Asteroids

14. Asteroids (Minor Planets)

Bode’s Law (The Titius - Bode Law)
Write down the series 0, 3, 6, 12, 24, 48, ...... add 4 and divide by 10. You get the Titius-Bode...

series	a (AU)	Planet
0.4	0.387	Mercury
0.7	0.723	Venus
1.0	1.000	Earth
1.6	1.524	Mars
2.8		The gap
5.2	5.203	Jupiter
10.0	9.539	Saturn
19.6	19.18	Uranus
38.8	30.6	Neptune
77.2	39.4	Pluto

All you have to do is memorize Titius’ progression and you can work out the planetary distances (except for Neptune and Pluto). Just remember "three and four".

This relation is from ~1772, just in time to predict where Uranus would be. When Uranus was accidentaly discovered by Herschel in 1781 at just the right distance this got Bode and other astronomers to take the gap at 2.8AU seriously. Astronomers started looking for a "dark planet" at a distance of 2.8AU. (And they started looking for Neptune at the 38.8AU distance -- hmmm.)

Discovery

In 1801 Piazzi discovered Ceres. He wrote of his discovery to Bode who suspected this was the missing planet. Unfortunately, Ceres was lost as it moved into superior conjunction. It was recovered by a method just worked out by Gauss.

Gauss invented Gauss's method of orbit determination. Given three observations (spaced far apart enough in time -say- days) of a body (not along a great circle) its orbit can be determined. Using this procedure Von Zach rediscovered Piazzi’s object, Ceres.

A year later, Olbers (of the paradox fame) found a second object (Pallas) at about the same distance. As time passed, more and more were found. When astrophotography was introduced (Max Wolf, 1891) discovery of minor planets became a routine thing. Now some astronomers consider them nuisances!

Asteroids are rocky fragments left over from the formation of the solar system about 4.5 billion years ago. Most of these fragments of ancient space rubble-(sometimes referred to as minor planets) can be found orbiting the Sun in a belt between Mars and Jupiter. This region, called the Asteroid Belt or Main Belt, contains thousands of asteroids ranging widely in size from Ceres, which at 940 km in diameter is about one-quarter the diameter of our Moon, to bodies that are less than 1 km across.

These bodies infrequently collide and fragment gradually chipping away at each other. They are heavilly cratered, many are quite oblong and a number are "binary asteroids" or asteroids with moons such as Ida and Dactyl. The "chips" gradually spiral into the sun. (The Poynting-Robertson effect will drag a 1mm diameter particle into the sun from the main belt in 10 million years and a 10cm rock in 100 million.)

Orbits
Revolving around the Sun in eccentric orbits, occasionally close encounters with a planet or another asteroid change the asteroid's orbits, knocking them out of the Main Belt and hurtling them into space across the orbits of the planets. Scientists believe that stray asteroids or fragments of asteroids may have slammed into Earth in the past, playing a major role both in altering the geological history of our planet and in the evolution of life on it. Some even surmise the extinction of the dinosaurs 65 million years ago may have been linked to a devastating asteroid impact near the Yucatan peninsula in Mexico.

Most minor planets have ordinary prograde orbits with 2.3 < a < 3.3 AU. A few have large i (Betulia has i~52° )

Icarus has the smallest a, (1.0777AU) and the highest e (0.83)

Hidalgo has the largest a (5.82, greater than Jupiter’s) and second highest e (0.66).

A number of minor planets have orbits which cross the earth’s orbit (the Apollo family). Is Icarus one? Why?

Kirkwood’s Gaps
Saturn’s ring system has gaps. Why? Because of perturbations by its moons? Now we think it is due to shepherding satellites. But the asteroid belt also has gaps, predicted by Kirkwood. These gaps are due to perturbations by Jupiter. Any object with an integral ratio of orbital period to Jupiter's 11.86 year period will be systematically perturbed by Jupiter and "encouraged to move along". What distance would you need for a 2:1 resonance? If P=11.86/2 then a=cube root of 5.93 squared or a=3.28AU. Sure enough, no asteroids are found at this distance. Ditto for 3/1, 4/1, 4/3, 5/2, 5/3... And just the opposite for ratios like 1/1 (the Trojans) and 3/2 (the Hilda group) which actually encourages asteroids to stick around in groups or families.

Earth Crossing (Apollo) Asteroids

Some asteroids pass very close to Earth's orbit around the Sun. Scientists have found evidence that asteroids have hit our planet in the past. Usually, asteroids and smaller debris called meteoroids are too small to survive the passage through Earth's atmosphere. When these burn up on their descent, they leave a beautiful trail of light known as a meteor or "shooting star." Larger asteroids occasionally crash into Earth, however, and create craters, such as Arizona's mile-wide Meteor Crater near Flagstaff and the Henbury craters near Alice Springs. Another impact site off the coast of the Yucatan Peninsula in Mexico, which is buried by ocean sediments today, is believed to be a record of the event that led to the extinction of the dinosaurs 65 million years ago. Fortunately for us, these big asteroid impacts are rare. A smaller rocky meteoroid or comet less than 100 yards in diameter is believed to have entered the atmosphere over the Tunguska region of Siberia in 1908. The resulting shockwave knocked down trees for hundreds of square miles.

By the way, it is pretty certain that comets are really weak ("dirty snowballs") and it is likely that by the time a comet gets within 10,000km of ground zero (we call this Judgement Day) it will be torn apart by tides. Is this what happened in Tunguska? Hit by a huge steam and waterball travelling 30km/s?

Appearance
The first close-up images of asteroids were captured in 1991 and 1993 by the Galileo spacecraft when it flew by two asteroids in the Main Belt on its way to Jupiter. Its pictures of asteroids Gaspra and Ida showed them to be irregularly shaped objects, rather like potatoes, riddled with craters and fractures, 19 km long and 52 km long respectively. Galileo also discovered that Ida has its own moon, Dactyl, a tiny body in orbit around the asteroid that may be a fragment from past collisions.

Composition
In the last few decades, astronomers have used spectroscopes to determine the chemical and mineral composition of asteroids by analyzing the light reflected off the asteroids' surfaces. Another method used to study the makeup of asteroids is by examining meteorites. Meteorites are chunks of space debris that fall to Earth and are believed to be bits of asteroids or comets.

Most asteroids are made of rock, but some are composed of metal, mostly nickel and iron. They range in size from small boulders to objects that are hundreds of miles in diameter. A small portion of the asteroid population may be burned-out comets whose ices have evaporated away and been blown off into space.

Most of what we know about asteroids comes from visual/infrared/radar observations and the assumption that most meteorites are asteroid chips. At present (1999) it seems that asteroids can be divided into distinct classes C, S, M, D and U.

Three-quarters of all belt asteroids are as reflective as pitch, "grey asteroids", designated "C". The asteroids 1-Ceres and 2-Pallas are type C and the spectra of type C asteroids resembles that of the carbonaceous chondrite class of meteorites.

Ten percent of all belt asteroids have spectra resembling stony-iron meteorites, relatively high reflectivity and reddish color, and are designated "S". The asteroid 3-Juno and most Apollo asteroids are type S. The type S asteroids are of order 100km and are found in the belt region closest to Mars.

Very few asteroids have a reflectance spectrum similar to iron meteorites, not surprising since few meteors are irons, and are designated "M" for metallic. The 250 km diameter asteroid 16-Psyche is one such.

But a number of asteroids have type M spectra but low reflectivities, the dark or type "D" asteroids. Found throught the belt, there is a concentration near Jupiter and some Trohans are thpe D.

And as many as 10% of asteroids such as 4-Vesta are just "U"nclassifiable.

SUPERNOVA TRIGGER
Now there is one puzzling thing about the metallic asteroids (which we suppose are responsible for the rare iron and stony-iron meteorites in museums). How in the solar system was a body a few hundred km across able to generate a molten core? The larger bodies like Earth were heated by the decay of long-lived radioisotopes such as U-235, U-238, K-40 and RB-87. But the heat generated by a small body would leak away too fast to build up appreciable heat in the core.
Could it be (hold on to your mouse, here we go) that when the solar system was formed there were short-lived radionucleides present? One line of support for this comes from the Allende meteorite which has an anomolously large amount of Mg-26. Now Mg-26 is stable but could come from the rapidly decaying isotope Al-26 (half life 740,000 years). Where would such short lived isotopes come from? Supernova! A supernova explosion could have enriched and actually caused the colapse and very formation of the solar system.

This is not too far-fetched. If you look at -say- the ratio of U-235 to U-238 and run the law of radioactive decay backwards then nearly five billion years ago the ratio was nearly unity, about what one expects of recent supernova debris. And the radioisotopes did have to come from a supernova event in any case. It just works out so neat if the supernova occurred right at the birth of the solar system. Then the short lived radioisotopes would melt the cores of small planetismals and we would have Allende meteorites. Like we do.