The Shapes and Spins of Kuiper Belt Objects Lacerda, Pedro Citation Lacerda, P. (2005, February 17). The Shapes and Spins of Kuiper Belt Objects. Retrieved from https://hdl.handle.net/1887/603 Version: Corrected Publisher’s Version Licence agreement concerning inclusion of doctoral thesis in the License: Institutional Repository of the University of Leiden Downloaded from: https://hdl.handle.net/1887/603 Note: To cite this publication please use the final published version (if applicable). CHAPTER 1 Intro d u ctio n 1.1 T h e o rig in o f co m e ts efo r e the X V IIth cen tu ry comets were seen as porten ts of d ivin e will, sen t Bby the g od s to pu n ish man k in d . N ewton (1 6 8 6 ) showed that the paths of these wan d erin g celestial objects were actu ally very well d e¯ n ed , an d obeyed the u n iversal law of g ravitation . N ewton 's theory, u n d ou bted ly on e of the g reatest achievemen ts of hu man in tellect, su ccessfu lly d escribes the motion s of the moon arou n d the E arth, of the plan ets arou n d the S u n , of the S u n arou n d the cen ter of ou r g alax y, an d so on an d so forth. M ak in g u se of N ewton 's laws, H alley (1 7 0 5 ) proposed that three comet ap- parition s in 1 4 5 6 , 1 5 3 1 , an d 1 6 0 7 were actu ally three retu rn s of the same comet. H e pred icted that the heaven ly bod y shou ld revisit the in n er solar system in 1 7 5 8 . The comet retu rn ed arou n d C hristmas of 1 7 5 8 , twelve years after H alley's d eath, an d has been called H alley's C omet ever sin ce. B u t u n d erstan d in g how comets move was on ly the ¯ rst step. H u man s are cu riou s bein g s, an d thereby beg an q u estion in g . W hat are comets? W here d o they come from? A ristotle (3 8 4 { 3 2 2 B C ) was the ¯ rst man that tried to ex plain comets as somethin g physical. H e specu lated they were atmospheric phen omen a| lu min ou s clou d s of g as| that becau se of their tran sien t charac- ter cou ld n ot be part of the perfect realm of the heaven s. A ristotle called them kometes, which mean s \ wearin g lon g hair" in an cien t G reek . A s with most scien ti¯ c d isciplin es, the A ristotelian way of thin k in g su rvived u n til the R en aissan ce. In the late X V th cen tu ry n atu ral philosophers recog n ized that ob- servation is an essen tial tool in u n d erstan d in g n atu ral phen omen a. The work s of L eon ard o d a V in ci (1 4 5 2 { 1 5 1 9 )| who was probably the u ltimate observer of n atu re| ex emplify how mu ch can be learn t from d etailed observation of the su rrou n d in g world . The pion eer in accu rate astron omical observation s was the D an ish astron omer Tycho B rahe. In 1 5 7 7 he u sed observation s of a comet mad e 2 Introdu ction Figure 1 .1 { Histogram of th e reciprocal semi-major ax es of comet orbits, in astron omical u n its. R eprod u ced from O ort & S ch mid t (1 9 5 1 ). from di® erent locations in Europe, to test the hypothesis of Aristotle. The small observed parallax1 indicated that the comet had to be much further out than the Earth's atmosphere|even further than the Moon. As the number of observed comets increased, statistical analysis of their orbits became possible. Astronomers have divided the comets into two classes, according to their orbital period: the sh ort-period comets, with periods shorter than 200 years, and the long-period comets, with periods longer than 200 years. The orbits of comets in each class are quite di® erent. Short-period comets have prograde2 orbits which lie close to the plane where planets move. This plane is called the ecliptic, and is de¯ned as the plane of the orbit of the Earth. By contrast, the long-period comets come into the inner regions of the solar system from all directions|there is no preferred orbital plane. Furthermore, their long orbital periods indicate that they come from large distances, as a consequence of K epler's 3rd law of orbital motion. The director of the Sterrewacht Leiden from 1945 to 1970 was J an Hendrik O ort. By the time of his appointment, O ort had already made key contributions to astronomy. He had observationally con¯rmed, and analytically described the rotation of the Milky Way3 (O ort 1927), following a hypothesis by Lindblad (1925), and had made important contributions to the theory of dark matter (O ort 1940). In the fall of 1948, a P hD student of O ort, van Woerkom, obtained his doctor degree with a dissertation titled \O n the origin of comets". The work of his student got O ort pondering on the subject. A little over a year later he published his conclusions (O ort 1950). The high frequency of comet orbits with very small reciprocal semi-major axes (see Fig. 1.1) led O ort to propose 1T h e apparen t d i® eren ce in position of a bod y on th e sk y (relativ e to th e back grou n d stars) as seen from d i® eren t poin ts of observ ation . 2A ll plan ets orbit th e S u n in th e same d irection , u su ally called d irect or prograd e. 3T h e M ilk y Way is th e h ome galax y to ou r solar system; it is a spiral galax y, con tain in g some 1 0 0 billion (1 0 11) stars. The S ha pes a nd S pins of K B O s 3 the existence of a vast spherical swarm of comets extending to a radius of about 150 000 astronomical units4. Oort ¯gured that this spherical cloud is occasionally be perturbed by stars passing close to the Sun. As a result, some comets are ejected to interstellar space, and some fall into the inner solar system along nearly parabolic orbits. The latter become the visible comets. The idea prevailed and the spherical reservoir became known as the \Oort cloud". Although its existence cannot be observationally con¯rmed, the Oort cloud provides the best explanation of the observed distribution of the orbits of long-period comets. U ntil late-1970s it was believed that short-period comets also originate in the Oort cloud. The evolution of cometary orbits, from randomly-oriented long- period to prograde low-inclination short-period trajectories, was attributed to perturbations by the giant planets, particularly Jupiter. It was necessary, how- ever, to demonstrate that such evolution is possible, and that it correctly predicts the observed number of short-period comets. The work of van Woerkom (1948) was partly an attempt to show that long-period comets could be brought into short-period orbits due to perturbations by Jupiter. His theoretical calculations predicted that this process was a factor »20 less e± cient than needed to explain the observed frequency of short-period comets. With the advent of computers the complex analytical calculations of orbital evolution became complemented by numerical simulations. Everhart (1972, 1973, 1977), who favoured the idea that all comets originated from nearly parabolic orbits, used Monte Carlo simulations to show that a fraction of long-period comets with perihelia close to the orbit of Jupiter (»5 AU ) could evolve into short-period orbits. As in van Woerkom's work, the e± ciency of the process was too low. Besides, neither Everhart nor van Woerkom could convincingly explain the preponderance of prograde orbits among short-period comets. Alongside the question of the origin of the short-period comets, there re- mained the issue of the origin of comets altogether: of where they formed. The- ories of a possible interstellar origin had been dismissed by van Woerkom (1948) on the basis that no comet had ever been found to have a hyperbolic orbit. Comets must have formed in the Solar System. Important clues to the origin of comets came from the work of Fred Whipple. He presented a model of the chemical composition of comets (Whipple 1950) consisting mainly of ices of H2O, NH3, CH4, CO2, CO, and other volatiles, \polluted" by smaller amounts of re- fractory5 material in the form of dust. This model, popularized by Whipple as \dirty snowball", explained the tails and com½ 6 of comets upon approaching the Sun. Due to the temperature increase, the icy material sublimates and becomes partly ionized|forming the coma and ion tail|and forces solid particles o® the surfaces of comets, which form the dust tail.