Chapter 7:Asteroids

1
Chapter 7Asteroids

• Spatial and size distribution
• Shapes, rotation and composition
• Heating and cooling

2
Detecting asteroids

• In deep exposures, asteroids leave tracks across
  the image, as they move

3
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.

4
Kirkwood Gaps

• gaps in period distribution due to periodic
  pull from Jupiter
• these asteroids gradually moved out of resonant
  orbits

5
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

6
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.

7
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 asteroids 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

8
Measuring albedos

• Now assume that the Earth is between Sun and
  asteroid (like the full Moon) and that we see the
  radiation reflected over 2p steradians. This
  means that what we actually observe is

where d is the distance to the asteroid. At
opposition drasteroid-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 4p

• Once we have measured fth and fref we can
  determine AV

9
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?

10
The largest asteroids
11
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

• This is a characteristic distribution which
  results from an evolution due to collisions and
  fragmentation.

12
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.

13
Ida and Dactyl

• Orbit 428 million km
• Size 58x23 km
• From (difficult) measurement of Dactyls 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

14
Asteroid densities

• Low-density Mathilde
• Huge crater evidence of large collision
• Probably broke up the asteroid, but it is still
  loosely held together

15
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.

16
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

17
Asteroid shapes

• How to distinguish light-curve changes due to
  asteroid shape from difference in albedo?
• Generally light-curve variations due to
  elongation will be more symmetric, than those due
  to spottiness
• 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

18
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

19
Why are small bodies irregularly shaped?

• Calculate the maximum size a body can be before
  its gravity will pull it into a spherical shape.

20
Rotation speeds

• What is the maximum rotation rate an asteroid may
  have, before it flies apart?

21
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.

22
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.

23
Break
24
Spectroscopy

• reflectivity spectra different for different
  materials
• metallic feldspar
• olivine
• pyroxene
• plagioclase feldspar

25
Spectroscopy

• matching asteroid and meteorite spectra shows
  that most meteorites are likely pieces of
  asteroids

26
Asteroid Types

• igneous (once heated) much more common in inner
  belt
• primitive (unaltered) mainly in outer belt

• 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

27
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

• What is the temperature of the piece of coal,
  orbiting at 3AU, assuming its infrared albedo is
  similar to its visible albedo?

28
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.

29
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