“Oh the weather outside is frightful
But the fire is so delightful
And since we’ve no place to go
Let it Snow! Let it Snow! Let it Snow!”
(According to Wikipedia, the song “Let it Snow, Let It Snow, Let it Snow”
was written in July 1945 in Hollywood on one of the hottest days on record.)
Today we’ll answer some questions about snow.
1. Is it true that no two snowflakes are ever the same?
Probably not absolutely true, but it’s easy to understand why we say this.
The diagram below comes from the website Snowcrystals.com. It shows
the life history of a single snow crystal. We are indebted to Kenneth G. Libbrecht,
Caltech, for his extensive research into snowflakes.
As Libbrecht explains: “The story begins up in a cloud, when a minute
cloud droplet first freezes into a tiny particle of ice. As water vapor starts
condensing on its surface, the ice particle quickly develops facets, thus
becoming a small hexagonal prism. As the crystal becomes larger, branches
begin to sprout from the six corners of the hexagon. Since the atmospheric
conditions (that is, temperature and humidity) are constant across the small
crystal, the six budding arms all grow out at roughly the same rate… While it
grows, the crystal is blown to and fro inside the clouds, so the temperature it
sees changes randomly with time. Since the six arms see the same conditions at
the same time, they all grow about the same way. The end result is a complex,
branched structure that is also six-folded symmetric.
“The six arms of a snow crystal all grow independently. But since they
grow under the same conditions, all six end up with similar shapes.”
So the answer to the question is that because the growth of a snow crystal
depends so much on the temperature and humidity of the crystal inside the
clouds, and since that may vary dramatically from place to place, the chance of
finding two identical snowflakes is small, but not impossible.
Shown below is a summary of all the shapes possible for a snowflake. This
is also from snowcrystals.com. (The print may be too small to read the name of
each shape, but you can at least see the wide variety of shapes.)
Aren’t you amazed by the variety of possible snowflake shapes? I certainly am.
2. Why is snow white?
First we need to talk about color in general. For instance, grass is green
because all the colors of the rainbow found in sunlight are absorbed into the
leaves of the grass except green. Green light, not being absorbed, is eventually
scattered back to our eyes, and so we see green grass. It’s all about what color of
light is not absorbed by the grass.
If you take a piece of clear glass and look at it, it appears to be clear. But if
you grind up the glass and look at the pile, it looks white. Similarly, if you look at
an individual salt or sugar crystal, it appears to be clear. But, as you know, a
spoonful of sugar appears to be white. Where did the white come from?
If you look at an individual snow flake, it will look clear like an icicle does.
But take a pile of snow flakes and it will look white. What’s going on?
Snow and sugar and salt look white because no particular color of sunlight
is absorbed. All the incoming light is reflected back to our eyes.
When you look at your front yard covered with snow, the incident light
bounces around and eventually scatters back to your eyes. All the colors are
scattered equally well, so the snow bank appears white.
3. Why is it so quiet after a snowfall?
According to the book “The Flying Circus of Physics” by Jearl Walker, “The
small spaces in the snow’s surface absorb the sound just as acoustic tile does in
most offices. As the snow becomes more packed, this sound absorption is
4. Why can’t you make a snowball if the temperature is very low? What holds a
snowball together, anyway? Approximately what is the lowest temperature you
can make a reasonably good snowball?
The Popular Mechanics Magazine web site tells us that ground temperature
has the most to do with making a good snowball. Wet snow packs better than dry
snow. The scientific reason is that melting snow can help to form “ice bridges”
that join two crystals together, while snow at very cold temperatures the crystals
remain separate. The best temperature for a snowball fight or making a snowman
is just below freezing. As many of you have discovered, it’s difficult to make a
snowball when the temperature is 20 degrees below zero or colder.
This is a magnificent season of the year! So if you also have no place to go,
join with all the snow-boarders, skiers, kids with sleds, and snow machine
hobbyists to echo the words, “Let it snow! Let it snow! Let it snow!”
I can see them now, thousands of square dancers, each one pairing up with
a partner for a few seconds and then moving on to someone else for an equally
brief time. Only when the music slows down do the dancers spend more time
together with an individual partner.
Strangely enough, that’s how I picture the bonding between water
molecules in a glass of water. (Stick with me here, okay? By the time we’re done,
you’ll hopefully understand why ice floats and also, why ice is slippery.)
A water atom has two hydrogen atoms and one oxygen atom. That’s why it’s
called H 2 O. The oxygen atom attracts the electron cloud from around the
hydrogen, leaving the hydrogen atom with a slight positive charge. It can use this
to attract the oxygen atom from another molecule of water. This is called hydrogen
bonding. We can see how this works from the figure below, provided by The
Interactive Library web site.
In the figure, each white ball represents a hydrogen atom and each red ball
represents an oxygen atom. The green dotted lines represent hydrogen bonding
between water molecules.
In square dancing a man and a woman become a new “couple” every few
seconds. Water molecules do the same thing, except each water molecule forms a
new bond with another water molecule a million-million times every second!
When water approaches its freezing temperature, the dance slows down
and water molecules begin to form more lasting partnerships. When that happens,
the chaotic pattern becomes more ordered, until the freezing point is reached.
Shown below are two structures from The Interactive Library web site.
(Note: Ice III is one of several forms of ice that form under various
conditions of temperature and pressure.)
Do you notice the empty spaces in the ice structure as compared to the
liquid water structure? This shows that water molecules in ice are not as tightly
packed as they are in liquid water. In other words, a cubic foot of ice will have
fewer water molecules that a cubic foot of water. We usually state this by saying
that the density of ice is less than the density of water.
Water has a density of 1.0 grams per cubic centimeter. Ice has a density of
.92 grams per cubic centimeter; oak wood has a density of .71 grams per cubic
Materials that have a lower density than water float in water. Therefore ice
floats. About 10 percent of ice is above water.
So why should you even care that ice floats?
Consider a pond about to freeze. Because the outside air is below freezing,
the coldest water will be near the top where all the cold air is.
If cold water about to freeze was more dense than the warmer water below
it, then it would sink to the bottom of the pond. Ice would then form on the bottom
of the pond. Because that ice would not feel the full warmth of the sun during the
summer, some ice on the bottom might remain all through the summer.
In time the entire pond might become frozen each winter. In the summer
perhaps only a few inches of ice near the top of the pond would melt.
Because so much water would be locked up in the form of ice for years, few
clouds would carry water to the rest of the planet. In time this would mean the
death of most all life on the Earth. But that doesn’t happen because ice floats!
What is even more remarkable is that water is one of only a few substances
that expand when going from a liquid to a solid state. Boy, did we luck out! !
Second question: Why is ice so slippery?
Even though ice is a solid, it’s not the same as other solids. For instance,
concrete, wood and glass are solids and yet we don’t skate on them.
According to The New York Times web site, the current explanation of why
ice is slippery can be introduced by the figure below from the 2006 New York
According to the New York Times, “…water molecules at the ice surface
vibrate more, because there are no water molecules above them to help hold them
in place, and thus they remain an unfrozen liquid even at temperatures far below
In other words, all ice at any temperature contains a thin liquid-like layer
that will never freeze because the ice crystals below them are not able to force
them into the ice structure.
Back to our square dance analogy. It’s like all the square dancers are sitting
around hexagon shaped tables having refreshments except for a small group that
are doing line dancing near the edge of the dance floor. While everyone else is
sitting around, they’re still bonding with new partners just like always.
According to the New York Times, “Michael Faraday in 1850 proposed this
idea after performing this simple experiment. He pressed two cubes of ice against
each other and they fused. Faraday argued that the liquid layers froze solid once
they were not on the surface. But because the layer was so thin, it was hard for
scientists to see.”
Based on the results of an experiment performed in 2000 by the Institute of
Physical Chemistry, I estimate this liquid-like layer to be about 100 layers of water
molecules thick. If any of you have a better number though, I’d be pleased to see
So what we’re saying is that the thin liquid-like layer which exists on the
surface of ice even when it’s very cold explains why ice is slippery. That probably
won’t give you much comfort the next time you slip and fall on the ice. My advice
for that is when the sidewalks are icy, wear boots and walk through the snow
because it’s not as slippery.
“And dosido, around you go!” See how much you can learn from square
Weyland welcomes your comments and can be reached at
If you’re like me, you enjoyed watching the Winter Olympics. Wasn’t it
exciting to see these exceptional athletes perform at such a high level of
competence and grace?
Today we’ll examine a few physics principles behind some of the
competitions we saw on TV.
First of all, let’s see what we can learn about figure skating. Whenever I
see a figure skater go into a spin, I’m tempted to tell my wife, “Of course you
know this can be explained by conservation of angular momentum, right?”
Her response might be to give me the look, which means “Why can’t you
just watch and enjoy this like everyone else?” So I don’t usually say anything.
But since I’m not married to you, I’ll proceed.
Angular momentum is defined as something called the moment of inertia
times angular velocity. Angular velocity is related to how many complete turns
the skater makes every second. We will call this her rate of rotation. The moment
of inertia of skaters is larger when they have their arms spread out, and is smaller
when their arms are close to their body.
You know you’re talking to a physicist when he or she says, “Let’s
approximate you by a cylinder.” Or, even worse, “by a sphere.” At which point,
you might say, “So you think I have the shape of a ball or a can of soup? How
Don’t take it personally, okay? All physicists know is cylinders and
The following comes from the web site “The Physics of Everyday Stuff”:
“A crude approximation of the skater’s shape, good enough for the purpose here,
says that she is a solid cylinder made up of most of her mass plus three rods
representing her arms and a leg.”
Thus we have below our representation of a lovely figure skater with her
arms and one leg extended. (Notice the grace and beauty.)
Next we see our figure skater with her arms and legs pulled into her body.
Now, as we said before, according to the principle of conservation of
angular momentum, the moment of inertia times the rate of rotation is a constant.
Don’t panic! This isn’t that hard. We have the product of two numbers
equals a constant. It’s just like: 16 x 1 = 8 x 2 = 4 x 4 = 2 x 8 = 1 x 16
When the skater has her arms and one leg extended, she has a large
moment of inertia and, therefore a small rate of rotation. But when she pulls in
her arms and one leg in, she has a small moment of inertia, so she will have a
greater rate of rotation.
The web site “The Physics of Everyday Stuff,” estimates that the moment
of inertia when a skater has her arms and one leg extended is about 12 times
greater than when she has her arms and legs tucked in. What this means is that
if a skater is rotating at 2 revolutions per second with her arms and leg extended
But when her arms and legs are pulled in, she will rotate up to 24 revolutions per
second! This is only an approximation because, of course, skaters are not
cylinders. (I do understand that, okay?)
Conservation of angular momentum also explains why high divers, when
they want to spin fast, tuck into a ball. But when they want to spin slow, they
extend their body straight out.
The Popular Mechanics web site gives additional insights into figure
skating. The following is quoted from “The Science Behind 7 Winter Olympic
“A 45-degree jump gives skaters 0.55 seconds of time–enough to complete
all but the devilish triple axel, which requires 0.65 to 0.75 seconds and a spin rate
of 420 rpm, the engine idling speed of some cars.”
The most baffling Winter Olympic sport to me has got to be curling. I spent
hours watching it, not because I cared who won, but because I had no idea what
was going on.
The same Popular Mechanics web site explains something about curling:
“In curling, teams slide a 42-pound granite stone down an ice sheet toward
a target…A liquid layer (on the ice) reduces front-ward friction, and the stone
spins and slides in the same direction. This is where the sweepers get involved.
Two players use brooms to scrub the ice ahead of the stone, enhancing the liquid
film in order to adjust curl (how much the stone veers to either side) and the
length. The U.S. squad’s tests have shown that sweepers can “drag” a stone up
to 16 extra feet.”
It makes sense that rubbing the brooms just ahead of the stone could
cause some of the ice on the surface to turn to water, which reduces the friction
between the stone and the ice. The same thing happens when a driver on an icy
road gets less traction by floor-boarding it. The spinning tires cause some of the
ice on the surface to turn to water, which makes it even more slippery, so the
driver has little chance to move forward. It’s the same idea except with a sliding
Next Olympics why not come over and we’ll watch figure skating together?
Please, my wife is pleading with you!
We start with a poem about the Sun written by my wife Sherry.
“You’re only a little star!
(The Sun, the Sun)
You’re not too close,
Not too far.
(The Sun, the Sun)
You make me warm all over,
You light up my way,
You keep everything alive
As you shine on us each day.
How can you do so much
When you are
Only a little star?”
According to the Natural Sciences 102 course website at the University of
Arizona, a planet which can support life needs to have the following
characteristics: 1. “Orbit a star that remains stable in output for billions of years;
2. Be at a distance from the star so that its surface water is liquid, not frozen; 3.
Have a circular (or nearly circular) orbit so constant conditions exist for its entire
One more condition: “Large amounts of water must be available. Water is
essential for the chemical reactions leading to and sustaining life on Earth. Water
also appears to be important in controlling the amount of carbon dioxide, thus
avoiding run-away greenhouse effects that lead to run-away warming.” (op.cit.)
Our earth and the sun are suited to support life. What other good news can
we learn about our favorite planet?
The earth rotates like a top, but its axis of rotation is tilted 23.5 degrees. If
you take the tilt away, then we don’t have any seasons: no winter, no spring, no
summer and no fall. Some areas of the earth would always be too cold, and other
areas too hot.
The following figure is courtesy of “Windows to the Universe”,
Notice that the tilt of the earth’s axis stays the same as the Earth rotates
around the Sun. But during the course of a year, there are times when the
Northern Hemisphere, where we live, is tilting away from the sun. We call that
winter. At other times the Northern Hemisphere is tilting toward the sun. We call
The summer solstice occurs when the earth’s axis is most inclined toward
the sun. For us in the Northern Hemisphere it is the longest day of the year It
occurs on or about June 21.
The winter solstice occurs when the earth’s axis is most inclined away from
the sun. It is the shortest day of the year for us. It occurs on or about December
Also notice from the figure there are times when the earth is tilting to the
“side.” In other words, the earth’s axis is not leaning toward the sun or away from
the sun. According to Google: “When the sun crosses the plane of the earth’s
equator, day and night is approximately the same length all over the world.” The
spring equinox just occurred on March 20. We call this date the beginning of
spring. Similarly, an autumnal equinox happens on or about September 22.
The figure below shows the path the sun takes across the sky on the
equinoxes and solstices.
Note that the path of the sun across the sky is longer on or about June 21
than it is at any other time. That’s why summers are warm (hopefully even here in
It is amazing when we consider the factors that make life possible here on
the earth. We’re a little like Goldilocks sampling the three bears’ porridge. One
bowl was too hot, another was too cold, but the third bowl was, according to her,
In terms of the earth we live on, we have a lot in common with Goldilocks.
If you would like to contact Weyland, his email address is
As a graduate student at BYU, I remember being in the Physics Department
office one day when a man entered and announced to the secretary, “Hi, there.
I’m a high pressure salesman.”
He was right of course. This salesman sold high pressure equipment.
My graduate research project involved subjecting small samples to
pressures as high as fifty thousand times atomospheric pressure. Since I didn’t
want to crush my samples, I enclosed them in a liquid, much like a baby before
birth is protected by amniotic fluid. However, the fluid for my research could not
be water, since ordinary water at high pressures, even at room temperature, turns
into a form of ice. Physicists are not particularly creative so they call these forms
of ice: Ice I, Ice II, Ice III, and so on.
Because of my previous work in high pressure, I was interested to read
about the first dome placed over the oil leak in the Gulf of Mexico. On the topic of
“Methane Clathrate” from Wikipedia, we read: “At sufficient depths, methane
complexes directly with water to form methane hydrates, as was observed during
the Deepwater Horizon oil spill in 2010. BP engineers developed and deployed a
sub-sea oil recovery system over oil spilling from a deepwater oil well 5,000 feet
below sea level to capture escaping oil. This involved placing a 280,000 pound
dome over the largest of the oil leaks to collect as much as 85% of the leaking oil.
BP deployed the system on May 7-8, when it failed due to the buildup of methane
clathrate inside the dome.”
The plan failed because of the buildup of a type of ice formed from both
water and methane. This ice obstructed the flow of the oil, and also because ice
doesn’t weigh as much as oil, it made the dome more buoyant.
The ice we’re talking about here has several names including methane
clathrate, and methane hydrate. However, my favorite name for it is fire ice.
Shown below is a photo of burning fire ice, doing what few other ices can do,
which is to burn.
(The picture comes from the article “Methane Clathrate,” previously cited.
Of course, ordinary ice doesn’t burn, and water doesn’t burn either, but the
methane locked up in methane clathrate will burn.
From the article entitled, “Volatile Methane Ice Could Spark More Drilling
Disasters”, located at Discovery.com, we read, “Methane hydrates only exist in
cold water–just above or below freezing–and at the undersea pressures found in
deep water off the continental shelf. ‘It’s a lot like ice,’ said William Dillon, a retired
marine geologist with the U. S. Geological Survey.’ The conditions that form them
exist at the sea floor and in the sediments below…And if hydrates are warmed by
oil moving through pipes, they can turn into methane gas (known as ‘kicks’ to
drillers) that can shoot back up the drilling pipe and ignite the rig. Investigators
are already focused on that scenario as a possible cause of the blast aboard the
Deepwater Horizon rig on April 20.
“Methane hydrates only exist 3,000 to 5,000 feet below the sea floor. The BP
drill went down to 18,000 feet.
“Robert Bea, a civil engineering professor at the University of California,
…has been interviewing workers who were aboard the rig before it blew. He said
the BP platform shut down several weeks before the accident because of hydrate
problems. ‘Whether it was either methane hydrate or gas, it really doesn’t make a
difference,’ he said. ‘It has unanticipated, undesirable effects. Based on my
interview and investigation, methane seeped into the core.’”
This volume change when methane ice turns to methane gas is not hard to
understand if you think about what happens when you pop corn. Moisture is
locked into each kernel of corn. When that water turns into steam, there’s a 1600
fold increase in the volume. That sudden increase causes a small explosion in the
kernel of corn.
The same thing happens when the methane trapped in methane clathrate
turns into a gas. In this case, there’s a 168 fold increase in volume. When this gas
is released in a drilling core, since its density is much less than water or oil, it will
quickly escape upward to the drilling platform. Furthermore, as methane gas rises
up the drill core to lower and lower pressures, by the time it reaches the surface,
the methane gas has undergone another 140 fold increase in volume. (“Methane
Clathrate,” Wikipedia, previously cited.)
From the Wikipedia article entitled, “Deepwater Horizon Explosion,”
“According to interviews with platform workers conducted during BP’s internal
investigation, a bubble of methane gas escaped from the well and shot up the BP
column, expanding quickly as it burst through several seals and barriers before
exploding. Survivors describe the incident as a sudden explosion which gave
them less than five minutes to escape as the alarm went off.”
Of course the difficulties with methane clathrate found in deep sea oil
production would not be a problem if we drilled at shallower depths off our coast,
or on land, such as in Alaska, or if we made better use of coal and natural gas that
we have in such abundance in the United States.
One thing the BP disaster may point out to us is that we need a more
rational energy policy.
By the way, does this discussion make me a high pressure newspaper
columnist? One can always hope.
Your comments are invited. Weyland can be reached at
Remember when you were a kid and had a beach ball and tried to sit on it
while floating in a lake? Did it ever surprise you how hard it was to get the beach
ball totally under water? I know it did me. We’re going to talk about that today.
Buoyancy is the property that allows us to happily float on an inner tube.
Before we talk about that though we need to talk about water pressure.
Almost all you need to know about water pressure in a lake you can learn
from Dr. Seuss’s classic poem Yertle the Turtle. In this poem, King Yertle, a turtle,
the king of the pond, the ruler of all he could see, decided he didn’t see enough.
In his mind, if he could get up higher, he’d be an even greater ruler. And so he
enlisted the help of the other turtles in the pond. According to the poem, “He
made each turtle stand on another one’s back.” And then he climbed up until he
was on top of them all. According to the poem:
“And all through the morning, he sat there up high
Saying over and over, “A great king am I!”
Until ‘long about noon. Then he heard a faint sigh.
“What’s that?” snapped the king
And he looked down the stack.
And he saw, at the bottom, a turtle named Mack.
Just a part of the throne. And this plain little turtle
Looked up and said, “Beg your pardon, King Yertle.
I’ve pains in my back and my shoulders and knees
How long must we stand here Your Majesty, please?”
(from Six by Seuss, Random House, 1991)
Mack, the turtle at the bottom of the stack, had to support the weight of all
the turtles above him. And that, basically, is the idea behind both atmospheric
pressure and water pressure. We say that standard atmospheric pressure is 14.7
pounds per square foot. That means that if you were to mark out a one foot by
one foot square on your lawn it would, just like Mack the turtle, have to support
all the air above it, which apparently weighs about 15 pounds.
The same is true of water, except of course water is much heavier than air,
so the pressure adds up faster. For example, if you are 5 feet below the surface of
the water, the water pressure on you is about 2 pounds per square inch. But if
you’re 5000 feet below the surface, where the Gulf Oil deep sea drilling rig is,
the water pressure is over 2000 pounds per square inch.
There’s one other thing we need to say about water pressure in a lake.
Pick a value for the depth underwater. Let’s say 5 feet. At that depth, the pressure
is the same in all directions. Furthermore, the pressure on a submerged object is
always perpendicular to the surface at each point on the surface. Materials that
have this property are called hydrostatic. If a prospective mom carrying a baby in
her tummy is involved in a car accident, the amniotic fluid surrounding the baby
will cushion the blow. Thanks to hydrostatic pressure.
Finally we can talk about buoyancy. Imagine a can of beans completely
submerged in a lake. (Don’t ask how it got there.)
What this shows is that the reason for buoyancy is because the bottom of
the can experiences a greater force upward from water pressure than the top part
of the can experiences.
If you do a little math, you can show that the buoyant force on an object in
water is equal to the weight of the water displaced by the object.
So what determines if some object in a lake floats or sinks? Basically we
have two forces competing with each other: the buoyant force and the Earth’s
greater pressure here
because the bottom of
the can is in deeper
less water pressure here
because the top of the can
is in shallower water
surface of lake
gravitational force, which we call the object’s weight. If the weight force is
greater, the object will sink to the bottom. If the buoyant force when the object is
completely submerged is equal to the weight force, object will just barely float.
submerged. If the buoyant force of the completely submerged object is greater
than the object’s weight, then part of the object will be above water.
Why is more of your body out of the water when you float in the Great Salt
Lake in Utah? Because salt water weighs more than regular water. Remember
that the buoyant force upward is equal to the weight of the water you displace.
Heavier water means more buoyant force so you don’t have to displace as much
water. Or, in other words, you float better.
Let’s go back to a boy or girl trying to sit on top of a beach ball in a lake. If
you have a 16 inch diameter beach ball, a boy or girl weighing 75 pounds should
be able to sit on a completely submerged beach ball. But of course it gets real
tricky to actually do it. I always ended up tipping over.
From all this you can probably guess how many friends I had as a child
and, even now, how much fun I am to be with at a family outing at a lake. “Look,
everyone, I’m sitting on top of a beach ball!”
It’s sad in a way, right? But look on the bright side. Who needs friends if
you have a beach ball?
On February 6, an inquisitive reader of this column, whom we will call
Dorothy, sent me an email: “I have a question for you. This year I have been
keeping track of the times of sunrise and sunset. I have been surprised that the
morning daylight isn’t increasing as much as the evening light. I took the times
from the weather report on TV. On December 22 the sunrise was at 7:58 am and
sunset was at 4:55 pm. On February 5, sunrise was at 7:39 am and sunset was at
5:45 pm. Am I right in figuring that means 50 more minutes of light in the
evening, but only 19 more minutes in the morning? I had expected that it would
be about the same increase both times. My question is why doesn’t it increase
the same morning and evening?”
I sent her an email saying that I’d wondered about that too, and that would
try to find an answer. (Translation: I was basically clueless!)
On March 6, Dorothy sent another email. “I have still been charting the
sunrise and sunset times. For the past 30 days the sunrise has gained 42
minutes while sunset has gained only 39 minutes of light. I am guessing that by
summer the total gain will be equal when it again begins losing minutes of light.
It will be interesting to see.”
Again, she got no explanation from me. I was still in the dark about the sun.
On April 12, Dorothy sent another email. “I notice now that morning light is
increasing faster than the evening one so the total is getting more even. I sure
don’t understand how it works though.”
Okay, Dorothy, let’s see if I can take a stab at answering your question.
First of all, the reason for our seasons is the 23.5 degree tilt of the earth’s
axis. In the summer, the Northern Hemisphere is tilting toward the sun. In the
winter, the Northern Hemisphere is tilting away from the sun. Winter solstice
occurs when the earth’s axis is most tilted away from the sun. It is the shortest
sun-lit day of the year for us in the Northern Hemisphere. It occurs on or about
December 21. From that day on, the Northern Hemisphere gets more and more
minutes of sunlight. From our point of view on the earth we see the path of the
sun, instead of being in the southern part of the sky, begin to creep northward.
Sunset and sunrise times change in such as way as to give us more sunlight every
day. The summer solstice occurs in June when the earth’s axis is most inclined
toward the sun. It is the longest sun-lit day of the year. We discussed this in the
March 27 issue of the Standard Journal.
Second big idea: There are two ways to define when one day has passed.
See the figure below, taken from the Millennium Mathematics Project, University of
Cambridge web site:
The figure shows the earth (in blue) at position 1 at noon at some place on
the earth. The earth then makes one complete rotation, shown as position 2.
Ordinarily, we would think that one complete rotation of the earth about its axis
should equal one day, right? But if we want to go from noon on day 1 to noon the
next day, the sun (yellow at the center of the figure) should be directly overhead
each time. However, because the earth has been traveling through space in its
orbit at the same time it’s rotating about its axis, it will take a little more rotation
for the sun to be directly overhead. This happens at position 3 on the figure.
Confusing? Try this analogy. Imagine you’ve taken a child named Johnny to
an amusement park. On one ride, kids sit on a large ball that is attached to a track.
The ball (and Johnny) moves slowly around an oblong track at the same time the
ball rotates. You stand in the middle and take Johnny’s picture when he’s directly
facing you at position 1 in the figure.
When Johnny is at position 2, he calls out, “Take my picture! Take my
You say, “No, Johnny, I’m not going to take your picture until you’re directly
Because Johnny is both rotating and moving along a track, before you take
the second picture, you have to wait until Johnny is at position 3, when he’s facing
you again. Replace you by the sun and Johnny by someone looking at the sun at
noon on two different days, and you’ve got the idea of what this is all about.
In astronomy, the time it takes to go from position 1 to position 3 is called a
solar day. The time it takes to go from position 1 to position 2 is called a sidereal
This extra time to go from position 2 to position 3, on average, is about four
minutes. According to the Cal Tech outreach web site, “This little difference in
time would cause no concern if it were always the same, but it is not!”
Now we have to add one more complication: The earth moves in an elliptical
orbit. (An ellipse looks like a circle that someone has sat on.)
As shown in the figure, on January 3, the Earth is the closest to the sun.
This position is called the perihelion of its orbit. On July 4, the Earth is the farthest
away from the sun. This is called the aphelion.
Back to you and Johnny again. Suppose that the ride that Johnny is on
speeds up along the track some of the time and slows down at other times. This
happens with the earth too. And that affects the length of the solar day.
According to the New Scientist web site: “The asymmetry in the rates of
change of sunrise and sunset times arises from the nature of the Earth’s orbit
around the sun, and is caused by variations in the length of the solar day, the time
between solar noons on successive days, throughout the year. Sunrise and
sunset are essentially symmetric about solar noon, but solar noon is not always
“The Earth speeds up as it approaches the perihelion of its elliptical orbit,
the point of closest approach to the sun, and slows down as it approaches the
aphelion. The increased speed at the perihelion, together with the shorter distance
to the sun, means the angle swept out by the Earth about the sun every day is
greater near the perihelion than near the aphelion. So more rotation is needed to
complete a solar day near the perihelion, causing the solar day to lengthen.”
That is what introduces the lack of symmetry between the changes in
sunrise and sunset as noticed by Dorothy. There’s much more that could be said,
but we’ll leave that for another day.
Thanks for the question, Dorothy! It’s been fun to try to fin d an answer.
Weyland welcomes your comments. He can be reached at
My worst exercise experience happened the one day I decided to try an aerobics
class. It was taught by a tireless young woman who insisted on changing movements
every five seconds. It took me that long to figure out what I should be doing, and by that
time, she’d moved on. And so basically I just stood there and looked confused. What I
needed was a few variations repeated over and over. I simply couldn’t adjust to the
‘Now we’re going to do this! Now we’re going to do that…”
Which, oddly enough, brings us to The Law of Unintended Consequences.
According to Andrew Gelman in the Seeking Alpha web site: “The law of
unintended consequences is what happens when a simple system tries to regulate a
Referring to my brief aerobics experience, I was the simple system. My aerobics
instructor was the complex system.
But what if the aerobics instructor is the simple system and she says, “Other
exercises are bad! Pushups are good for you! I will have you do pushups for the entire
Others in the class might suggest alternative routines, but she won’t budge. “No
variations! Just pushups! Pushups are good for you!”
Her zeal to make us do “good exercises” would have the unintended
consequence that before long nobody would be in her class.
Returning to Andrew Gelman again, “The political system is simple. It operates
with limited information, short time horizons, low feedback, and misaligned incentives.
When simple systems try to regulate a complex system, you often get unintended
Here’s an example of an unintended consequence produced by a political
system. According to the Google Answers website, “In India, a program paying people a
bounty for each rat pelt handed in, intended to exterminate rats, led instead to rat
Another example from the same web site: “Prohibition, intended to suppress the
alcohol trade, drove many small-time alcohol suppliers out of business, consolidating
the hold of large-scale organized crime over the illegal drugs industry.”
Here’s an example of a positive unintended consequence. The Library of
Economics and Liberty website says that “…the law of unintended consequences is one
of the building blocks of economics. Adam’s Smith, invisible hand, the most famous
metaphor in social science, is an example of a positive unintended consequence. Adam
Smith maintained that each individual, seeking only his own gain, ‘is led by an invisible
hand to promote an end which was no part of his intention,’ that being the public
interest. It is not from benevolence of the butcher or the baker that we expect our dinner
but from regard to their own self interest.”
In other words, the butcher’s main goal is to make money to provide for his
family. Because he wants customers to return to his shop, he strives to provide the best
meat at a reasonably low price. We the consumer just want a nice steak for dinner. The
steak the butcher sells comes from a rancher who likewise only wants to provide for his
family. All of this self-interest of millions of people provide for a healthy economy with
hopefully very little unemployment. And yet a healthy economy for the nation was never
the goal of the butcher or the rancher. It is an unintended consequence of free
In terms of our economy, self interest is what has made America great! We shop
for bargains. If enough people don’t buy a product, the company goes out of business.
Some of those who used to work in that company start another business. If it succeeds,
we buy the product, the company prospers, and more employees find work. If it fails,
that individual may start another business until he finds something that will be
successful. Sometimes failure is essential for success.
And so a positive unintended consequence of self-interest is prosperity and jobs.
(Although, certainly, of course, it has also brought social problems as well.)
In terms of Gelman’s definition, free enterprise is a complex system. Think of all
the decisions that take place in the stock market each day! People buying, people
selling, just wanting to provide for their families. Some companies prosper, some don’t,
but life goes on.
Just as an aerobics instructor who only allows a class to do push-ups, the
Federal Government is very good at imposing regulations. Is it possible that some of
these regulations may have the exact opposite result than that intended? Let’s look at
In regard to the recent Gulf of Mexico oil spill, Charles Krauthammer in the May
28th Washington Post writes: “Here’s my question: Why were we drilling in 5,000 feet of
water in the first place?
“Many reasons, but this one goes unmentioned: Environmental chic has driven
us out there. As production from the shallower Gulf of Mexico wells declines, we go
deep (1,000 feet and more), and ultra deep ( 5,000 feet and more), in part because
environmentalists have succeeded in rendering the Pacific and nearly all the Atlanticcost
off-limits to oil production. And, of course in the safest of all places, on land, we’ve
had a 30-year ban on drilling in the Arctic National Wildlife Refuge. Why have we
pushed the drilling from the barren to the populated, from the remote wilderness to a
center of fishing, shipping, tourism and recreation? Not that the environmentalists are
the only ones to blame. Not by far. But it is odd that they’ve escaped any mention at
On May 11, Louisiana officials asked permission to build temporary sand islands
or berms to block the flow of oil into fragile wetlands and marshes. No action was taken.
Why? According to the AOL news website, “…Louisiana Gov. Bobby Jindal said he was
frustrated that the U.S. Army Corps of Engineers has taken too long to approve his
state’s plan to construct sand berms in an attempt to block oil from flowing into the
wetlands. As Jindal said, ‘We have been frustrated with the disjointed effort to date that
has too often meant too little too late to stop the oil from hitting our coast.’”
Jindal first requested the construction of the berm on May 11. It finally received
approval on June 2, after the oil had contaminated the wetlands.
In the June 14 issue of Time Magazine Bryan Walsh writes: “On June 2
he (Admiral Thad Allen) announced that he had approved five additional sand berms
and that BP would foot the bill. Anything, it seems, is better than waiting helplessly for
the oil to envelop the wetlands completely.”
It took nearly a month for the Federal Government to decide that erecting
sand berms along the coast of Louisiana would cause less environmental damage than
letting the oil get into the wetlands. Is it possible that regulations and procedures
designed to save the environment at least partially contributed to the unintended
consequence of damaging the environment for years to come?
Just as we expect that an aerobics class will give us a variety of exercise
routines that will exercise all our muscle groups, we should expect the same multifaceted
approach to the nation’s energy development and production. For some federal
agency to say that some energy sources are good, such as solar and wind, but other
energy sources are bad, such as nuclear, coal, or oil production in the Alaska National
Wildlife Reserve (ANWR), is short-sighted. Most reasonable people would say, “Let’s
do it all and see what we can do to protect the environment at the same time.”
And that is what I’ve learned from participating in one aerobics class!
I may go back. We’ll see.
HOW TO TALK TO A MAN
1. Instead of saying: “The steps are so icy!”
Some men might answer with one of the following:
a. “I know. I nearly fell myself coming up the stairs.”
b. “Duh! That’s why they call it winter.”
c. “Come into the house through the garage like I do.”
Say this, “I need you to get the ice off the steps.”
2. Instead of asking, “Are you going to wear that tie?”
Some men might answer with one of the following:
b. “Duh! That’s why I’m tying it around my neck.”
Say this, “That tie doesn’t go with your shirt.”
3. On your anniversary, instead of saying, “Honey, what do you think? Did we do the right thing to get married?”
Some men might look puzzled and ask, “As opposed to what?”
Say this: “I am so happy to be married to you!”
4. Instead of saying, “You’ll never believe what crazy policy my boss announced today for all the secretaries!”
After you explain what your boss said, some men might answer with one of the following:
a. “If you don’t like your job, just quit!”
b. “That’s it! You’re not working there anymore.”
c. “I’m going down there and telling him what I think of him!”
c. “Maybe you and the other secretaries did something to cause him to do that.”
Say this: “I am so mad at my boss today for a policy he announced today for all the secretaries! All I need you to do is listen and sympathize.”
Question: Can you come up with any other phrases which women say that men never respond to properly? Also, please give suggestions on how to say it so a man will understand.
In my latest novel, “Brianna, My Brother, and the Blog,” I have Austin hauling Brianna, her harp, along with Sophie, her friend who plays flute, to wedding receptions where they provide background music to make a little money. Austin sits among the guests and listens in on their conversations.
The truth is I’m a lot like Austin in that I also listen to conversations of people I’ve never met.
Several months ago I was standing in the hall just before a meeting was about to begin. A young wife hurried in. As she came into view, he scowled and grumbled, “It’s about time! Everyone’s waiting for you.”
I thought he could have done better than that. This is the woman he loves more than anyone else, his partner, and she deserves kindness and respect.
She knew she was late. I’m sure there were reasons for it too. Him saying “Everyone’s waiting for you” did not make her feel appreciated. What will he say when they have kids and she’s trying to get them ready for church?
This is not about being late. It’s about showing kindness and respect.
Here’s my question for you: What should this young husband have said to her when he first saw her?