Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Precession," section #7: on disk Sprecess.htm, on the web |
Goals: The student will|
Terms: First point in Aries or vernal equinox point, precession of the equinoxes, "precession" in modern usage, glaciers, ice ages (glaciations).
Stories and extras: The idea of Hipparchus, of measuring the position of the eclipsed Moon to find the Sun's position. "The Dawning of the Age of Aquarius" in the musical "Hair." Precession of artificial satellites and "nutation dampers", also (optional--details below) "magnetic resonance imaging" in medicine and "proton precession. " The story of Louis Agassiz, and the fact Cape Cod and its islands are a legacy of glaciers.
Start by noting we are quite lucky to have a bright star--Polaris--within half a degree of the north pole. Actually, the celestial sphere slowly shifts its pole; 3000 years ago, it was not too close to Polaris, and ancient seafarers used another star, not nearly as convenient.
The shift is very slow, and takes many centuries to be noted. The remarkable thing is that it was discovered so early, around 135 BC, by the Greek astronomer Hipparchus.
Then go into section 7 of "Stargazers. ". If there is time, the teacher may conclude by telling about NMR--nuclear magnetic resonance; see below.
Guiding questions and additional tidbits
-- Around 130 BC, the Greek astronomer Hipparchus of Nicea discovered that something about the celestial sphere was slowly changing. What was changing?
-- What did that observation tell about the Earth's axis in space
-- What is the half-angle of that cone?
-- What does the change imply for the Pole Star?
-- If Polaris is now at the pole of the celestial sphere, how far (in degrees) will the pole be from Polaris in 13000 years?
-- What is the meaning of the word "precession" today?
-- What do you know about the precession of spinning satellites?
(Optional story: Nutation dampers will reduce precession of a satellite, but only when its original spin is stable--e.g. if it spins around the shortest axis possible. That was not the case with the first US satellite--Explorer 1, launched in 1958. It had the shape of a fairly long cylinder (that included its attached last-stage rocket), spinning around its long axis. Mechanics (and intuition) suggest that a long cylinder (e.g. the round cardboard box in which rolled-up posters are mailed) does not "like" to spin around its long axis, and that any secondary effects will try to convert its rotation to one around an axis perpendicular to the cylinder in its middle.
That is indeed what happened to Explorer 1. The agent transforming the rotation were the four flexible small "whip antennas" sticking out from its middle. The waving of these antennas gradually made the satellite precess around its spin axis, and the cone of precession grew wider, until in the end it was essentially flat and the satellite spun around an axis perpendicular to it, through its middle. That could be told from the beaming of its radio signals.)
Optional excursion--the teacher may keep this for the end:
-- Does anyone know what "NMR" stands for?
Has anyone in the class had an "MRI test"--"Magnetic Resonance Imaging"--or watched one? (If so, let the student tell about it).
Nuclear Magnetic Resonance is a technique of using the precession of hydrogen atoms and has nothing to do with nuclear radiation.
How does it work?
The nucleus of hydrogen, the proton, has a spin, and is magnetized along its spin axis; a bit like the Earth, except, with Earth the two axes are slightly different. In the proton this is a quantum effect, the result of the physics of very small particles, not the kind of spin we see in a gyroscope. In a glass of water, or in the human bodies, the spin axes of protons usually point in random directions. If an electromagnet is suddenly switched on nearby, the nuclei will try to line up, like pins near a magnet. However, as is well known, spinning objects tend to keep their direction (that is how the gyro-compass operates) and resist any force which tries to shift their axis.
The result is that the little nuclei begin to precess around the direction in which the magnetic force is trying to line them up. Coils connected to sensitive amplifiers can sense the frequency of that precession and from it, measure the strength of the magnetic field: the Vanguard 3 satellite in 1959 carried such an instrument to measure the magnetic field of Earth.
Medical MRI (Magnetic Resonance Imaging) instruments are also based on this phenomenon, but in a much more sophisticated way, using it to tell where in the body hydrogen atoms are concentrated. MRI is a modern technique, using computers to analyze complicated data to produce pictures of internal organs. The result is a bit like X-rays, with the big difference that while X-rays, or their modern extension "CAT scans, " see the dense materials, such as bones, NMR targets hydrogen atoms, making tissues stand out if they are rich in hydrogen-containing substances such as water, proteins etc.
All of MRI machines contain big magnets, and if you ever have an MRI picture taken, you will be asked to remove anything made of iron before entering the MRI room. You will have to lie down in a hole inside the machine, very quietly and not moving (MRI is like a time exposure), while the machine measures the precession signatures of your hydrogen nuclei from many different angles.
-- What were the ice ages (or "glaciations")?
-- What is a glacier?
--When did the last ice age end?
-- What made Louis Agassiz conclude that glaciers once covered land which is now ice-free?
-- Milutin Milankovich in the 1930's proposed that slow changes in the motion of the Earth in space were responsible for ice ages. How can the precession of the Earth's axis be connected to climate changes?
In the Southern Hemisphere, this would make the seasons more extreme, but the oceans prevent dramatic climate changes.
In 13,000 years, because of the precession of the Earth's axis, we will be closest to the Sun in midsummer and most distant in mid-winter. Our Northern Hemisphere has much more land, and Milankovich proposed more snow would fall in the winter. Snow, being white, would reflect sunlight and reduce the heating of the ground later in the year. This small change may perhaps be enough to trigger ice ages, though other orbital changes may also be a factor.
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 12 September 2004