Dr. Jeff's Blog on the Universe » 1.1. Dr. Jeff’s Weekly Challenge

Weekly Challenge 8: How Big is Big? The Earth Edition

DrJeff — Fri, 16 Oct 2009 18:01:12 +0000

This post is a Dr. Jeff’s Weekly Challenge and a Driving with Jordi.

Photo caption: the Hawaiian Islands, with the Big Island of Hawai’i at lower right. The Big Island was formed from five volcanoes including Mauna Kea. True color from the NASA Terra satellite, May 27, 2003.

The solution to this Challenge will be posted Monday, October 26, 2009.

It’s a new school year, and I couldn’t wait to get back into the routine of my morning drive with Jordi. I missed our daily conversations about Earth, space and everything else in his known universe while we navigate the fabled Washington, DC, Beltway to his school. Sure, we spent lots of great family time together over the summer at the pool club, and in New York. But there was something magical about taking 30 minutes of dull driving each morning and turning it into a free-for-all ‘Jordi where do you want to take the conversation today?’

To help you picture it, I’m always driving with my cup of coffee, glancing in the rear view mirror—waiting. He’s usually staring forward, transfixed. You’d almost think that my now 7-year-old is just zoning—except that he’s got that slight squint which tells me wheels are turning furiously inside. Then BOOM! He launches our great morning adventure with a simple, elegant, deep thought.

So last week, like always, just out of the blue—

“Daddy, how many Empire State Buildings tall is the tallest mountain?”

Today he wanted daddy to help him conceptualize the height of a really tall mountain. He wanted to use a familiar ruler.

Whenever we take a family a drive to New York (my Mom and sister are an hour north of the City) we always take time to go into Manhattan. We bike the Park or along the Hudson, eat in Little Italy making sure to get a box of the best pastries in the City at La Bella Ferrara—and then drive up 34th Street where we stop the car and let Jordi look straight up to the top of the Empire State Building. He LOVES that building. To him, it just touches the sky. I know exactly how he feels. For me it was always the World Trade Center.

So for Jordi, if one wanted to measure the size of the tallest mountain, using the Empire State Building as a ruler was surely the way to go. Cool kid. (Proud daddy.)

Not too long ago, I actually wrote a Post that used the height of the Empire State Building, so I remembered it was about 1,500 feet tall. I also know something about the height of mountains. My planetary atmospheres research took me to the telescopes on the summit of Mauna Kea so many times that I could be a tour guide for the Big Island of Hawai’i. On the summit I liked walking over to the U.S. Geological Survey marker identifying the highest point on Earth in the Pacific. But the short walk at 13,803 feet (4,207 meters) above sea level always left me out of breath. On one trip to the marker I had a friend take a picture of me next to it, with the clouds in the background a mile below us. I love to show that photo when I talk to kids and families and tell them that’s Jeff on top of the World (it is!)

But before going ‘UP’ with Jordi (something I suspect that’s much like what Carl Fredricksen felt flying off with Russell the wilderness explorer), I decided to go ‘down’ (because good stories have to build to a crescendo.) So we first talked about the Grand Canyon in Arizona, a hole in the ground that left me awestruck when I visited many years ago. At its deepest, the Grand Canyon is 6,000 ft (1,830 m) measured vertically from the rim of the Canyon to the Colorado River below. “Jordi, imagine you’re walking toward the rim and see this really large spike sticking up 100 feet above you. That’s about the height of a 10-story building. As you get closer to the rim and start to look down, you see the spike extends another 100 feet below you, and it’s attached to the top of a BIG building sitting in the Canyon. It’s the antenna mast …. of the Empire State Building.” He thought that was just so cool! Then shock set in when I told him this was just the top of a stack of FOUR Empire State Buildings with the base of the first sitting in the Colorado River! BIG canyon.

Then we went ‘up’, going back to his mountain question. Everybody thinks the tallest mountain on Earth is Mt. Everest and so did Jordi. So I went with the flow. “Jordi, Mt. Everest is about 29,000 feet above sea level. The Empire State Building is about 1,500 feet tall so, you’d need (daddy calculating in his head while driving) nearly …. TWENTY of them, one on top of the other, to get to the top of Everest.” Then … Jordi says, “20?!! 20?!!! … (5 second delay)…. 20?!!!!!” He was jaw—dropping stunned. In his mind that Building was huge! But How Big is Big? is all relative.

Now that I’ve got the internet and a calculator right here, I can do it more precisely. The summit of Everest is 29,029 feet (8,848 m) above sea level, and the Empire State Building is 1,472 feet (449 m) to the top of the antenna mast. So Everest is 19.7 Empire State Buildings Tall.

Ok, just getting you primed for your challenge. You didn’t think I’d give everything away did you?

Here now the challenge—

1. How many Empire State Buildings tall is the tallest mountain on Earth (Jordi’s original question)?

Hint: when is a mountain not just a mountain.

And by the way, my 210 mile high (340 km) mountain pictured in THIS Post, a photo presumably taken from the space shuttle, WASN’T REAL (the power of Photoshop). The fact that it was located “south of the Land of Make-Believe” was supposed to be the clue.

2. You’re on a cruise ship in the Pacific, 1,700 miles south of Tokyo and 200 miles south west of Guam (get out your maps.) You’ve slipped the captain a big wad of bills to stop the ship so you can go swimming. The crew lowers the inflatable zodiac, you jump into the water, but realize you left your spiffy waterproof, gold-encrusted watch in the dingy. The captain’s only given you 30 minutes of frolic time. “Hey crew member guy, can you toss me my watch?” Oops … he did and you missed. You do a quick dive and …. almost catch up to it as it gently descends. But you needed to stop ’cause you felt you were going too deep. There goes your watch on its way to the bottom. But come on, how deep could it really go? You figure if you slip the captain another wad of bills he’ll send in a diver to fetch it. Does he? How far is the bottom?

Hint: I want the answer using a (now) familiar ruler.

3. How many Empire State Buildings do you need to stack on top of one another to go from sea level to ‘outer space’?

Hint: read my Post The Business Trip for a clue.

Use a familiar ruler:

There’s a good chance you’re not familiar with the Empire State Building, so you might choose to use a different ruler for the heights and depths we’re considering above. Here are some tall structures in other parts of the USA and around the world you might want to use instead—

Statue of Liberty, New York City, USA: 305 ft (93 m) above ground level
Washington Monument, Washington, DC, USA: 555 ft (169 m)
Space Needle, Seattle, USA: 605 ft (184 m)
Eiffel Tower, Paris, France: 1,063 ft (324 m)

Tokyo Tower, Tokyo, Japan: 1,092 feet, (333 m)
Kiev TV Tower, Kiev, Ukraine: 1,263 feet (385 m)

Empire State Building, New York City, USA: 1,472 feet (449 m)

Petronas Twin Towers, Kuala Lumpur, Malaysia: 1,482 feet (452 m)

Shanghai World Financial Center, Shanghai, China: 1,614 feet (492 m)

Taipei 101, Taipei, Taiwan: 1,671 feet (509 m)

Willis Tower (formerly Sears Tower), tallest building in US, Chicago, USA: 1,730 feet (527 m)

CN Tower, Toronto, Canada: 1,815 ft (553 m)

Guangzhou TV and Sightseeing Tower, Guangzhou, China: 2,001 ft (610 m)

KVLY-TV mast, Blanchard, USA: 2,063 feet (818 m)
World’s tallest building—Burj Dubai (Dubai Tower) , Dubai, UAR: 2,684 feet (818 m)

Photo credit: NASA

THE SOLUTION TO Weekly Challenge 7: Spaceship Earth

DrJeff — Tue, 15 Sep 2009 23:02:21 +0000

Read Original Challenge HERE.

Photo caption: Computer-generated image of the Milky Way galaxy based on real data.

This post is a Dr. Jeff’s Weekly Challenge. It was requested by (teacher extraordinaire) Jami Lupold and her class in the great city of Houston, Texas, USA.

If you’re a teacher and your class has an idea for a blog post, slip me a note!

Last week I gave you a scare. It happened when I told you that you’re really on a spaceship hurtling through space. I was in the midst of describing all of Earth’s motions—it spins, it orbits the Sun, the Sun orbits the center of our galaxy carrying Earth and the Solar System along for the ride—and that’s when I saw panic on your face. You started to get a bit dizzy, so I turned on the “fasten seat belt sign” in light of all the conceptual turbulence ahead. To keep your mind off all the spinnin’ and revolvin’ I gave you an assignment to calculate Earth’s speed—your speed—due to these three motions. Does this all ring a bell? No? Why don’t you go and re-read the original challenge from last week, so you can refocus.

Good. Now that you’re back. Let’s get to the answers. Did I mention this week’s challenge was in our in-flight magazine in the seat pocket in front of you? By the way, I see you dug your fingernails into your seat, and your fingertips seem a bit blue. (Hope the answers don’t send you into a panic.)

And now the answers—

1. The Effect of Earth’s rotation: say you’re just standin’ there on Earth’s equator, all peaceful-like (a shout-out to my favorite class in Texas), minding your own business. How fast are you moving due to Earth’s rotation?

Hint: the Earth rotates once in 24 hours, and think “circumference of Earth.”

Answer: Just STANDING on the equator you are moving about 1,000 mph (nearly 1,700 km/hr)! You’re moving 1 mile every 3 seconds (1 km every 2 seconds)!

See the “How did I come up with those Answers” section below.

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

Now you’re standing on the North Pole. Why? Well it’s a place where we can forget about the speed you’re carried due to Earth’s rotation. Up here (excuse me for a moment …. brrrrr) Earth’s rotation just gently rotates you once in 24 hours on the spin axis you’re standing on. But you’re still movin’ through space, yes you are … ’cause the entire Earth is zipping along in its orbit around the Sun. Your assignment #2 if you choose to accept it: how fast are you moving due to Earth’s motion around the Sun?

Hint: the Sun is 93,000,000 miles or 149,600,000 km (on average) from Earth, and it takes 1 year to go around once. This time think “circumference = 2 x pi x r”

Answer:

STANDING on spaceship Earth, you are being carried around the Sun at a speed of 19 MILES PER SECOND (30 KM PER SECOND)!! Say “one mississippi” …. there, you just moved 19 miles (30 km)! That’s the same as 67,000 miles/hour (107,000 km/hour)!! (Maybe you should keep your seat belt on.)

See the “How did I come up with those Answers” section below.

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

Your assignment #3 is to figure out how fast the Sun (carrying the entire Solar System along for the ride) is moving in its orbit around the center of the Milky Way galaxy.

Hint: assume the Sun is 28,000 light years from the center, and completes 1 orbit in 240 million years

Oh, other needed Hint: 1 light year = 5.9 trillion miles or 9.5 trillion km

And yeah: think “circumference = 2 x pi x r” (again)

Answer:

For you to orbit the center of the Milky Way once in even the unfathomable time of 240 million years still requires you to be moving very, exceedingly, incredibly, *unbelievably* fast. Right now you are cruising through the galaxy at 495,000 MILES/HOUR (795,000 km/hr)!! That’s 140 MILES/SECOND (220 km/second)! Count out 17 seconds. Cool. You just moved the length of the continental United States, from New York to San Francisco. REALLY!

What? You’d like to travel the entire diameter of planet Earth? Wait 1 minute (actually 57 seconds). Done.

See the “How did I come up with those Answers” section below.

Look up in the sky! It’s a bird! It’s a plane! It’s superman! … big deal. Just sittin’ there, [insert your name here] is WAY faster than a speeding bullet.

Teachers and Parents:

You don’t need to do the calculation with your class (or child at home) to use this post as a powerful lesson. The speeds described above are remarkable, and are sure to impress. Some points:

1. The first calculation is the easiest because you don’t need scientific notation, and you don’t need to convert units. So you might want to do this one to demonstrate the geometry of a circle (the path traveled), and the relation: speed = distance / time.

2. Show some examples of speed = distance / time, e.g., if you travel 100 miles in a car at 50 mph, how long did it take?

3. Have them guess what speeds might be associated with each motion before you tell them the answer.

4. With the answers above in hand, have them calculate how long it would take to travel distances that are familiar to them, e.g., the distance between two cities. Calculate separately the time it would take due to Earth’s rotation, Earth’s orbit around the Sun, and the Solar System’s orbit around the center of the galaxy.

And now—how did I come up with those answers?

Note that calculating answers 2 and 3 below requires an understanding of scientific notation.

There are two key relationships you need for all three questions. In each case the motion you’re investigating carries you once around a circle in a given period of time:

The first is the relationship between a circle’s diameter (d) or radius (r) and the circle’s circumference (c):

circumference = pi x diameter

circumference = 2 x pi x radius

where pi = 3.14

The second relationship provides your speed if you know the distance you’ve traveled in a given time:

speed = distance / time

1. The Effect of Earth’s rotation

The important point: you travel around the circumference of Earth once in 24 hours.

Earth’s equatorial diameter: 7,926 miles (12,756 km)

Earth’s circumference = pi x diameter: 24,888 miles (40,054 km)

speed = distance / time = circumference / time

English units: speed = 24,888 / 24 = 1,037 miles/hr Or: 0.29 miles/sec

Metric units: speed = 40,054 / 24 = 1,670 km/hr Or: 0.46 km/sec

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

The important point: you travel the path of Earth’s orbit around the Sun once in 1 year. You can assume the orbit is a circle whose radius is 93,000,000 miles (149,600,000 km), which is the average distance between Earth and the Sun.

Circumference of Earth’s orbit around Sun:

= 2 x pi x radius: 584 million miles (939,5 million km)

Time to orbit Sun once:

= 1 year = 365.25 days = 8,766 hours = 3.16 x 10 ⁷ seconds

speed = distance / time = circumference / time

English units: speed = 584 x 10⁶ / 8,766 = 66,600 miles/hr Or: 18.5 miles/sec

Metric units: speed = 939.5 x 10⁶ / 8,766 = 107,200 km/hr Or: 29.8 km/sec

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

The important point: you travel around the center of the Milky Way galaxy once in 240 million years. You can assume the orbit is a circle whose radius is 28,000 light years (each light year is the distance light travels in a year.)

Let’s convert 28,000 light years to meaningful units of miles and km. The hint said that 1 light year = 5.9 trillion miles or 9.5 trillion km

English units: 28,000 light yrs x (5.9 x 10¹²miles /light yr) = 1.65 x 10¹⁷ miles

Metric units: 28,000 light yrs x (9.5 x 10¹² km / light yr) = 2.66 x 10¹⁷ km

Now let’s calculate the circumference of the orbit around the galactic center:

= 2 x pi x radius:

English units: 2 x pi x (1.65 x 10¹⁷ miles) = 1.04 x 10¹⁸ miles

Metric units: 2 x pi x (2.66 x 10¹⁷ km) = 1.67 x 10¹⁸ km

Time to orbit the center of Milky Way once:

240 x 10⁶ years = 8.8 x 10¹⁰ days = 2.1 x 10¹² hours = 7.6 x 10¹⁵ seconds

speed = distance / time = circumference / time

English units: speed = 1.04 x 10¹⁸/ 2.1 x 10¹² = x 495,000 miles/hr

Or: 140 miles/sec

Metric units: speed = 1.67 x 10¹⁸ / 2.1 x10¹² = 795,000 km/hr

Or: 220 km/sec

Photo Credit: National Geographic Society Image Collection, 1999.

Weekly Challenge 7: Spaceship Earth

DrJeff — Fri, 04 Sep 2009 15:26:29 +0000

Photo caption: Computer-generated image of the Milky Way galaxy based on real data.

This post is a Dr. Jeff’s Weekly Challenge. It was requested by (teacher extraordinaire) Jami Lupold and her class in the great city of Houston, Texas, USA.

If you’re a teacher and your class has an idea for a blog post, slip me a note!

You wanted to be an astronaut? Poof. Done.

You and your friends are on a spaceship called Earth—with all known life aboard. With you sitting there calmly reading this, and no obvious need to hold on to something for dear life, it might seem that the spaceship under your feet is carrying you on a nice steady trajectory through space. Uh … Nope. Right now you’re being carried along on something more akin to a cosmic-sized amusement park ride. Earth is rotating on its axis, it’s orbiting the Sun, and the whole Solar System (the Sun and its planets, dwarf planets, asteroids, comets, and Trans-Neptunian Objects) is orbiting the center of the Milky Way galaxy. The Milky Way itself is moving relative to other nearby galaxies, the local group of galaxies is moving through a greater space, and all this is set against a backdrop of an expanding fabric of space and time across the entire universe. I know!!!! (© Craig Ferguson) Dizzy?

[Pleasant Ding] The captain has just turned on the seat belt sign. There may be some conceptual turbulence up ahead. But I’ll make the ride as smooth as possible.

OK, I think a Weekly Challenge requesting that you calculate all the spinning, and revolving, and free-flying is a bit much, so let’s concentrate on three things:

Here now the Challenge—

Hint: the Earth rotates once in 24 hours, and think “circumference of Earth.”

2. The Effect of Earth’s revolution (it’s orbit around the Sun):

Hint: the Sun is 93,000,000 miles or 149,600,000 km (on average) from Earth, and it takes 1 year to go around once. This time think “circumference = 2 x pi x r”

3. The effect of Earth’s revolution around the center of the Milky Way galaxy:

This one is the toughest ’cause now I’ve relocated you to the north pole of … the SUN. Here, you don’t experience effects 1 and 2 above. From here you can just watch the spinning Earth as it orbits you. (Excuse me a minute …. hot, hot, hot!) What? Why did I put you on the NORTH POLE of the Sun? So I would not confuse you with your motion due to the Sun’s ROTATION. (Hey, get with the program …. everything is in motion.)

Your assignment #3 is to figure out how fast the Sun (carrying the entire Solar System along for the ride) is moving in its orbit around the center of the Milky Way galaxy.

Hint: assume the Sun is 28,000 light years from the center, and completes 1 orbit in 240 million years

Oh, other needed Hint: 1 light year = 5.9 trillion miles or 9.5 trillion km

And yeah: think “circumference = 2 x pi x r” (again)

So get to figurin’, and remember that while you’re sittin’ there, you’re ZOOMING THROUGH SPACE due to those three effects you’re figurin’!

Thanks Jami and Jami’s class! Have a great school year!

—Doctor Jeff (Honorary Texan)

Answer now posted here!

Photo Credit: National Geographic Society Image Collection, 1999.

THE SOLUTION TO Weekly Challenge 6: Today’s Special in the Cosmic Kitchen is …

DrJeff — Mon, 24 Aug 2009 17:09:01 +0000

Read Original Challenge HERE.

This post is a Dr. Jeff’s Weekly Challenge.

Welcome humans nice folks. We have assumed you are here for the answer to Weekly Challenge 6. Men in black team #26,342 is therefore now en route to your home. If you don’t know why, before reading any further we recommend (with great strength) that you read Weekly Challenge 6. Our team is rolling (very fast).

And now the answer—

Last week in the Cosmic Kitchen, Chef Jeff pushed the green button on the pasta press, and a single strand of Earth spaghetti was created that just stretched across the 93 billion light-year diameter of the observable universe.

What was the diameter of the spaghetti required? 1 millimeter (0.04 inches)

It is not microscopically thin. It is not the diameter of a fire hose. It is precisely the diameter of—angel hair pasta, a thin spaghetti. Go to your local store buy a box and measure it for yourself. By the way, help support us by purchasing our sponsor’s brand of angel hair. Look for Cosmic Kitchen Pasta #42 available in most supermarkets.

We also submit for your consideration that this was not magic, or some remarkable coincidence. In the Cosmic Kitchen we have the ability to realign the laws of nature. In this case, we have ensured that the Earth, when squeezed into a single strand of Earth spaghetti capable of spanning the observable universe, has the thickness of … spaghetti. We hope you humans nice folks appreciate the effort. We wanted your planet to still be recognizable to you, at least as today’s special entree.

We also hope you have enjoyed your visit to the Cosmic Kitchen. Its existence is a closely guarded secret, and we are honored to have shared it with you. The men in black will be knocking on your door at any moment. Won’t you please help them fill out our survey? And remember that you can receive a special gift if you answer their final question correctly. Since we have spent this last week together, I now consider us friends, and I want to see you receive your special gift. So remember I gave you the answer to the question last week. Just say “cheese.”

How did Chef Jeff come up with the answer?

The volume of the Earth, a sphere, is to be transformed into the volume of a strand of spaghetti, a cylinder. Recognizing that the volumes are equal, here is how it is done:

1. The volume of a sphere is: 4/3 x pi x R³ where:

pi = 3.14

R is the radius of the sphere, in this case the radius of Earth:

6,378 km = 6.378 x 10⁶ meters

2. The volume of a cylinder is: pi x r² x h where:

r is the radius of the cylinder, here the radius of the spaghetti, which is to be calculated

h is the height of the cylinder, here the length of the spaghetti:

93 billion light-years = 9.3 x 10¹⁰ light-years

converting to meters (see hint last week):

9.3 x 10¹⁰ light-years x 9.46 x 10¹⁵ meters / light-year = 8.8 x 10²⁶ meters

3. Setting the two volumes equal yields the equation (note the pi cancels out):

4/3 x R³ = r² x h

4. Now enter the following data into the equation and solve for r, the radius of the spaghetti:

R = 6.378 x 10⁶ meters

h = 8.8 x 10 ²⁶ meters

You will find r = 0.00063 meters = 0.63 millimeters

Thus the diameter of the spaghetti = 2 x r = 1.2 millimeters, which is the diameter of angel hair pasta.

Weekly Challenge 6: Twilight Zone, the Missing Episode – “Today’s Special in the Cosmic Kitchen”

DrJeff — Mon, 17 Aug 2009 15:12:18 +0000

This post is a Dr. Jeff’s Weekly Challenge.

On a recent tour of CBS, I got separated from my group, got pretty lost, and ended up in a dusty storage room filled with nightmarish props that really creeped me out. In the corner I found an old envelope marked “Rod Serling’ with a script inside. Wow. I decided to turn it into a BotU Weekly Challenge and introduce a new character kinda like, well, me. (It is my Blog.)

First a word from our Sponsor—

Come back Monday, August 24. for the solution to this Weekly Challenge.

Come back Friday, August 21, for a new post “The Scale of the Solar System—A Voyage in Corpus Christi”

Submitted for your consideration, I invite you to accompany me to a Cosmic Kitchen where each entree is of galactic proportions, and ingredients are folded together with forces both unimaginable and seemingly limitless. As we enter the infinite spaces allocated for baking, a solar-system-sized pasta press has just been loaded with planet Earth, and an ejector plate has been inserted which has but a single hole in the center with an adjustable diameter. Chef Jeff has closed the massive door behind the planet, and now the only way out for Earth is through that small opening—for today’s special in the Cosmic Kitchen is Earth spaghetti.

Before pushing the unassumingly small green start button on the pasta press, the diameter of the spaghetti must be set. Once the hydraulics are engaged no adjustments can be made—for the forces at work could result in a catastrophic accident. It has happened in the past. 350,550 years ago the pasta press exploded, planet was everywhere, and the kitchen had to be closed down for cleaning by precisely 10,000,042 workers. (Note that in the Cosmic Kitchen, 42 must be included in the solution to everything).

Given the potential consequences, setting the diameter of the spaghetti required Chef Jeff to consult Cosmic Kitchen’s head chef. Her reply—adjust the diameter so that the single strand of Earth spaghetti could just stretch across the entire observable universe.

Back in the Cosmic Kitchen’s research library, with rows of workstations extending to the horizon, Chef Jeff goes on line to determine the size of the observable universe. He’s come across this before. It came up when he was asked to keep folding a humongous sheet of paper until its thickness could extend to the edge of the observable universe. He remembered the link to the web site with the answer. The diameter of the observable universe is 93 billion light-years.

Chef Jeff (originally trained as an astrophysicist, but thought cooking was more lucrative) now knows that the entire volume of Earth is to be stretched into the volume of a single strand of spaghetti that just spans the 93 billion light-year diameter of the observable universe. A quick calculation gives him the required diameter for the spaghetti.

Back at the pasta press, he transports to the ejector plate, sets the spaghetti’s diameter, and transports back to the control room where he stands ready to push the green button.

Here now the challenge—

By reading this, you have accepted an invitation to be one of the spectators in the Cosmic Kitchen’s gallery. Before Chef Jeff pushes the button, you are asked to submit your guess for the diameter of the spaghetti he will be making today. Leave your guess as a comment below.

If you are in fact brave enough to undertake the calculation before submitting your guess (and you know how to use scientific notation) then here is your hint:

What is the volume of a sphere?

What is the volume of a cylinder?

1 light-year = 9.46 x 10¹⁵ meters

After the answer is posted next week, please wait by your door for my colleagues to arrive. You will easily recognize them. They will be men in black. They will be interviewing you on the quality of this post, and will be taking notes with a rather interesting pen. Please take a close look at their pen. They will also ask you a question to see if you should receive a special gift for taking the survey. Let me help. I know what they will likely ask: “what milk product is often aged before being brought to market.” You should say “cheese.”

Answer now posted here!

Submitted for your consideration, I invite you to accompany me to a Cosmic Kitchen where each entree is of galactic proportions, and ingredients are folded together with forces both unimaginable and seemingly limitless. As we enter the infinite spaces allocated for baking, a solar-system scale pasta press has just been loaded with planet Earth, and the ejector plate has been inserted with a single adjustable diameter hole. Chef Jeff has closed the massive door behind the planet, and now the only way out for Earth is through that small opening-for today’s special in the Cosmic Kitchen is Earth spaghetti.

Before pushing the seemingly small green start button on the pasta press, the diameter of the spaghetti must be set. Once the hydraulics are engaged no adjustments can be made-for the forces at work could result in a catastrophic accident. It has happened in the past. 350,550 years ago the pasta press exploded, planet was everywhere, and the kitchen had to be closed down for cleaning by precisely 10,000,042 workers. In the Cosmic Kitchen, 42 must be included in the answer to everything.

Given the potential consequences, setting the diameter of the spaghetti required Chef Jeff to consult Cosmic Kitchen’s head chef. Her reply-adjust the diameter so that the single strand of Earth spaghetti can just stretch across the entire observable universe.

Back in the Cosmic Kitchen’s research library, with rows of workstations extending to the horizon, Chef Jeff goes on line to determine the size of the observable universe.

Chef Jeff (originally trained as an astrophysicist, but thought cooking was more lucrative) now knows that the entire volume of Earth is to be stretched into the volume of a single strand of spaghetti that just spans the diameter of the observable universe. A quick calculation gives him the required diameter of the spaghetti.

Back at the pasta press, he transports to the ejector plate, sets the spaghetti’s diameter, and transports back to the control room where he stands ready to push the green button.

By reading this, you have accepted my invitation as one of the spectator’s in the Cosmic Kitchen’s gallery. Before Chef Jeff pushes the button, I ask you to submit your guess for the diameter of the spaghetti he will be making today. Leave your guess as a comment below.

After the answer is posted next week, please wait by your door for my colleagues to arrive. You will recognize them. They will be men in black. They will simply be interviewing you on the quality of this post, and will be taking notes with a rather interesting pen. Please take a close look at their pen.

THE SOLUTION TO Weekly Challenge 5: Dr. Jeff’s Interplanetary Travel Agency

DrJeff — Fri, 07 Aug 2009 20:44:48 +0000

Read Original Challenge HERE.

This post is a Dr. Jeff’s Weekly Challenge.

Nice to see you again! Now that you’re back from your interplanetary romp through the Solar System, let’s see those cool photographs you took for the Dr. Jeff’s Interplanetary Travel Agency tour brochure.

[Hmmm .... silence.] You there?? Earth to my contracted photographer, you seem to be processing all this a bit slowly. I suspect you’re suffering from ‘rocket lag’. It’s perfectly understandable after traveling over 10 billion miles and visiting 7 worlds. I don’t think any photographer has ever been this dedicated. You’re clearly worth more than I’m paying you. So take a load off, and first re-read Weekly Challenge 5 to get back up to speed.

And now the answers—

Now that you’ve re-read Weekly Challenge 5, let’s take a look at those photographs and your notes.

I sent you to Earth’s Moon, and to moons of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. What I wanted to know was how big each moon’s parent planet looks from that moon’s surface, compared to how big the Full Moon appears from the surface of Earth. As creatures living on the surface of Earth, we have a sense of how large the Full Moon looks. So using the Full Moon as a ruler of sorts, how many Full Moons across would, e.g., Neptune appear from the surface of its moon Triton?

The key is to recognize that the apparent size of the planet depends on the actual size of the planet and its distance from you. The larger the actual size of the planet, the larger it will appear. The more distant the planet, the smaller it will appear. The answers are below. I’ve described how I got the answers in the last section of this post.

Compared to the Full Moon in Earth’s sky:

From the Moon, Earth appears nearly 4 times wider than the Full Moon in Earth’s sky. Imagine the view, the continent of Africa—nearly 3 Full Moons across; the browns and greens of the land masses, the blues of vast expanses of ocean, and an ever-changing global arrangement of clouds afloat in the atmosphere. All this as Earth slowly rotates once every 24 hours, with whole continents passing from daylight, through a region of twilight, to darkness—or the reverse—depending on the phase of Earth as seen from the Moon. And since the same side of the Moon always faces Earth, from the Moon’s surface you see an Earth that never sets. It hangs forever in your sky. The sight must be beyond words.

From Phobos, Mars appears 80 times (!) wider than the Full Moon. Mars’ 4 largest volcanoes—Ascraeus Mons, Pavonis Mons, Arsia Mons, and Olympus Mons—all found in the same Tharis region on the planet, each appear more than 5 Full Moons across. And the Martian canyon system Valles Marineris—which is as long as the Continental U.S. (making the Grand Canyon look like a small ditch)—can be seen cutting across the face of Mars, appearing more than 50 Full Moons long.

As you look around on Phobos where you’re standing, you see it’s nothing more than a large rock whose edge is only 5 to 8 miles (9 to 13 km) in any direction. Hang on to something, because gravity is pretty weak here—and definitely don’t jump. Why? Well, imagine a jump on Earth where you rise to a height of 2 feet. The same jump on Phobos would take you 4,000 feet—3/4 mile—(1.2 km) above the surface. (I guess some of you are now going to want to jump. Think of the extreme sports you could dream up.)

From Io, Jupiter appears 37 times wider than the Full Moon. The largest planet in our Solar System, like Saturn, Uranus and Neptune, has no solid surface. You’re witnessing what might be described as an organized maelstrom, with bands of multicolored clouds that ring the planet interacting to form swirls and hurricane-like storms of immense size. One storm, the Great Red Spot—big enough to swallow 2 to 3 Earths—appears 9 Full Moons across.

On the Ionian horizon, thankfully a good distance from where you are standing, multiple volcanoes are seen erupting with plumes shooting hundreds of miles into the sky.

From Tethys, Saturn appears 45 times wider than the Full Moon; but Saturn’s visible rings are much wider than Saturn. From Tethys the ring system would be 105 Full Moons across! It is equivalent to sitting in the back row of an IMAX theater and Saturn is filling the massive screen. Tethys always presents the same side to Saturn, so from Tethys surface Saturn never sets. You see this immense planet, as if pinned in place to the starry sky, rotate once every 10.5 hours. Looking at the center of Saturn’s disk from the surface of Tethys, the planet rotates through the width of a Full Moon every 4 minutes. You can SEE the planet rotate. Like carefully watching a hand on a giant clock to truly see the flow of time, every 8 seconds you can noticeably see that the planet has turned.

Finally:

From Ariel, Uranus appears 29 times wider than the Full Moon

From Triton, Neptune appears almost 16 times wider than the Full Moon

From Charon, Pluto appears 13 times wider than the Full Moon

Our lives are constrained to the surface of Earth, which greatly limits our experiences. One day, something akin to Dr. Jeff’s Interplanetary Travel Agency will be a reality. Future generations will be able to book a trip, board a rocket at a local spaceport, and with some equipment changes along the way travel to these other worlds in our neighborhood. They will be able to see these remarkable sights for themselves, and talk to their children about an era not too long ago when these trips were only a vision of the future.

Teachers and Parents:

Explore with your child or your class the relationship between the APPARENT size of an object, the physicial size of the object, and the distance to the object. Here are some ideas:

1. A thumb is clearly a lot smaller than a person. Have kids explore how they can make their thumb APPEAR larger than a person. All they need to do is close one eye, and place their thumb at just the right distance from their open eye to cover up a person in the distance. Once the person is covered up, it’s clear their thumb APPEARS larger than the person. This demonstrates two things:

something small (your thumb) can APPEAR large if it’s placed close to you

something large (the person) can APPEAR small if placed at a great enough distance from you

2. Take a photo of kids that APPEARS to show them holding something really large in their hand, like a tree or a tall building. Position each child and the camera so that the child’s hand APPEARS big enough to hold the large object that’s obviously at a great distance.

3. Take what was learned in 1 and 2 above and discuss how this applies to what you might see in your sky from the surface of another world.

And now—how did I come up with those Answers?

Since we’re comparing the planet’s apparent size to the Full Moon, we’re interested in two things:

1) how much bigger is the planet’s diameter than that of Earth’s Moon? (The diameter of Earth’s Moon is 3,475 km.)

Let’s call this “SIZE”, where:

SIZE = planet diameter / Moon’s diameter

and

2) how much farther is the planet from its moon, than Earth is from Earth’s Moon? (The Earth-Moon distance is 384,400 km.)

Let’s call this “DISTANCE”, where:

DISTANCE = planet-moon distance / Earth-Moon distance

The apparent size of the planet in units of Full Moons = SIZE / DISTANCE

Some examples:

If SIZE = 10 (so planet is 10 x the diameter of the Full Moon), and DISTANCE = 10 (so planet-moon distance is 10 x Earth-Moon distance) then SIZE/DISTANCE = 10/10 = 1 and the planet appears 1 Full Moon across.

If Size = 10 (so planet is 10 x the diameter of the Full Moon), and DISTANCE = 0.5 (so planet-moon distance is 1/2 Earth-Moon distance) then SIZE/DISTANCE = 10 / 0.5 = 20, and the planet appears 20 Full Moons across!

Here are the answers:

Earth diameter: 12,756 km; SIZE = 3.7 Moon diameters

Earth-Moon distance: 384,400 km; DISTANCE = 1 Earth-Moon distances

SIZE / DISTANCE = 3.7 / 1 = 3.7 Full Moons Across

Mars’ diameter: 6,792 km; SIZE = 1.95 Moon diameters

Phobos-Mars distance: 9,380 km; DISTANCE = 0.0244 Earth-Moon distances

SIZE / DISTANCE = 1.96 / 0.0244 = 80.3 Full Moons Across

Jupiter’s diameter: 142,984 km; SIZE = 41.1 Moon diameters

Io-Jupiter distance: 421,600 km; DISTANCE = 1.1 Earth-Moon distances

SIZE / DISTANCE = 41.1 / 1.1 = 37.4 Full Moons Across

Saturn’s diameter: 120,540 km; SIZE = 34.7 Moon diameters

Tethys-Saturn distance: 294,700 km; DISTANCE = 0.77 Earth-Moon distances

SIZE / DISTANCE = 34.7 / 0.77 = 45.1 Full Moons Across

Saturn’s Diameter across visible rings: 280,400 km; SIZE = 80.7 Moon diameters

Tethys-Saturn distance: 294,700 km; DISTANCE = 0.77 Earth-Moon distances

SIZE / DISTANCE = 80.7 / 0.77 = 104.8 Full Moons Across

Uranus’s diameter: 51,120 km; SIZE = 14.7 Moon diameters

Ariel-Uranus distance: 191,200 km; DISTANCE = 0.5 Earth-Moon distances

SIZE / DISTANCE = 14.7 / 0.5 = 29.4 Full Moons Across

Neptune’s diameter: 49,530 km; SIZE = 14.3 Moon diameters

Triton-Neptune distance: 354,800 km; DISTANCE = 0.92 Earth-Moon distances

SIZE / DISTANCE = 14.3 / 0.92 = 15.5 Full Moons Across

Pluto’s diameter: 2,340 km; SIZE = 0.67 Moon diameters

Charon-Pluto distance: 19,400 km; DISTANCE = 0.05 Earth-Moon distances

SIZE / DISTANCE = 0.67 / 0.05 = 13.4 Full Moons Across

Photo credit: Michael Collins (NASA)

Weekly Challenge 5: Dr. Jeff’s Interplanetary Travel Agency

DrJeff — Mon, 13 Jul 2009 17:37:55 +0000

This post is a Dr. Jeff’s Weekly Challenge.

Photo caption: Photograph by Michael Collins in Apollo 11 command module Columbia, as Neil Armstrong and Buzz Aldrin return from the lunar surface in Eagle. With the exception of Michael Collins, the entire human race is in the picture. It happened almost exactly 40 years ago. Eagle blasted off from the surface at 1:54:00 pm EDT, July 21, 1969.

I decided to start a new business. I know space flight for us average folk is just around the corner. As a shrewd business person (hah) I recognize the market potential for interplanetary vacation travel. So I’m therefore happy to report that I’ve just established my new company—Dr. Jeff’s Interplanetary Travel Agency, LLC, and I need some help from you all in designing my marketing material. I’m thinking images of alien vistas is the way to really entice clients.

Last night I happened to look up at the Moon as it was rising above the trees (read why HERE) ,and I thought to myself “Wow! If I didn’t live on Earth, a picture of that would certainly make me want to visit Earth!”

So I started imagining the view from the surface of other worlds. In particular, I’m thinking of a tour package to moons of some of the planets, with stays at the Best Western Satellite Hotels, each located a comfortable distance from the regional spaceport. (Sorry, the Four Seasons and Hilton Hotels only wanted to build on the planets.)

I’m hiring you as my interplanetary photographer. I’d like you to travel to some moons and get me some cool pictures for my brochure. For each shot, I’d like something comparable to what I saw when I looked at the full Moon from Earth.

Here now the Challenge—

From Earth’s surface I have a sense of how big the full Moon looks in my sky. So let’s use the full Moon’s apparent size from Earth as a ‘ruler’.

If you were on the surface of the Moon, how big would Earth appear in your sky compared to the full Moon from the surface of Earth?

And now for the other marketing materials I need—

How big would:

Mars appear from the surface of its moon Phobos?

Jupiter appear from the surface of its moon Io?

Saturn appear from the surface of its moon Tethys?

Uranus appear from the surface of its moon Ariel?

Neptune appear from the surface of its moon Triton?

Pluto appear from the surface of its moon Charon?

And by the way, when you’re on the surface of these other worlds, take a look around and tell me what you see. I want to have a really great description of the local landscape for the travel brochure!

Hint: you need to think about 2 things for each question:

1) what’s the diameter of the planet your looking at compared to the diameter of our Moon?

2) what is the distance between the surface you’re on and the planet you’re looking at compared to the Earth-Moon distance?

Answer now posted here!

Photo credit: Michael Collins (NASA)

THE SOLUTION TO Weekly Challenge 4: You Want Me to Do What With a Bathroom Scale?

DrJeff — Wed, 08 Jul 2009 19:08:27 +0000

Read Original Challenge HERE.

This post is a Dr. Jeff’s Weekly Challenge and a Teachable Moment in the News.

Ok, I know you’ve been perplexed for a week. You’ve been patiently waiting for me to read my bathroom scale on top of my 210 mile high mountain that apparently even the U.S. Geological Survey knows nothing about (I checked at their web site.) Wait! You say you have no clue what I’m talking about?? Hey, you’ve got to read Weekly Challege 4 FIRST! None of this lazy stuff going right to the answer.

Go read Weekly Challenge 4, think about it for a while, and come back. I’ll wait right here for you.

And now the answer—

So I go to the top of my 210 mile (340 km) high mountain, and look … here comes the space shuttle … and there it goes! Man, it was moving fast. It was cruising at a whopping 4.5 miles PER SECOND (7 km/s)! So 2 seconds ago, it was 4.5 miles away heading right for me. A second ago it flew right by my face, and I looked in the window really really fast. And now it’s 4.5 miles away heading away from me.

Sure enough, when I looked inside, the astronauts were weightless—just floating around. So then I looked down at my bathroom scale, also expecting to be weightless—after all I’m at the same place they were. BUT WAIT!! My scale says I weigh nearly the same as my weight in my bathroom at home. More precisely, on top of my mountain I weigh 90% of my weight at sea level! So if I weigh 150 lbs (68 kg) at sea level, I weigh 135 lbs (61.2 kg) on my mountain. Hmmm, wonder if I’ve discovered a new way to diet. (And I bet some of you won’t buy this without seeing the calculations. That’s good. That’s being a great scientist. Keep reading.)

But this can’t be right! Why are the astronauts weightless?

Lots of folks assume that a weightless astronaut means that gravity is somehow turned off in space. But you don’t need to think about this long to realize that’s a big-time misconception. Gravity is keeping the space shuttle in orbit around the Earth, the Moon in orbit around the Earth, and the Earth in orbit around the Sun. If we suddenly turned gravity off, the Earth would fly out of its orbit, off in a straight line, and head out of the Solar System. Gravity GOOD. No gravity BAD.

First some gravity basics. The force of gravity exists between any two masses, e.g., you and your chair, or your car and the fire hydrant it’s parked next to (hey move your vehicle.) But as forces of nature go it’s a weak force. So for you to easily see it in action, at least one of the masses needs to be really massive. A good example is the force of gravity between YOU and the EARTH. The Earth is pretty massive, and the force exerted on you by the Earth is what we call YOUR WEIGHT. The force between two masses also depends on the distance between them. If you increase the distance between two masses, the force of gravity decreases. This comes together mathematically in the LAW OF UNIVERSAL GRAVITATION, a cool and pretty simple equation courtesy of Mr. Isaac Newton.

Ok, now let’s apply this. In the case of you and Earth, the distance between you and Earth is actually the distance between you and the center of Earth. But that distance is just the radius of Earth, or 3,963 miles (6,378 km.) When I go from sea level to the top of my really tall mountain, 210 miles (340 km) high, I’m increasing the distance between me and the center of Earth only a little bit. So my weight only goes down to 90% of its value at sea level. I actually used Mr. Newton’s equation to calculate my weight on top of my mountain. For those of you that want to see the calculation, I wrote it in my scratchy long-hand HERE.

Here’s another thing to ponder. The space shuttle is pretty massive compared to you, and when it goes into orbit at 210 miles altitude, the space shuttle weighs 90% of its weight at sea level. The weight of an astronaut is also therefore 90% of his/her weight at sea level. THEY ARE NOT WEIGHTLESS. The term WEIGHTLESS leads to a deep misconception. They APPEAR weightless. Big difference. Remember that your weight is the force of gravity exerted on you by the Earth. There is NO question that such a force is exerted by Earth on both the space shuttle and the astronauts inside.

But why do they APPEAR weightless? Well in my case, I’m standing on top of my mountain, where the mountain is holding me up and keeping me from falling under the action of gravity. Gravity is pulling me down with a force defined as my weight, and the mountain is reacting under the ‘load’ with an equal and opposite force up. So for me, I feel two forces: gravity pulling me down, and the mountain pushing me up. The forces cancel, and I just stand there at 90% of my sea level weight. I know that because the spring in my bathroom scale is being compressed between the two forces, and it’s causing the scale to record my weight. My bones also feel the resulting compression, which lets my body know they’re doing a good thing and are useful to keep (not the case in orbit where bone calcium is excreted.) But the space shuttle is not resting on a mountain or anything else. The space shuttle is ONLY experiencing the force of gravity. When that happens we call the situation free fall. The space shuttle is falling!! I know! (says Craig Ferguson.) This seems contrary to the way most of us think about falling objects, where an object that is falling is headed toward the Earth. But that too is a misconception. The space shuttle is falling around the Earth! Here’s something I wrote for a grade 5-8 lesson on free fall (See “To Teachers” section below), and it explains how you can be falling around the Earth.

Now back to the idea of weightlessness. Here is the analogy to help you understand. You’re in an elevator in a tall building. The elevator is on the top floor. Inside the elevator you’re standing on your bathroom scale. You note the scale reads your correct weight plus a couple of pounds ’cause you just finished lunch at the spiffy top floor restaurant. Two forces are acting on you—gravity pulling you down, and thankfully the floor of the elevator pushing you up. Now (sorry) I cut the elevator cable. You feel that in your stomach? You’re now in free fall. You’re falling because I removed the ability of the elevator’s floor to push you back. The floor of the elevator is now falling WITH you. And the bathroom scale between your feet and the floor? Well, it’s also falling WITH you! There is now no way for the spring in the scale to be compressed between your feet and the floor … because the floor isn’t going to be pushing back. Look at the scale … it reads ZERO. You are weightless … look—you’re floating in the elevator.

Ok, just stopped you with the emergency brakes.

So here is the deal. If you are inside something falling (in free fall) like an elevator or space shuttle, you appear weightless. That’s because everything inside is falling with you, including the floor, walls, and ceiling—though calling them floor, walls, and ceiling is now rather meaningless.

A note to the sneaky (those that want to say “but Dr. Jeff you’re wrong.”) Yes, if the object is falling inside the atmosphere (like our elevator), it is technically not in free fall since the drag caused by the air is a real force to be considered. For instance, if you jump out of a plane, you’re not in free fall long. Soon you get up to about 100 mph (160 km/hr) and you won’t go any faster because the force of gravity down is balanced by the drag force up due to the air. But that’s still a bit too fast for a landing, so you open a parachute to dramatically increase the drag from the air, and you live to jump another day.

To teachers:

We developed a great grade 5-8 lesson which easily demonstrates that astronauts inside a free falling soda bottle space shuttle appear weightless. The lesson is part of the Building a Permanent Human Presence in Space compendium of lessons for our Journey through the Universe program. The lesson is titled Grade 5-8 Unit, Lesson 1: Weightlessness, which can be downloaded as a PDF from the Building a Permanent Human Presence in Space page. You can also read an overview of the lesson conducted as part of one of the many Journey through the Universe Educator Workshops, this one in Muncie Indiana.

Contact me if you would like to bring Journey through the Universe to your community, which is programming for hundreds to thousands of grade K-12 students, their teachers, and their families, based on a community-wide engagement model for STEM education. Or you might want to consider just a professional development workshop for educators, or a family and public program, through the Center’s To Earth and Beyond initiative. Here is a list of the family and public program topics with descriptions, which are presentations we routinely conduct after hours at the Smithsonian’s National Air and Space Museum for 450 attendees as part of the Center’s Family Science Night program.

Photo credit: NASA (there was no mountain in their photo—promise.)

Weekly Challenge 4: You Want Me to Do What With a Bathroom Scale?

DrJeff — Mon, 29 Jun 2009 18:08:52 +0000

This post is a Dr. Jeff’s Weekly Challenge and a Teachable Moment in the News.

As I write, NASA engineers at Kennedy Space Center are working mightily on space shuttle Endeavour to repair a hydrogen leak that scrubbed the June 13, then June 17 launches. Endeavour is headed for the International Space Station. NASA reports that the next flight opportunity is July 11—WHICH MEANS I’ve got plenty of time to get ready for my way cool experiment.

I’ve heard a lot about weightlessness, and astronauts having a great time floating around. The shuttle flies at an altitude of 210 miles (340 km) when rendezvousing with Space Station. (For a cool take on this read my earlier post The Business Trip.) So I wanted to find out first hand what’s going on up there. Since they don’t have a spare seat, I looked far and wide to find an amazingly tall mountain whose peak rises to the shuttle’s orbital altitude. See my mountain in the picture? Mt. Everest is only 5.5 miles (8.8 km) high. MY mountain is 210 miles (340 km) high. It took me some time but I finally found it south of the Land of Make-Believe, down a not too well traveled path. Still, you’d think someone would have noticed it.

While the shuttle is delayed I’m going to take the time to climb my mountain, and in my hand is my trusty bathroom scale, spring-loaded and guaranteed to be accurate at any altitude. I’ll camp out at the top until the shuttle is launched, and I’ll wait until it flies right by my mountain, so I can look in the windows and see them weightless.

Here now the challenge—

As soon as I confirm they’re weightless in the shuttle, I’ll look down at my bathroom scale to see my weight. If I weigh say 150 lbs (68 kg) when I’m standing on my scale in my bathroom at home, what will I weigh on top of my mountain?

Hint: I’m not asking you to actually calculate my weight. I’ll do that (if I need to) in the Solution to the Challenge. Your assignment—if you decide to accept it—is to guess what you think I’ll weigh. Hmmmm, lots of possibilities.

Answer now posted here!

Photo credit: NASA (there was no mountain in their photo—promise.)

THE SOLUTION TO Weekly Challenge 3: What Can You Do With a Humongous Piece of Xerox Paper?

DrJeff — Tue, 23 Jun 2009 17:53:30 +0000

Read Original Challenge HERE.

This post is a Dr. Jeff’s Weekly Challenge and a Dr. Jeff’s Jeffism.

Last week on BotU, your challenge was to take an imaginary, truly humongous piece of xerox paper—but with normal xerox paper thickness—and figure out how many times you’d need to fold it in half so the folded thickness is the height of you, the Statue of Liberty, the Empire State Building, and Mount Everest. For those that really wanted to challenge themselves, I invited you to keep folding so it would be thick enough to reach the Moon, the Sun, the nearest star, and beyond.

How’d you do?

BUT WAIT! If you haven’t yet read Weekly Challenge 3, DON’T LOOK AT THE SOLUTION HERE JUST YET! First read Weekly Challenge 3, or I’ll take back my paper.

First, a word from our sponsor—

You Want Me To Do What With a Bathroom Scale?

Weekly Challenge 4 to be posted Monday, June 29, 2009