David M. Schwartz
The amazing, engaging, math exponent
Imagine Earth as a button. I don’t mean you’re going to sew it onto your shirt. But imagine the planet Earth shrunk to the size of a button. (Of course Earth is not flat like a button but we’re giving our shrunken Earth the same diameter as a shirt button.)
Go ahead and draw a circle around a shirt button. Call it “Earth.” Suppose you wanted to draw Jupiter, the largest planet, at the same scale as this micro-Earth. That means you’re going to shrink it to the same fraction of its original size as our button-Earth. What size would little Jupiter be?
One way to find out would be to calculate how many times bigger the real Jupiter is than the real Earth. Earth’s diameter is about 8,000 miles (13,000 kilometers). Jupiter’s is about 88,000 miles (143,000 km). Divide the size of Jupiter by the size of Earth to see that Jupiter is about 11 times bigger.
So, since Jupiter’s diameter is 11 times that of Earth’s, put 11 buttons in a line to show the diameter of Jupiter. Then draw the circle that represents Jupiter. If you don’t have 11 buttons, just look at the picture. Did you think the Earth was a big place? Look at it compared with Jupiter!
But what about the sun? The sun’s diameter is about 865,000 miles (1,400,000 km). That means it’s almost 10 times bigger than Jupiter. Can you find a way to draw a circle 10 times the size of our Jupiter? We’ve drawn part of it for you, on the same scale as our button-sized Earth. On the picture, it’s labeled “our arc.” (An arc is part of a circle.) Looking at the arc, you can imagine the rest of the circle and compare the sun to Jupiter and Earth. A minute ago, you thought Jupiter was big. Now it looks shrimpy compared to the sun!
But is the sun really gigantic? Do some research to find out the size of a red giant star like the strangely named Betelguese (pronounced “beetle-juice.”) Figure out what it looks like compared to our sun, which is a medium-sized star. You may be amazed at the difference. And you thought the sun was big!
Is anything truly big? Is anything truly small? Or does that depend on what it’s being compared to?
Both images are by Marissa Moss, the illustrator of David M Schwartz's book, G is for Googol.
G is for Googol: A Math Alphabet Book is a wonder-filled romp through the world of mathematics.
For more information, click here.
David Schwartz is a member of iNK's Authors on Call and is available for classroom programs through Field Trip Zoom, a terrific technology that requires only a computer, wifi, and a webcam. Click here to find out more.
Schwartz, David M. "If the Earth Were a Button." Nonfiction Minute, iNK Think
Tank, 16 Jan. 2018, www.nonfictionminute.org/the-nonfiction-minute/
Nonfiction is the new black
The onset of spring, summer, fall, and winter every year is precisely measured, depending on the sun’s position. But there’s no similar astronomical or scientific reason for celebrating New Years on January 1.
Many people don’t. The Chinese New Year occurs on the second new moon after the winter solstice, between late January and mid-February. Muslims mark the occasion on the first day of Muharram, the first month of the Islamic calendar. That calendar is based on the lunar cycle, 11 or 12 days shorter than the solar calendar. So their New Year comes a little earlier every year. Rosh Hashanah, the start of the Jewish New Year, is a two-day observance that begins 163 days after Passover and varies between September 5 and October 5. Unlike other New Year’s celebrations, Rosh Hashanah is holy, a time for piety rather than parties.
There was just as much variation in ancient times. In Babylon, the first new moon after the vernal equinox marked the New Year. Egyptians celebrated it in early August, when the annual Nile River flooding began. In Greece, Athens and Sparta couldn’t get along, so their respective new years didn’t occur at the same time. In Athens, it was the first new moon after the summer solstice, while the Spartans waited until early fall.
So how did January 1 become the most widely accepted start of the New Year? The answer: Julius Caesar. For centuries, the Roman calendar was in a state of chaos, with the number of days in the year fluctuating widely. In 46 BCE, Caesar worked with the brightest Egyptian astronomers to retool the calendar. He wanted the year to begin on the first of January, a month named after the god Janus. Janus had two faces: one looking backward (at the year just ending) and the other facing forward. For the Romans, it was party time!
Caesar didn’t stick around very long after his innovation. On the Ides of March—March 15, 44 BCE—he went to the Roman Senate as usual. While one senator distracted him, others swarmed around him with knives they’d hidden inside their togas, hacking and gashing. He collapsed and died.
His calendar proved more durable. When Roman legions conquered new territories, the natives had to adopt the Roman calendar. Every day, especially at the start of the new year, it was a reminder of Roman power.
You've been hearing from Jim Whiting almost weekly, so we thought you might want to know more about him. He's an interesting fellow:
Children's book author. Acclaimed multi-genre freelance editor. Entertaining and informative classroom visitor. Middle school running coach. Award-winning magazine publisher. Workshop presenter. Sportswriter. Light versifier. E-commerce and e-book writer. Teacher. Runner. World traveler. Sailor. Scuba diver. Photographer. Actor. Patron of the arts. Hometown Hero. And of course Voracious Reader.
For more about Jim, read his biography and background.
MLA 8 Citation
Whiting, Jim. "Happy New Year--in August?" Nonfiction Minute, iNK Think Tank, 2 Jan. 2018, www.nonfictionminute.org/Happy-New-Year-in-August.
by David M. Schwartz
the amazing, engaging, math exponent
A light year is not a year that has gone on a diet. It is not a year that’s been trimmed to 300 days. It’s not a year spent under high-wattage lamps. A light year isn’t any kind of year.
A light year is a distance. It is a vast distance; the distance light travels in a year. To appreciate a light year, you have to understand how fast light travels.
The speed of light is truly mind-boggling: 186,000 miles per . . . second. That’s “per second,” not “per hour.” In one tick-tock second, light travels a distance of 186,000 miles. If it could go in circles, it could travel around the earth more than seven times in just one second! But light travels in straight lines, not in circles. Imagine something traveling that fast in a straight line—not for a second, not for a minute, not for an hour, not for a day, but for an entire year. The distance it goes in that year is called a light year.
A light year is a convenient unit of measure when distances are enormous. You could talk about the same distances in miles. It's about 5,878,499,810,000 (5 trillion, 878 billion, 499 million, 810 thousand ) of them. But these measurements are so large that they are unwieldy. It's much easier to just name that enormous distance with two simple words: a "light year."
The star closest to our solar system is Proxima Centauri. Some of the light that leaves Proxima Centauri goes to Earth, cruising along at 186,000 miles per second. At that speed, light takes about 4.2 years to get to Earth from Proxima Centauri So how far away is Proxima Centauri? It is 4.2 light years away.
To give you an idea of how far that is, imagine going to Proxima Centauri in a spaceship traveling at the speed of the space shuttle — about ten miles per second. (That’s much faster than airplanes can fly.) You would get there in about 70,000 years.
Our Sun is much closer than Proxima Centauri. It is 93 million miles away. There is another way to refer to the distance from the earth to the Sun. Light leaving the Sun takes about eight minutes to get to Earth, so we say the Sun is eight “light minutes” away. If you traveled at the speed of light, you could get there in eight minutes. Have a nice trip!
© David M. Schwartz, 2014
David Schwartz has been fascinated by big numbers and big distances ever since he was a little boy riding his bicycle, wondering “How long would it take for me to ride to Proxima Centauri, 4.2 light years away?” He wrote about light years in his math alphabet book G Is for Googol.
David is a member of iNK’s Authors on Call. He can visit in your classroom via interactive video conferencing. Learn more here.
MLA 8 Citation
Schwartz, David M. "What Is a Light Year?" Nonfiction Minute, iNK Think Tank, 14 Sept. 2017, www.nonfictionminute.org/the-nonfiction-minute/what-is-a-light-year.
Stories that Surprise and Inspire
When musicians play a lively tune, they often find themselves spontaneously tapping their toes and moving about to the pulsing beat. But when Ellen Ochoa played her flute at work one day in 1993, she couldn’t be spontaneous at all. If she hadn’t made careful plans, she could have been blown about the room, just by playing one long note on her flute. That’s because she was an astronaut working on the U.S. Space Shuttle as it circled Earth more than a hundred miles out in space.
Gravity is so weak far out in space that astronauts—and any of their gear that isn’t fastened down—will float about inside a space craft. Blowing air into her flute could have created enough force to actually send Ochoa zipping about the space shuttle cabin. So, to keep herself in place as she played, she had to slip her feet into strong loops attached to the floor.
Dr. Ochoa, now the director of NASA’s Johnson Space Center, was the first U.S. astronaut to bring a flute on a space mission, but she wasn’t the first to make music in space. Nearly thirty years earlier, in December 1965, two astronauts onboard the Gemini 6 space craft played a musical joke on mission control officials down on Earth. Those astronauts—Walter M. Schirra, Jr., and Thomas P. Stafford—told mission control that they saw an unusual object near their spaceship, a satellite perhaps, moving from North to South. They said they would try to pick up some sound from this mysterious object. Then they used the harmonica and bells they had secretly brought with them on that December mission to surprise folks listening down below by playing “Jingle Bells.”
In recent years, other astronauts have brought musical instruments on space missions to help lift their spirits, especially those who spend many months on the International Space Station. Like Dr. Ochoa, these astronaut musicians have to make adjustments, such as using a bungee cord to attach an electronic piano keyboard to a pianist’s leg.
Some astronauts have composed music in space, including Canadian Chris Hadfield. On May 6, 2013, he sang the song he wrote—called “I.S.S. (Is Somebody Singing)”—in a live TV broadcast from the space station as thousands of Canadian schoolchildren sang along with him down on Earth. Click here for a recording of that space-to-Earth performance
Learning to play an instrument can be fun and, at times, frustrating. Amy Nathan's lively book helps young people cope with the difficulties involved in learning a new instrument and remaining dedicated to playing and practicing. Teens from renowned music programs - including the Juilliard School's Pre-College Program and Boston University's Tanglewood Institute - join pro musicians in offering practical answers to questions from what instrument to play to where the musical road may lead. For more information, click here.
MLA 8 Citation
Nathan, Amy. "Music That's Out of This World." Nonfiction Minute, iNK Think
Tank, 11 May 2018, www.nonfictionminute.org/the-nonfiction-minute/
Do you ever feel spaced-out before you take a test? Yes or no, let’s go!
1. TRUE or FALSE?
It’s possible for a spacecraft to fly from Earth to Venus, to Mars, back to Earth, then to Saturn, out to Pluto, back to Jupiter, and come home to Earth on one tank of fuel.
2. It’s possible for a spacecraft to fly all over the solar system on one tank of fuel because of:
a. the sling-shot effect
b. gravity assist
d. all of the above
e. none of the above
The sling-shot effect, also known as a swing-by or gravity assist, is used to accelerate a spacecraft. Acceleration means to change the speed and/or the direction of a moving body. A spacecraft that is speeding up, slowing down, or following a curved path is accelerating.
Gravity accelerates objects everywhere in the Universe. When you ride your bike up a hill it takes a lot of effort to make it to the top because the Earth is massive compared to you, and gravity pulls you toward its center. When you coast down the other side, gravity is your friend!
Spacecraft can use the gravity of a planet to accelerate. Picture a spacecraft falling toward a planet. The spacecraft will crash unless it steers away.
3. As a spacecraft accelerates toward a planet, the motion of the planet is also affected by the gravity exerted by:
a. the spacecraft
b. the Sun
c. cosmic rays
d. both (a) and (b)
e. both (b) and (c)
f. all of the above
g. none of the above
All bodies in space, no matter how big or small, exert gravity on each other. Planets stay in orbit around the sun because of gravity. A planet is also affected by the tiny mass of a spacecraft. Gravity assist was used to increase the speed of Voyager 1 by 36,000 mph on its swing by Jupiter, which sling shot it to Saturn. And Jupiter slowed down infinitesimally, at a rate of 12 inches per one trillion years.
4. The person who discovered the math for using gravity assist to accelerate a spacecraft from planet to planet to planet…was:
a. Aristotle (384 B.C. to 322 B.C)
b. Galileo (1564-1642)
c. Sir Isaac Newton (1643-1727)
d. Katherine Johnson (1918- )
e. Michael Minovitch (1936- )
END OF TEST!
DON’T STOP WORKING.
GO TO THE LIBRARY TO FIND THE ANSWERS.
In this drawing a spacecraft gets an assist from Jupiter as it "slingshots" toward Saturn. Image courtesy of NASA/JPL
Voyager 1 and Voyager 2 used gravity assist to fly by the outer planets. Image courtesy of NASA
The twin Voyagers have no people on board on their interstellar journey, but carry The Golden Record, which contains messages, music, and pictures from Earth. Image courtesy of NASA/Alexandra Siy
In case you didn't make it to the library: In 1961, UCLA graduate student Michael Minovitch used math and the new IBM 7090-7094 computers to invent gravity assist trajectories for space flight. Used with permission of Michael Minovitch
Alexandra Siy's Voyager's Greatest Hits tells the story of the twin space probes that traveled to Jupiter, Saturn, Uranus, and Neptune, a journey beyond our solar system into interstellar space, where no probe has ventured before. Siy tells the fascinating story of how the Voyager probes work, where the probes have been and what they’ve seen, and what they carry on board.
Alexandra Siy is also a member of Authors on Call. You can bring her to your classroom via interactive videoconferencing and learn more from her and ask her questions. To find out more go here.
MLA 8 Citation
Siy, Alexandra. "Spaced Out." Nonfiction Minute, iNK Think Tank, 2 May 2018,