PHY 101 Study Guide: Final Exam

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Study Guide I
Study Guide II
Asteroids and Meteorites
Icy Leftovers
Extrasolar Planets

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Asteroids and Meteorites


The solar system contains numerous small bodies, including asteroids (or "minor planets") and comets.  Most asteroids can be classified by orbit: main belt, near-Earth, or Trojan.  Another classification scheme works by using reflectance spectroscopy to estimate chemical composition: we have C (for carbon-rich), S (for stony), and M (for metallic) asteroids.  Not all M-class objects are in fact metallic, but those that are were formed when large, differentiated asteroids were smashed in collisions; pieces of the metallic cores became the metallic asteroids we see today.  C-class objects, at the other extreme, are thought to have undergone little heating -- and therefore little change -- since the solar system formed, so most of them presumably are undifferentiated.  (The largest, Ceres, may be an exception.)

Asteroids have only come in for intensive study over the last quarter-century, because most of them are unresolved points of light in even the largest ground-based telescopes.  For example, here's a link to a movie, made by an amateur astronomer, of near-Earth asteroid 433 Eros; Eros is just a tiny point drifting against the backdrop of distant stars.

Note that the brightness of such a point generally varies with time, because asteroids rotate.  That is, an elongated asteroid will reflect more sunlight our way when its broad "side" is facing us and less when its small "end" has rotated around to face us.  One can learn the rotation period by measuring these brightness variations.  We also saw how one can combine visible and infrared brightness data to learn an asteroid's albedo and diameter.

Recently we have been able to do better for a handful of asteroids.  For example, the Hubble Space Telescope was used to confirm earlier suspicions that Vesta has a basalt crust that has had a large impact basin gouged into it; the olivine mantle is exposed within this basin.  This implies that Vesta was once hot enough to differentiate, since the crust chemically differs from the mantle.  Pieces of Vesta's crust have been collected here on Earth as meteorites.

Three main-belt objects (Gaspra, Ida, and Mathilde) have been viewed at close range by spacecraft passing by.  They are odd-shaped, heavily cratered bodies.  Ida has its own satellite, Dactyl, which isn't merely a piece chipped off Ida.  Mathilde has so many large craters that the impacts must have come close to destroying it; in fact, its density is so low that it is probably a shattered, porous "rubble pile" weakly held together by gravity.

(More recently we determined that near-Earth asteroid Itokawa is a rubble pile -- quite a surprise, since it's a small object with very weak gravity for holding together disconnected bits of rock.)

The other method used to study asteroids in detail is radar.  Echo strength rapidly weakens for distant objects, so the technique has been most useful for near-Earth asteroids.  (Why do I study main-belt asteroids instead?  Because life shouldn't be easy....)  The best method is "delay-Doppler" mapping, in which one measures not only when each bit of the echo is received (the delay), but also at what frequency it is received (the Doppler shift).  It's the same sort of thing that was done by Magellan for Venus, only we're operating from Earth rather than from an orbiting spacecraft.  Delay tells you about an object's size and topography, while Doppler shifts result from rotation; putting the two together enables us to figure out size, shape, rotation period, and rotation axis direction, among other interesting quantities.  Results for objects like Castalia show that these objects are odd-shaped, cratered, elongated, and (in the case of Castalia) bifurcated.

The above paragraph is a somewhat incomplete summary of our discussion of radar, so be sure to review the analysis of Kleopatra to see how this works for a concrete example -- no, make that a metallic example.  Remember, the reason that radar is so sensitive to metal content is that metal is much denser than rock, and surface layers with high average density ("bulk density") produce stronger echoes than low-density surfaces, all else being equal.

Most meteorites are thought to be pieces of asteroids, broken off in collisions and sent into orbits that eventually cross Earth's path.  Metal-rich meteorites (irons and stony-irons) are commonly found in museum collections, but if you go to Greenland and Antarctica, or if you limit yourself to meteorites that are actually seen falling to Earth, you find that that chondrites are in fact the most common variety.  Chondrites are stony meteorites that have undergone relatively little heating and other geochemistry (metamorphism) since first forming.  Most of us now think that ordinary chondrites are chips of S-class asteroids.  You should also know what carbonaceous chondrites are and why they're special.  Iron meteorites presumably come from metallic asteroids like Kleopatra.


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Icy Leftovers


Comets are the most primitive material in the solar system, being cold chunks of ice mixed with rocky material.  These "dirty snowballs" are comet nuclei: faint, nondescript leftovers from the formation of the solar system.  But their highly elongated orbits occasionally bring them close to the Sun, at which point the surface ice sublimates and produces the lovely glowing head and tails that everyone thinks of when comets are mentioned -- and, for some comets, meteors ("shooting stars") as a side effect.  (A meteor is simply a bit of rocky comet "dirt," released from the comet when the ice surrounding it sublimated, that gets in the way of Earth and heats up and glows due to atmospheric drag.)

Each time a comet passes close to the Sun, it loses some material, so it only takes a few hundred orbits before there's no more surface ice left to sublimate.  Hence the comets we see today can't possibly be the same comets that were around 4.5 billion years ago: There must be at least one "reservoir" of icy leftover planetesimals that constantly replenish our supply of comets.

Actually there are at least two such reservoirs.  Short-period comets like Halley, which take less than 200 years to complete a trip about the Sun, have orbits which are roughly coplanar with the planets' orbits.  These objects are thought to originate in the Kuiper Belt, the outer disk of our solar system beyond Neptune.  Hundreds of Kuiper Belt Objects (KBOs) have been discovered since 1992, including one, Eris, whose diameter is larger than Pluto's.  This discovery led to a year of debate on what constitutes a planet, culminating in the decision that Eris, Pluto, and Ceres (the largest asteroid) are "dwarf planets" rather than planets.

(Yes, I know: grammatically speaking, all dwarf planets must be planets, just as all foreign cars must be cars and all carnivorous animals must be animals.  The International Astronomical Union ignored grammar and defined "planet" and "dwarf planet" to be two mutually exclusive categories.  Sigh.)

Remember, when Pluto was announced as the ninth planet in 1930, it was thought to be about as massive as Earth, whereas we now know that it only has about 1/6 the mass of our Moon.  It also used to be thought that the presence of Pluto's moon -- Charon, discovered in 1978 -- was evidence that Pluto is a planet, but today we know that many asteroids and KBOs have satellites.

What methods were used to obtain the diameter of Eris?  What is the new, official definition of the term "planet"?

When an icy body -- a leftover planetesimal -- from the Kuiper Belt is gravitationally pulled into an elongated orbit that passes into the inner solar system, a short-period comet is born.  The several dozen known Centaur objects are thought to be in the middle of this transformation, as their orbits cross those of the outer planets.

Long-period comets like Hyakutake and Hale-Bopp typically have highly tilted orbits, so they must originate in a different reservoir, a spherical "cloud" of icy bodies rather than a flattened belt.  This is the Oort Cloud, whose trillion or so citizens are so distant that none of them has ever been observed.

The Stardust mission flew close to Comet Wild-2; what was the point of this mission, and what's been learned so far?


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Extrasolar Planets

We now know of nearly 300 planets around other stars -- including as many as five planets orbiting the same star!  The idea is that you look for tiny Doppler shifts in the absorption lines present in the star's spectrum: first blueshift, then redshift, then blue, then red, then....  This implies that the star is moving slightly back and forth as a planet orbits it and pulls on it.  Just as the Sun pulls on Jupiter, Jupiter pulls equally hard on the Sun; but because the Sun is so large it doesn't respond much to Jupiter's pull.  So it is for other stars with planets.

We discussed at length precisely how we can use these data -- Doppler shift as a function of time -- to figure out the semimajor axis and the eccentricity (degree of flattening) of the planet's orbit; we also get a lower bound (why?) on the planet's mass.  In some cases the data are too complex to be explained by a single planet, so we instead infer a planetary system with two or more members.

The Doppler method is biased towards massive planets orbiting close to their parent stars, because those are the planets that pull hardest on the parent stars and hence produce large, easily measured Doppler shifts.  And indeed we've found a fair number of "hot Jupiters."  Many of them are so absurdly close, however, that we've had to rethink our ideas on planetary system formation, which held that giant gas planets would have to form far enough away from the parent star that ices could solidify.  Ice would add to the rock and metal to give the forming planet's solid core enough mass (and hence gravitational pull) to gather in a massive Jupiter-style atmosphere.  This theoretical idea still makes sense to us, so we suspect that the hot Jupiters do indeed form at Jupiter-like distances and then "migrate" inward due to gravitational interactions with other planets, spiral density waves in the gas disk surrounding the newborn star, whatever.

(NOTE: Just because a method involves the Doppler effect doesn't mean that it's radar!  The Doppler technique for finding extrasolar planets has nothing whatsoever to do with radar.)

The prospects for life evolving and thriving on an Earthlike planet would appear to be dim in any planetary system in which a giant planet comes migrating through the neighborhood: The gravitational influence will make it hard for the Earthlike planet to maintain a stable orbit at a reasonable distance from the star.  The massive planets found to be in highly eccentric orbits would have equally ugly influences on terrestrial planets, threatening to make a close approach and gravitationally fling them into the deep freeze of interplanetary space.

We have found extrasolar planets that are "only" the mass of Uranus and Neptune, but smaller than that, the pull on the star gets too small for the star's motion to be reliably measured.  We'll need new telescopes and new techniques to detect Earth-like planets.

For example, how can we detect planets by the "transit" method?  What extra information does this give us that we wouldn't get from Doppler data alone?  Can you say a few words on what "gravitational microlensing" is and what we've found using this method?

OK, so some day, perhaps a decade from now, we find an Earthlike planet orbiting a Sunlike star: What do we look for to check if there's life on that planet?  A promising idea (albeit very, very difficult in practice!) is to use reflectance spectroscopy: take the faint starlight that's reflecting off the planet, spread it into its spectrum, and look for the absorption bands of particular gases in that planet's atmosphere.  Two gases that exist in Earth's atmosphere because of living organisms are oxygen, O2 (and its cousin ozone, O3), and methane, CH4.  Now, if you find absorption bands due to just one of these gases, perhaps you could come up with some other way of producing them that doesn't involve life.  But finding both oxygen and methane in the same atmosphere would be a sure sign that they're being pumped into that atmosphere on a daily basis.  Why?  Because they rapidly react with each other to produce carbon dioxide and water.  Why, then, are both gases found in Earth's atmosphere if they're so good at destroying each other?  Because life (living plants, decaying plants, cows, etc.) keeps producing them to replenish the supply.

(The practical difficulty of this technique is due to the extreme faintness of the planet relative to its parent star: the "firefly in the spotlight glare" effect.  Yet here we're proposing not merely to see the firefly but to analyze its light in detail!  Thus the technique relies on finding some advanced method of blocking the star's light without blocking the light of the nearby planet.  For example, the nulling interferometry method is discussed in an optional link.)

The Galileo spacecraft actually tried this out when it passed close to Earth (to get a gravity assist) on its way to Jupiter: it carried out spectroscopy on the sunlight reflecting from Earth in order to verify that there's life on Earth.  Perhaps some day we'll even verify the existence of intelligent life here. . . .


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