Chapter 7:Asteroids Spatial and size distribution Shapes, rotation and composition Heating and cooling.

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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: where R is the asteroid’s radius and A V 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:

Measuring albedos 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: Once we have measured f th and f ref we can determine A V : 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: where d is the distance to the asteroid. At opposition: d=r asteroid -r Sun

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 asteroid Number of asteroids >900 km1 >800 km3 >250 km15 >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: 6x10 18 kg  Inferring a size from its brightness, we find a density of only about 1200 kg/m 3.  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 ~2.5x10 17 kg. Density is therefore ~2600 kg/m 3, about as expected for solid rock. Similar density found for Eros (right), visited by the NEAR spacecraft

Asteroid densities Low-density Mathilde: Huge crater evidence of large collision Probably broke up the asteroid, but it is still loosely held together AsteroidDensity 1 Ceres2050 2 Pallas4200 4 Vesta4300 16 Psyche1800 20 Massalia2700 45 Eugenia1200 121 Herminoe1800 243 Ida2700 253 Mathilde1300 433 Eros2670

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 Earth- crossing asteroid Itokawa; will return samples to Earth June 2010 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-A v ) of the solar flux is absorbed, and reradiated as a blackbody.  Assume body is rotating, so is heated evenly all over surface 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

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