Now you can find out where you are even if you don’t have GPS. Learn how to find south along with your latitude and longitude using only a few household items. I should note, that in using the home-made quadrant cited, the precision of your findings will be rather low. Don’t worry, you’ll be within a few hundred miles. ;)

Transcript:
The Tabletop Explainer
(Honda Pilot DIY Contest Entry)
How to Navigate by the Sun

Today if you want to know where you are, chances are you’ll use one of these, but we’re going to go ahead and focus on using the materials here and the sun to figure out due south, your latitude, and your longitude.

Our measurements of time are based on the apparent motion of the Sun, the stars, and the moon. Which means a lot of information is packed into your watch.

Take for instance the idea of noon. Before standardized time zones, noon was simply the time of day when the sun crossed an imaginary line connecting due north and due south, called a meridian.

Let’s look down on the earth from the north pole. Here in Somerville, noon occurs when the Sun is due south. In Beijing it’s the same thing.

Anyhow, at local noon in the northern hemisphere, the sun is due south, at midnight, it’s half a world away.

We could make a clock with an hour hand that went around once every 24 hours, but most hour hands go around twice a day. This means the hour hand moves half as fast as the sun appears to.

Meaning if you take your watch and point the hour hand at the sun, halfway between the hour hand and noon is due south. In the southern hemisphere it’s due north.

So the next time you need to find south, just take your watch hold it parallel to the ground, point your hour hand at the sun, and halfway between the hour hand and noon is due south. Now that’s if you’re in the northern hemisphere. Keep in mind, your watch doesn’t run local time. So if daylight savings time is in effect, you’ll have to subtract an hour, and thanks to standardized time zones, you’ll be off by a few minuets. Plus there’s the fact that the geometry of the situation means that things will be less precise around sunrise and sunset, but you get the idea.

Now how does something like this [points to sextant] help us find out where we are. Well this is a sextant, and it’s really just a super-protractor.

You look at one object, like the horizon, through the sighting scope and a half mirrored piece of glass lets you line up the reflected image of some other object like the sun, the sextant telling you the angle between the two. [fade to table of materials]

You can make a similar device called a quadrant from these materials here. It’s basically a protractor that we are going to affix a straw to as a sight and a string too, to help us find the vertical. You can print these plans out from the URL you’ll see here.

http://www.davidcolarusso.com/handouts/quadrant.pdf

A quadrant lets you measure the angle between the horizon and an object, in this case, the sun. So do not look through the sight. Instead, place an object behind the quadrant, and look for the shadow cast by the straw. When the shadow’s a circle, you’ve got the sun lined up.

Two numbers can describe every place on earth: latitude and longitude. These are measured in degrees from two imaginary lines, the prime meridian, and the equator.

All points at a certain longitude are the same amount of degrees east or west of the prime meridian, and all points at a certain latitude are the same number of degrees north or south of the equator.

We know from working with our watch that at noon here in Somerville, the sun is due south. That is, it falls on an imaginary line connecting north and south—a meridian. So let’s look at the noon-time sun.

Keep in mind, the sun is really far away. So anyone pointing at the sun will point in the same direction.

Knowing this, if the sun were directly above the equator, we could find our latitude by simply finding the angle between the sun and overhead.

That is, 90 degrees minus whatever our quadrant reads.

Unfortunately, the sun doesn’t stay directly over the equator. The earth has a tilt in its axis. So over the year the sun moves above or below the equator by roughly 23 degrees.

This is called declination, and we simply add or subtract it from our measurements.

Sailors used to produce books listing the sun’s declination for every minuet in the year, but today you can find this on the web

We know local noon is when the sun crosses the local meridian, and probably noticed that a meridian is also a line of longitude. So if you know when noon happened you already know you longitude.

All we have to do is convert our time to GMT, the local time at zero longitude. Every minuet the sun covers a quarter of a degree. So if your noon took place 5 hours and 4 minuets after noon GMT your longitude is 76 degrees west.

3 hours before GMT, 45 degrees east.

Of course, we had to find local noon first.

To do that, plot the mid-day measurements from your quadrant against your watch time. They’ll make a curve and the top of the curve is local noon.

I’m David Colarusso for the Tabletop Explainer.

So if you speak two or more languages, head over for some translating fun. Here’s an example of a subtitled video. As of this posting, it’s only available in English. Want to change that? Register. View this link; then choose a language under “Translate This Film.”

Transcript:
The Tabletop Explainer
Episode Eight (9)
Special Relativity (2 of 5): Nomenclature

Last week we covered the two postulates of special relativity, and next week we’ll use geometry to derive some of its consequences, but first we need to learn some nomenclature. It’s not exciting, but it will prove helpful in the long run. Keep an eye out for the following terms: space-time diagram, line of constant position, line of constant time, space-time event, and world line.

We’re used to documenting things with film, but let’s make things even simpler. Say we replace film with a large roll of paper and attach a marker to those objects we find interesting. For now, this block on wheels, and a road sign. All the while our paper moves with a constant speed downwards. This produces what physicists call a space-time diagram.

By virtue of our setup, the vertical contains information about time and the horizontal about position. The lines traced by the markers are know as world lines because they document the history, the world, of their owners.

To read our diagram, we employ the use of constant lines of position and time.

A line of constant position represents one place. Any collection of events occurring on a line of constant position occur at the same place, just at different times.

Similarly, a line of constant time represents one instant. Any collection of events occupying a line of constant time take place at the same time but in different places.

This diagram is simply a graph of time verses position.

With our two types of constant lines, we can define any point in our diagram. Such a point represents a particular place at a particular time, something we’ll call a space-time event.

A world line is nothing more than a record of these events for its owner. By working backwards, from our intersection of constant lines we can tell where and when something happened.

Next time, we’ll make use of space-time diagrams and the two postulates to derive consequences of special relativity using only simple geometry.

The bizarre consequences of special relativity arise from two postulates, two things which once accepted lead to Einstein’s space-time. In this series of five episodes, we will introduce and build upon these postulates to derive the consequences of special relativity.

Transcript:
The Tabletop Explainer
Episode Eight (8)
Special Relativity (1 of 5): Two Postulates

The bizarre consequences of special relativity arise from two postulates, two things which once accepted lead to Einstein’s space-time. In this series of five episodes, we will introduce and build upon these postulates to derive the consequences of special relativity. So are you ready? Okay then, fasten your safety belt and prepare for take off.

Imagine you’re waiting on the runway and decide to take a nap. When you awake all the window shades are drawn, and no one is in the cabin. So can you determine, without peaking out the window, whether you’re on the tarmac or flying in a straight line at a constant speed?

You might think that dropping something would help, but it doesn’t. Some people reason that if they drop something and it falls “straight down” they aren’t moving, but really all this does is establish that they aren’t accelerating.

This is sometimes known as Galilean relativity, and it’s why we don’t perceive the Earth’s rotation. For a sailor traveling at a constant speed in a straight line, a cannon ball dropped from the crow’s nest falls “straight down.” To a land locked observer, however, [black mask telescope thing] both the ball and the ship are moving forward, and so the ball is seen to follow an arch.

This means dropping something can’t tell you if you’re moving. It looks the same to you either way as long as you’re undergoing uniform motion. Now if the plane was to suddenly speed up after you released the bag of peanuts then it wouldn’t land directly below your hand.

However, this is what’s special about special relativity, we are concerned only with things standing still or moving in straight lines at a constant speed, what we call uniform motion.

This introduces the first postulate. There is no experiment you can perform to determine if you are standing still or moving in a straight line at a constant speed. Yes, you could have looked out the windows, but all you could have said for sure is that the ground and the earth were moving relative to each other. The plane could be the “still” one with the earth rotating below. It’s all a matter of perspective; it’s all relative.

Alright then, are we happy with the first postulate? The most one can say is that she is not speeding up, slowing down or changing direction. She cannot say whether this is because she is standing still or moving at a constant speed in a straight line.

It might help to consider that there is no absolute reference frame in the universe with which to compare one’s motion. Remember the earth is hurtling around the sun and the sun around the center of milky way. The best we can say is, “I’m moving relative to this or to that.”

Okay, let’s go to a parade.

You’re throwing candy to onlookers, and normally you throw candy at five miles an hour relative to yourself. The truck is trotting along at two miles an hour. So when you throw candy to people behind the truck you are throwing opposite the truck’s motion and the candy reaches them traveling slower than it would if you were standing still relative to them. How much slower? Well you subtract the truck’s speed from that of your throw and find three miles an hour.

When you throw the candy forward, it’s moving with the truck and so hits the spectators going seven miles an hour, your pitching speed plus that of the truck.

Got it? Good, ‘cause now things get weird.

Light it turns out is special. It doesn’t behave like candy, trucks baseballs, or any material object for that matter. To see what I mean, let’s wait for nightfall.

Now imagine you’re standing still next to a stationary truck. We can think of the light coming from the headlights as little particles or waves, take your pick. What’s important is that we measure how fast they’re leaving the truck. This is like your pitching speed at the parade. When we do this, we find the light is leaving at 670 million miles an hour.

Now let’s have the truck zoom towards us at 10 miles an hour, and measure the speed of the light leaving the headlights. How fast do you think it’s going? 670 million miles an hour plus ten? Well, that would be wrong. No matter what, we measure the speed of light to be 670 million miles an hour. It doesn’t matter if the truck is moving at 600 million miles an hour, we don’t add its speed to that of the light leaving the truck.

That’s the second postulate. The speed of light is the same for all observers undergoing uniform motion, that is, standing “still” or moving in a straight line at a constant speed. This is an empirical fact. Yes, the speed of light changes when it moves through glass or water, but we’re not concerned with these complications. The speed of light in a vacuum is always 670 million miles an hour.

It might seem odd, but experiment shows this to be true. Now if you can accept this and the first postulate, you’re ready for relativity. They’re all you need. Everything else just follows.

For our purpose this means:

All uniform motion is relative. That is, you can not determine if you are standing “still” or moving in a straight line at a constant speed, and the speed of light in a vacuum is the same for all observers undergoing uniform motion.

You cool? All right then, now for some specialized nomenclature.

Transcript:
The Tabletop Explainer
Episode Seven (7)
How to Build a Paper Quadrant

Start by visiting http://www.davidcolarusso.com and downloading the PDF document located at slash handouts slash quadrant dot PDF. Print out this document, and simply follow the instructions.

To find the altitude of an object, point the business end of the quadrant straight at it. Then read the number under the string. Usually you can do this by looking through the straw and aming. For the Sun, however, do NOT do this. Instead take something and hold it behind the quadrant. When the Sun is properly sighted, the rays of light from the Sun will be traveling parallel to the straw. This will cause the straw to cast a circular shadow as the Sun’s rays travel straight down the center.

Good… Bad… Good. Then simply read the altitude.

[roll credits]

What do you think?

Now that you have a quadrant, what can you use it for?

Why don’t you try measuring the altitude of celestial objects over the course of several days?

Update: People have been asking for the math. So here it is. The Sun’s core temp is ~13.6 MK. For hydrogen nuclei the Coulomb barrier is roughly 0.1 MeV. This corresponds to a temperature in excess of 1 GK! Luckily, tunneling and the distribution of speeds among nuclei lower the actual temperature required. So without tunneling even the Sun’s core isn’t hot enough for fusion. To see most of this worked through, check out this link:
http://burro.cwru.edu/Academics/Astr221/StarPhys/coulomb.html
for a less mathematical explanation, try:
http://en.wikipedia.org/wiki/Nuclear_fusion#Requirements

Transcript:
The Tabletop Explainer
Episode Six (6)
What is quantum tunneling?

Some of us were taught in high school that the electron orbits around the nucleus like a planet around the sun. However, this description has been understood as a gross mis-representation for the better part of the last century. As it turns out, there is a characteristic uncertainty related to the very small. No one can tell exactly where something is; the best one can do is figure out where something is most likely to be. We can visualize this with something called a probability cloud. Here we see the probability cloud of a proton at the center of a hydrogen atom. The denser regions are where the proton is more likely to be found. However, this uncertainty is not due to an inability of ours to measure the small in an exact manner; it is a fundamental aspect of the world in which we live, and its implications are extraordinary.

Let us take for example the phenomenon of tunneling. If we can’t tell exactly where something is then it follows that we can’t tell exactly where it’s been or where it will be. The best we can hope for is where it most probably will be. So there’s a small chance that a racket ball thrown repeatedly at a barrier could just tunnel through the barrier, appearing almost magically on the other side. We don’t see this often because a racket ball’s pretty big and its uncertainty pretty small. But if we deal with matter on the subatomic scale it becomes much more likely. Here our projectile approaches the barrier, we see here its probability cloud, although it’s most likely near the center of the cloud we can see that there is a small chance of it being on the other side of the barrier, and so sometimes it is. Tunneling isn’t a mathematical trick or an assumption, it’s an observable fact. It’s made use of commonly in modern electronics and in a real way allows for life on earth. To see why, let us trace the creation of a photon in the sun. The light from the sun that we see reflected off the moon, the light which drives the earth’s weather, that provides the energy for life all originates from the process of nuclear fusion in the sun. Two light atomic nuclei collide, forming a new element, and in the process light is released. But these nuclei are both positively charged and so repel each other. Only if they have enough energy can they overcome this potential barrier and fuse. But if you do the math, the nuclei in the sun don’t have enough energy. The sun’s just not hot enough, non the less, the sun shines, and it does so because of tunneling. Just like our physical barrier, there’s a chance that our particle could be on the other side, and so the sun shines.

[roll credits]

What do you think?

This piece was designed to get you thinking. So find a physicist and get talking, or post a comment and get a discussion going. The main point is that quantum mechanics is real because it properly describes nature. Einstein may have believed that God doesn’t play dice, but God need not conform to Einstein’s beliefs.

Transcript:
The Tabletop Explainer
Episode Five (5)
Could that actually happen?
Phylm examines the bus jump from Speed
Why not enter the first Annual Phylm Prize

In the movie Speed a bus is forced to jump an unfinished portion of highway to avoid setting off a bomb on the bus. This bomb is rigged to explode if the bus goes below fifty miles an hour.

[clip of jump]

Of course, they make it, but we want to know if this could really happen.

First it’s important to understand how projectiles fly through the air. All objects, regardless of their mass, fall at the same rate in a vacuum. [Apollo 15 video clip] Additionally, an object’s time falling is independent of its horizontal velocity. So no matter how fast the bus is traveling, should it launch horizontally, it will always fall some amount and fail to make it.

So for the bus to make the jump, it must launch at some angle. Now this is a little bit of a cheat as I should explain more. However, there is an equation in mechanics know as the range equation which relates the initial velocity of a projectile to the distance it covers horizontally. If we examine the movie, we can find the speed the bus is traveling and the distance it is meant to cover. “g” is the acceleration due to gravity which we know. So we can check to see how much of an incline we need for a lunch something that will just make it.

We simply rearrange the equation, solving for the launch angle. Plug in our values, and presto. We get approximately five degrees. That’s not much of an angle. Now there’s no clear shot of the highway. So it’s hard to say if there’s actually an incline, but it seems possible there could be.

Oddly, the bus seems to jump upwards at the last moment, an artifact of Hollywood tinkering, but it does seems we’ve cleared one hurtle. If we really believe the bus left the road going 68 miles and hour, and the jump adjusted for the length of the bus was a mere 50 feet, as long as there was a 5 degree incline, it seems possible the bus could have made the jump.

However, a quick glimpse at the Speed DVD’s special features makes it clear the landing would most likely wreck the bus. Not to mention, we haven’t thought about wind resistance or the bus’s rotation. Nonetheless, it’s not entirely absurd.

If you liked this video, please make your own, tell your friends, and enter to win the First Annual Phylm Prize. Be sure to mind your video quotes. If you choose to repurpose someone else’s copywritten work, be sure it’s fair use. I’m not your lawyer, but I suggest keeping it under two minuets or 10%, which ever’s shorter, and be sure quotes are not for ambiance but critical examination only. There is no clear test for fair use, so use common sense, do a google search, or consult an attorney. Of course you can always enter an entirely original work. For official rules, visit http://www.phylm.com/

Transcript:
The Tabletop Explainer
Episode Four (4)
What is the conservation of angular momentum?

Nature conserves spinning. Here a person stands on a turntable capable of turning parallel to the ground. He is holding a spinning wheel perpendicular to the ground and at first he does not spin.

However, when he rotates the wheel, making it spin parallel to the ground, the turntable starts spinning in the opposite direction of the wheel to maintain (that is, conserve) the zero horizontal spinning we started with. As he turns the wheel over, the turntable changes direction again, the wheel’s spinning always canceling out that of the man holding it.

You might notice that the man doesn’t spin as quickly as the wheel. This is because his spinning counts for more because he is more massive. Essentially, there’s more stuff spinning.

However, nature doesn’t only care about mass when spinning is concerned. Distance matters too.

Here a skater brings her arms inward and we notice she turns faster as a result. This is because the large circle spinning counts for more then the small one. So nature in an effort to balance the books, speeds her up.

Scientists call this spinning “thing” angular momentum, and there’s a fixed amount of it in the cosmos. In fact, angular momentum plays an important roll in astronomy, explaining why this binary star collects debris from its neighbor in a rotating disk.

To review, there’s this thing called angular momentum, and it cares about three things.

How fast something’s going
How massive that thing is
How big a circle it traces