Transcript Lecture8
Chapter 7:Asteroids •Spatial and size distribution •Shapes, rotation and composition •Heating and cooling Detecting asteroids • In deep exposures, asteroids leave tracks across the image, as they move The asteroid belt • The main asteroid belt lies between Mars and Jupiter • Orbits are low-eccentricity and in the plane of the SS; but not as much so as the planets. Kirkwood Gaps • gaps in period distribution due to periodic “pull” from Jupiter these asteroids gradually moved out of resonant orbits Gaps and families • Groups of asteroids with similar orbital properties are called Hirayama families Probably consist of fragments of a single asteroid that suffered a collision Pieces break off with small random velocities, and spread out along original orbit Measuring asteroid sizes • • • Angular size of asteroids is very small, so not generally possible to measure sizes directly Amount of light reflected depends on size, distance and reflectivity (albedo) Compare infrared (reradiated) and optical (reflected) luminosities to determine albedo. Measuring albedos • First, we need to know how much solar flux is intercepted by the asteroid at its distance from the Sun, r. • The total energy reflected depends on both the cross section and albedo of the body. In the visible wavelength region we have: LSun f Sun (r ) 4r 2 lref AV f Sun (r )R 2 where R is the asteroid’s radius and AV is the visual albedo • Any flux not reflected is absorbed and will go to heating the asteroid which will then emit thermal radiation; so we can write: lth (1 AV ) f Sun (r )R 2 Measuring albedos • Now assume that the Earth is between Sun and asteroid (like the full Moon) and that we see the radiation reflected over 2π steradians. This means that what we actually observe is: f ref where d is the distance to the asteroid. At opposition: AV f Sun (r ) R 2 2 2d 2d 2 lref d=rasteroid-rSun • For the case of the thermal radiation from the asteroid we use similar logic, in this case assuming that the asteroid rotates rapidly enough that it is uniformly heated and the thermal radiation we observe is similarly normalized, this time by a factor of 4π: l (1 A ) f (r ) R 2 f th th 4d 2 Once we have measured fth and fref we can determine AV: V Sun 2 4d f ref f th AV / 2 2 AV (1 AV ) / 4 1 AV Albedos • Coal has an albedo of ~0.05. What is the ratio of emitted thermal energy, to reflected sunlight? If the coal is orbiting the Sun at a distance of 3 AU, what is its (thermal) luminosity per unit area? The largest asteroids Asteroid Sizes • A plot of the number of asteroids larger than a given diameter vs. diameter shows a slope which can be represented as a power law distribution of the form: D N ( D) N ( D0 ) D0 Dasteroid Number of asteroids >900 km 1 >800 km 3 >250 km 15 >150 km ~100 >30 km ~1150 >1 km ~100,000 • This is a characteristic distribution which results from an evolution due to collisions and fragmentation. Densities • Requires mass measurement, from orbiting spacecraft or small moons • E.g. Eugenia (below) Orbit of small moon can be measured. From this orbit we can get a pretty good mass estimate: 6x1018 kg Inferring a size from its brightness, we find a density of only about 1200 kg/m3. Probably a loosely bound rubble pile. Ida and Dactyl • • • • • Orbit: 428 million km Size: 58x23 km From (difficult) measurement of Dactyl’s orbit, mass is ~2.5x1017 kg. Density is therefore ~2600 kg/m3, about as expected for solid rock. Similar density found for Eros (right), visited by the NEAR spacecraft Asteroid densities Asteroid Density 1 Ceres 2050 2 Pallas 4200 4 Vesta 4300 16 Psyche 1800 20 Massalia 2700 45 Eugenia 1200 121 Herminoe 1800 243 Ida 2700 253 Mathilde 1300 433 Eros 2670 Low-density Mathilde: • Huge crater evidence of large collision • Probably broke up the asteroid, but it is still loosely held together Aside: Asteroid moons • Moons of asteroids were first detected indirectly, during occultations of distant stars • Close-up images of asteroids confirm that many do have moons. • This also explains the presence of adjacent impact craters on Earth, Moon and Mars that have the same age. E.g. Clearwater Lakes in Quebec. Now believed to be the result of a strike by an asteroid and its moon. Asteroid shapes • How can we measure the shape of an asteroid? A few have been visited by spacecraft, but most require indirect measurement • If an irregularly shaped asteroid is rotating, the size of the reflecting surface will vary with time. Changes in brightness can therefore be related to the shape (assuming the albedo is constant!) • E.g.: Gaspra Asteroid shapes • How to distinguish light-curve changes due to asteroid shape from difference in albedo? 1. Generally light-curve variations due to elongation will be more symmetric, than those due to “spottiness” 2. Compare reflected and re-emitted (thermal) radiation • • • Elongated: both components will peak at the same time Differences in albedo: dark side will be warmer and emit more infrared radiation Can also determine the orientation of the rotation axis: An elongated asteroid with rotation axis pointed directly at Earth shows no variation As Earth moves along in its orbit we see the asteroid from a different angle, thus see a change in the light curve variation Asteroid shapes • For some near-earth asteroids, we can use radar • This technique was applied to the asteroid Kleopatra Unusual, elongated shape may be the result of a collision Why are small bodies irregularly shaped? Calculate the maximum size a body can be before its gravity will pull it into a spherical shape. Rotation speeds What is the maximum rotation rate an asteroid may have, before it flies apart? Eros • In 2001, the NEAR mission made a soft landing on Eros • the majority of the small features that make up the surface of asteroid Eros more likely came from an unrelenting bombardment from space debris than internal processes. Itokawa • The Japanese robot probe Hayabusa recently landed on the Earthcrossing asteroid Itokawa; will return samples to Earth • Shows a surface unlike any other Solar System body yet photographed - a surface possibly devoid of craters. • One possibility is that the asteroid is a rubble pile, so craters get filled in whenever the asteroid gets jiggled by Earth. • Alternatively, surface particles may become electrically charged by the Sun, levitate in the microgravity field, and move to fill in craters. Break Spectroscopy reflectivity spectra different for different materials: (a) metallic feldspar (b) olivine (c) pyroxene (d) plagioclase feldspar Spectroscopy • matching asteroid and meteorite spectra shows that most meteorites are likely pieces of asteroids Asteroid Types • stony (S) and metallic (M) asteroids mainly in inner belt • carbonaceous (C) mostly at 3AU and farther • composition vs. distance trend mainly original – formation driven • igneous (once heated) much more common in inner belt • primitive (unaltered) mainly in outer belt Surface Heating • Radiation from the Sun heats the surface of planets, asteroids to a temperature that depends on distance. Assume a fraction (1-Av) of the solar flux is absorbed, and reradiated as a blackbody. Assume body is rotating, so is heated evenly all over surface 1/ 4 1 AV T 1 AIR 280 K d / AU 1/ 2 • What is the temperature of the piece of coal, orbiting at 3AU, assuming its infrared albedo is similar to its visible albedo? Moons and asteroids • Are moons distinct from asteroids, or are they the same thing? • Outermost moons of Jupiter, Saturn, Neptune and two moonlets of Mars: About half of these have retrograde orbits Low reflectivity, like the distant (>2.5 AU) asteroids • Phoebe (retrograde moon of Saturn) clearly a C-type (carbonaceous chondrite) asteroid • Others are controversial – in some ways resemble types of asteroids, but not others… could indicate that they are different from asteroids. Next Lecture: asteroids and comets • Asteroids Heat sources and transport • Comets: Their relation to asteroids and meteor showers Composition Formation of tails Origin and evolution