than Earth. (Image credit: NASA Ames/JPL-Caltech/Tim Pyle)
In 2009, NASA launched the Kepler Space telescope to find stars with exoplanets. It tracked the brightness of over 100,000 stars for over 4 years. It has discovered at least 900 confirmed exoplanets, and has provided scientists with so much data that will take years to completely review.

The Kepler scientist have found lots of weird planets. Huge planets bigger than Jupiter yet closer to their star than Mercury, orbiting every few days! They found planets twice the size of Earth, dubbed “Super Earths” really far away from their stars. They found planets orbiting two stars!

Scientists have even been able to determine all sorts of characteristics about these exoplanets including:

  • How big they are.
  • How long is their year.
  • How far away from their star is their orbit.
  • What chemicals are in their atmosphere

Naturally, astronomers want to locate planets that have the right conditions for life. They are looking for exoplanets that have orbits that means they are not too hot and not too cold, planets that are “just right” for life. They call this the Goldilocks zone. They have many candidates, so who knows what they’ll learn in the future?

The Gemini Planet Imager’s first light image of Beta Pictoris b (Processing by Christian Marois, NRC Canada)
The Gemini Planet Imager’s first light image of Beta Pictoris b (Processing by Christian Marois, NRC Canada)
In just a few years exoplanets have gone from science fiction to science fact. Earlier this year, scientists in Chile used special techniques and even took a photograph of an exoplanet! See below the image of Beta Pictoris b, a planet orbiting the star Beta Pictoris. In the picture below, the light of the star itself is blocked out by a disk so the planet can be seen. It’s great to see science in action.

Keep up with the latest exoplanet discoveries yourself at http://kepler.nasa.gov/Mission/discoveries/

8. How to Think Like a Scientist — Following the Evidence

Nobel Prize-winning physicist and accomplished bongo player Richard Feynman, in the classroom.
Nobel Prize-winning physicist and accomplished bongo player Richard Feynman, in the classroom.

When he was a kid, my buddy Richard was smart enough to be afraid of dragonflies.  They had a wicked bite or sting or whatever.  They were dangerous and scary.  Every kid in his town knew this.  The flying terrors were even nicknamed “darning needles”.  When a dragonfly would buzz by during school recess, kids would scream and scatter away.  The same thing was true in my hometown.  My brother even played baseball with a guy who got bit or stung or whatever by a dragonfly and had to be taken to the hospital.

My friend Richard was afraid but also curious.  He wanted to know how bad these ‘darning needles’ really were.  Was it a bite?  A sting?  How painful?  Deadly?  What were the best tactics to stay safe?

He wasn’t a freakazoid, though.  He wasn’t crazy enough to want to experiment with them personally.  Instead, Richard researched the topic to learn what other scientists had found.

This was the days before Google searches and Wikipedia.  So Richard got a book about dragonflies and read all the facts.  Guess what he found?  Dragonflies don’t bite or sting; they are totally harmless!

So when a dragonfly landed on his foot at the beach that summer, he amazed everyone by casually observing the bug and not flinching.  The other kids were screaming and running away in terror, and Richard just stood there, as cool as an ice cube.  Richard was small for his age and not physically strong, but on that day he was the Big Man on the beach.

Thinking like a scientist, Richard followed the evidence he learned and changed his ideas about dragonflies.  To continue being scared after learning they were harmless would be just silly.

Everyone has ideas they believe to be true.  But good scientists are not afraid to follow the evidence wherever it leads.  It’s okay to experiment on your own, and even try a few times.  But if the evidence clearly contradicts your original position, a good scientist admits he’s wrong, and revises his position.   A bad or lazy scientist ignores evidence or make excuses and just keeps his old views.

It takes courage.  I’m sure that Richard was a little scared when that dragonfly first appeared at the beach.  But he trusted the facts he had learned.  Science is about making accurate predictions.  Accuracy comes from following the evidence.

Talking like a scientist, Richard did 5 important things:

  1. He had a hypothesis – “dragonflies are dangerous”
  2. He researched the topic, learning facts that others have already discovered
  3. He found evidence that falsified his hypothesis
  4. He revised his hypothesis – “dragonflies are dangerous harmless”
  5. He experimented, testing and confirming the new idea

My buddy Richard’s last name is Feynman.  I never met Richard Feynman but I call him a friend because he is one of my heroes.  He grew up to become a Nobel Prize winning physicist and accomplished bongo player. Learn more about him at http://www.feynman.com/

Fun Phineas Feynman Quote

“Nature doesn’t care how smart you are. You can still be wrong.” –Richard P. Feynman

Far Out, Dude! (Really, We Mean It…)

This artist's concept shows NASA's Voyager spacecraft against a field of stars in the darkness of space. (NASA/JPL-Caltech).
This artist’s concept shows NASA’s Voyager spacecraft against a field of stars in the darkness of space. (NASA/JPL-Caltech).
When I was 11 years old, my family went on a 1,500 mile, two-week, car trip from New England to Florida. I got to see New York City and Washington, D.C., from the car window. Highlights of the trip included Disney World and the Kennedy Space Center at Cape Canaveral. However, I was trapped in a station wagon with my older brother and sister for two weeks. To me, it was a very long voyage.

What did I know?

In 1977, three months after I returned to Connecticut, NASA launched two spaceships from Cape Canaveral. They were named Voyager 1 and Voyager 2. Their mission was to go as far from the sun as possible, to take the longest voyage ever.

The thing is: space is really big. It takes a really long time to get around.

The two Voyagers spent more than three years flying through the middle of our solar system, giving us Earthlings our very first up-close views of Jupiter and Saturn. The images they sent back were incredible — rings were found around Jupiter, volcanoes were seen on Jupiter’s moon, Io…

However, the Voyagers only gave these worlds a passing look, like driving past New York City going 100 miles per hour. It would be up to future missions to return to the outer planets for more in-depth research.

The Voyagers didn’t even slow down as they flew by the planets. While Voyager 2 took the long road, spending another ten years checking out Uranus and Neptune, Voyager 1 left Saturn in 1980 and headed out of town.

At this point, it is important to remind you that space is really big. It takes a long time to get anywhere! And the solar system is much bigger that orbit of Pluto (See: What Happened to Pluto?).

In August 2013, scientists determined that Voyager 1 had left the solar system. It is the first machine built by humans ever to leave the solar system — truly a triumph for all mankind! It is about 11.8 billion miles away in interstellar space, the space between stars! Voyager 2 is about four years behind. Their journey will continue for another 40,000 years before they reach another star.

The Golden Record sent with the Voyager Spacecraft. (NASA)
The Golden Record sent with the Voyager Spacecraft. (NASA)
In case space aliens ever find the Voyagers, NASA put some amazing items inside to explain Earth and humanity to them. There is a golden phonograph record album (before there were CDs or compact discs, there were phonograph records … ask your parents). Recorded on the album are samples of 55 Earth languages, and various music selections, everything from Mozart to rock-n-roll legend Chuck Berry. Steve Martin, (the comedian, author, actor, & musician) noted that it is quite possible, thanks to Voyager, that the first message we ever receive from an alien space civilization may very well be them asking us to “send more Chuck Berry”. Far out, in every sense.

Fun Phineas Facts

We are still in contact with both Voyagers. They have a radioactive power source onboard with lots of power and still send data regularly. Due to the vast distances, it takes over 35 hours to get a response after sending a message to them. By timing how long these communications take, we can calculate exactly how far away they are at all times. The messages travel at 186,000 miles per second – the speed of light.

Can you make the calculation yourself to solve how far away Voyager 1 is? Grab a calculator and be sure to ask you math teacher for help if you need it!

— Time to send message and get reply back from spacecraft: 35 hours
— How fast the messages travel: 186,000 miles per second
— Question: How far away is the spacecraft, in miles?

Process:
1. Determine the number of seconds in an hour (60 minutes times 60 seconds)
2. Multiply the number of seconds per hour times 35 hours (the total time it takes to send and get a reply)
3. Multiply your total by the speed of light — 186,000 miles per second. This gives you the total number of miles the message traveled.
4. Divide your answer by 2, since the message made two trips — one to the spacecraft and one back home.


References:

NASA Voyager Site

Voyager Program

More Info on Voyager’s Golden Record

7. How to Think Like a Scientist – Shaving the Truth with Occam’s Razor

William of Ockham (c. 1287 – 1347) was an English Franciscan friar and scholastic philosopher and theologian, who is believed to have been born in Ockham, a small village in Surrey. (William of Ockham, from stained glass window at a church in Surrey.)
William of Ockham (c. 1287 – 1347) was an English Franciscan friar and scholastic philosopher and theologian, who is believed to have been born in Ockham, a small village in Surrey. (William of Ockham, from stained glass window at a church in Surrey.)

As Mac would say, I’m a freakazoid.  I don’t put milk in my cereal.  Never.  But I love a cold glass of milk with my cereal. So having finished off the gallon last night with dessert, I was keenly aware that we were out of milk, and that this morning was going to start off badly.

Instead, when I awoke I was pleasantly surprised and a bit shocked to find a fresh gallon sitting in the fridge!  Where did it come from?  My pre-breakfast mind quickly came up with three possible answers to the presence of the mysterious milk jug.

  1. My wife got up early and picked up some groceries before going to work.  or…
  2. Burglars broke into my house and left behind a gallon of milk.  or…
  3. My wife bought a cow last night, stabled it in the garage, and milked the cow this morning.

Of course there are many more possible answers.  But these were my top three pre-breakfast guesses and all successfully explained the mystery milk.

Before doing any investigation, how do I choose?  Which answer should I prefer?  Talking like a scientist, “which one would be my working hypothesis?”  Fortunately science has a great tool to help.  It’s called Occam’s Razor.

Occam’s Razor is named after 14th century philosopher, William of Ockham, who argued that “simpler explanations are, other things being equal, generally better than more complex ones.”

razorHis razor blade shaves away details that are unnecessary.

Very often in science (and in life), there is more than one solution that can explain a mystery.  Occam’s Razor picks the simplest solution, until there is a need for more accuracy.  The principle allows you to quickly decide where to focus your efforts.

In my case, scenario 1 is the simplest answer.  My wife bought some milk this morning.  This may be wrong.  But until I hear mooing coming from the garage, or see a newspaper headline about “Burglar Bandits Leave Milk Behind”, this is my working hypothesis.

Your math teacher would use the Razor if a student claimed that space zombies stole his homework.  Occam’s Razor would suggest that maybe the student just forgot to do the assignment.

Remember, Occam’s Razor is a guide. not a judge.  Start simple, and only add complications when you need to explain additional observations.  It may turn out that space zombies did steal the kid’s homework.   And I may have a cow in my garage.  I’ll go check after breakfast.


Illustration Credit: Razor detail from linen texture postcard, Boston Public Library. “Since 1731, J.A. Henckels Twin Brand Razors and Shears, radiant with quality and beauty like the rising sun, have been recognized by the discriminating master barbers as the best the world produces and the most satisfactory and the most economical to use.” Harry H. Baumann, 216 W. 18th Street, New York.1930 – 1945 (approximate)