Fall Back

I hate the fall time change back to standard time.  I woke up earlier than I had to this morning since my internal clock is still on daylight savings time.  And it was bright outside way too early.  I'd much rather have some sunlight later in the day rather than leaving work in the dark (to hell with those kids waiting outside for the bus in the dark in the morning - give them flashlights!).

The real problem, of course, is that we're moving toward the winter solstice, the shortest day of the year when we'll only have about 9 hours of daylight.  That basically means many of us will be leaving home in the dark in the morning and returning in the dark each evening.  I personally find it very depressing and have to force myself to get outside in the middle of the day to get some sunlight.

What I really need is more money so I can vacation somewhere sunny in January.

The Way North

One of the most recognizable "constellations" in the sky is the Big Dipper. Most people are taught how to identify it as children and virtually all cultures have a name for this pattern of stars – in England it’s the plough, in Thailand a crocodile, and the ancient Egyptians saw the hindquarters of an ox. Technically speaking, however, it’s not really a constellation. The Big Dipper is what astronomers call an asterism – a recognizable pattern of stars. The asterism of the Big Dipper is actually part of a larger constellation called Ursa Major, the Great Bear of Greek mythology, although I must confess to having some difficulty seeing a bear in that pattern of stars!

Knowing how to identify the Big Dipper has a practical application in that it can be used as a pointer to Polaris, otherwise known as the North Star. Polaris is located almost directly above the North Pole of the Earth and is thus always found due north of your location (assuming you’re not south of the equator where it’s invisible). And, because Polaris is located directly above the rotational axis of the Earth, it doesn’t appear to move over the course of the night like all of the other stars. In the Northern Hemisphere, Polaris never rises or sets which gave it an undeserved reputation for constancy as noted by Cassius in Shakespeare’s Julius Caesar (Act III, Scene I):

But I am constant as the northern star,
Of whose true-fix'd and resting quality

There is no fellow in the firmament.

In astronomy, however, a common-sense observation like this is often incorrect. The North Star is not constant. As the Earth rotates on its axis it wobbles a little bit, like a spinning top does as it slows down, and this wobble traces out a cone-shaped path in the sky with a 26,000 year cycle. When the ancient Egyptians began building the great pyramids in Egypt a few thousand years ago, the dim star Thuban in the constellation of Draco the dragon was the North Star. A few thousand years in the future, the obscure star Alderamin in the constellation of Cepheus the king will be the North Star. The North Star is constant only on the scale of human life spans which, to be fair, is usually good enough for most purposes.

If you go outside this week at 6:00 pm or so, thanks to the time change, you’ll see the Big Dipper low in the northern sky. Polaris can be located by taking the two stars (called Merak and Dubhe) on the right side of the Dipper’s cup and extending a line from them upward in the sky about 28º where you’ll find the North Star. How do you estimate 28º in the night sky? An old astronomical trick is to make a fist and extend your arm. Your extended fist will now span about 10º of the sky. Slightly less than three fist-widths will bring you from the top corner of the Dipper’s cup to Polaris. Many people are under the mistaken impression that Polaris is a strikingly bright and prominent star but that’s not the case, it’s actually quite average looking and some stars in the Big Dipper are actually a bit brighter.

Locating Polaris enables you to tell which way is north and, by inference, the other three cardinal directions as well which is a useful skill for backyard astronomers who want to locate something in the night sky. Polaris also tells us our latitude north of the equator. In the mid-Hudson Valley, our latitude is 42º and Polaris is, not surprisingly, 42º above the horizon (a little more than four fist-widths). Is it any wonder that many of the ancient cultures that developed the science of astronomy, the Babylonians, Egyptians, and Greeks to name a few, lived near trackless deserts or on the seacoast? A little knowledge of the stars might have meant the difference between returning home or dying in the middle of nowhere.

The navigational help offered by the Big Dipper also played a key role during a sad chapter in the history of our country. In the mid-1800s, many black slaves in the southern United States learned a song called “Follow the Drinking Gourd” – a song whose lyrics described an escape route from the deep south along the Underground Railroad. Slaves commonly used a hollowed-out gourd for scooping drinking water out of buckets in the fields. The drinking gourd in the song, of course, refers to the Big Dipper and following the gourd brought one north to freedom.

I thought I heard the angels say

Follow the drinking gourd

The stars in the heavens

gonna show you the way

Follow the drinking gourd

Next time you gaze up at the Big Dipper, cherish your freedom as you try to imagine what it was like for over 60,000 American blacks who had to travel hundreds miles on foot from the South to all the way to Canada while following the direction of this well-known group of stars.

Archimede's Principle & Breast Size

Good post for Friday...

So I happened to come across an interesting reference the other day from the journal of Plastic & Reconstructive Surgery (2000 Mar;105(3):1019-1023).  The title of the paper was "Practical do-it-yourself device for accurate volume measurement of breast."  No, I wasn't Googling "breast" I was perusing other science blogs!  Anyway, the abstract reads:

A simple and accurate method of measuring differences in breast volume based on Archimedes' principle is described. In this method, a plastic container is placed on the breast of the patient who is lying in supine position. While the breast occupies part of the container, the remaining part is filled with water and the volume is measured. This method allows the measurement of the volume differences of asymmetric breasts and also helps the surgeon to estimate the size of the prosthesis to be used in augmentation mammaplasty.

This is actually very clever.  The problem is how to measure the volume of an irregular three-dimensional object (oh let's see, like a breast, for example).  The brilliant Greek mathematician, Archimedes of Syracuse (c. 287-212 BCE), figured this out over 2,000 years ago.  The story goes that Archimedes was tasked with determining if a crown made for King Hiero II was made with all of the gold the king provided for the object or if the unscrupulous goldsmith substituted a baser metal for the crown.  Archimedes could determine this if he could calculate the density of the crown since the density of pure gold was known (19.32 grams per cubic centimeter in modern units).  Substituting other metals into the crown would change the overall density.

To determine density, we weigh the object (grams in the 19.32 g/cm³ in the density value).  The next step, however, is more tricky.  We need to determine the volume of the object (the cm³ in the density value).  If we could melt down the crown and cast it into a gold bar it would be easy.  The volume would then be the length times the width times the thickness.  But how do you determine the volume of an ornate golden crown?

The story goes that Archimedes was lowering himself into a bath when the answer came to him - water is essentially incompressible so that an object immersed into water displaces an amount of water equal to the volume of the object.  Sit in a tub and the water level rises.  Archimedes was so overjoyed he dashed through the streets of Syracuse, buck naked, shouting Eureka ("I have found it!").  The experiment was done, the crown was determined to have silver mixed in, and the dishonest goldsmith presumably suffered for his sins.

I have students determine the density of an unknown mineral in geology lab using the same technique.  It's low tech, easy to do, and gives a reasonable value.

Anyway, I didn't request this paper via interlibrary loan, just read the abstract above, but I supposed one would take a plastic cylinder of known volume which was open at both ends.  If you used an 8-inch diameter plastic pipe one foot long, for example, the volume would be (pr²h) or (p 4² 12) = 603 in³.  The woman lies on her back, the pipe is placed over the breast tight against the skin, and water is poured into the pipe.  If it takes 200 in³ of water, the volume of the breast would be 403 in³.  Eureka!

Not sure what kind of accuracy you can obtain with this method (perhaps some of you can experiment at home) but it is clever.

Comet Hartley 2 Images

Looks like the flyby was successful.  Here are some images from the very slow NASA site - higher resolution images haven't even been released yet.

Pretty cool.  The comet nucleus is irregular in shape (not unusual) and covered with rubbly material.  The bright streaks are jets of gas streaming off from the solar wind.