Transcript Chapter 3: the Sun - University of Waterloo

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:
2
lref  AV f Sun (r )R
LSun
f Sun (r ) 
4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
2d
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
4d 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 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-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 
280K
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