924 Elementary Problems and Answers in Solar System Astronomy

Answers to Chapter 6. Asteroids, Comets, and Meteoroids

ANSWERS TO CHAPTER 6 Asteroids, Comets, and Meteoroids 730. (b) A minor planet. 731. A minor planet. Most of the known asteroids are in more or less circular orbits near the plane of the ecliptic with semimajor axes (median value 2.7 AU) between those of Mars and Jupiter. 732. (c) Size. 733. Over 3,000. 734. See answer to problem 731. 735. (a) 4.4 years. 736. (b) 2.9 years. 225 226 / Asteroids, Comets, and Meteoroids 737. Principally by its movement relative to the star field. Also by characteristic spectral modification of reflected sunlight and by cyclic variation in brightness, the latter because of rotation of a nonspherical body having perhaps also a variable albedo over its surface. 738. (c) Juno. 739. (a) An asteroid. 740. (b) Europa. (False) 741. 5.67 m S-I. 742. The gravitational field of an asteroid is too weak to retain an atmosphere. Stated otherwise, the gravitational escape speed is less than the typical speed of a molecule of gas. 743. 1.25 pounds. 744. 0.20. The fraction of sunlight reflected is equal to the albedo A and the fraction absorbed and then emitted in the infrared is (1 - A). In this problem (1 - A)/A = 4. 745. (d) A special class of asteroids. 746. (c) lllustrate a special solution of the three-body gravitational problem. 747. (b) Are near the Lagrangian points L4 and L5 relative to the Sun and Jupiter. 748. By observing the cyclic variation of its brightness. 749. (b) Observing cyclic variations in their brightness. Asteroids, Comets, and Meteoroids / 227 750. There is substantial geological evidence that a large asteroid struck the Earth at that time, presumably causing a cloud of dust and smoke in the atmosphere that persisted for many years and caused a marked cooling of the Earth's lower atmosphere and surface. A large, buried crater in the Yucatan Peninsula of Mexico is tentatively identified as the impact site. 751. An asteroid is an inert rocky or metallic body whereas a comet consists of frozen light compounds (H2 0, CO2 , CH4 , etc.) and inert dust such that a mixture of gas and dust is emitted from its nucleus as it approaches the Sun and is heated by sunlight. 752. 2 million years. 753. (b) 2.0 x 106 years on its inbound flight to perihelion. 754. (c) The orbit of a comet can be determined by observing its motion on the star field and using Kepler's laws. 755. Kepler's laws are assumed to be applicable to its motion. 756. (c) Have prograde orbits. (Comet Halley in a retrograde orbit is a noteworthy exception.) 757. (d) The orbit of a comet can be determined by observing its motion on the star field. 758. The propulsive force resulting from the emission of gas and dust as the comet approaches the Sun (sometimes referred to as the nongravitational force and generally impossible to predict). 759. (d) Have orbits inclined at more-or-Iess random angles to the ecliptic plane. 760.• It arrived from outside the solar system or • Its orbit was converted from a near-parabolic or elliptical orbit to a hyperbolic one in a close flyby of Jupiter or another major planet (gravitational assist). See answer to problem 127. 228 / Asteroids, Comets, and Meteoroids 761. (b) Have prograde orbits. (Comet Halley in a retrograde orbit is a noteworthy exception.) 762. 28 AU. 763. By a close flyby of Jupiter or another major planet (gravitational assist). See answer to problem 127. 764. As a comet approaches the Sun, its nucleus is progressively heated by sunlight and there is a correspondingly increased rate of emission of gas and dust. 765. (a) Solar heating of volatile constituents. 766. See answer to problem 767. 767. The value n = 2 for asteroids (inert bodies) corresponds to the inverse square dependence of the intensity of sunlight on R. In contrast, the effective reflecting area of comets increases as they approach the Sun because of the increasing emission of gas and dust from their nuclei; this effect causes n to be greater than 2. 768. 2 billion. If a sphere of radius R is disintegrated into n identical smaller spheres, each of radius r, The ratio of the sum of the projected areas of the small spheres to the projected area of the large sphere is The increase in reflected sunlight (if no shadowing) is by this same factor...