Chapter 7: Asteroids and CometsChapter 7: Asteroids and Comets

Review: asteroidsReview: asteroids

•Mostly rocky bodies•Found in the asteroid belt between Mars and Jupiter

Also the Trojans at the Jupiter Lagrangian points

•The source of most meteorites Asteroids get perturbed from their orbits, into Earth-crossing

trajectories

SpectroscopySpectroscopy• reflectivity spectra different

for different materials• matching asteroid and

meteorite spectra shows that most meteorites are likely pieces of asteroids

Asteroid TypesAsteroid 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

Moons and asteroidsMoons and asteroids

•Are moons distinct from asteroids, or are they the same thing?

•Consider the outermost moons of Jupiter, Saturn, Neptune and two moonlets of Mars

Surface HeatingSurface 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 at a distance r, and reradiated as a blackbody.

Assume body is rotating, so is heated evenly all over surface

2/1

4/1

/

280

1

1

AUr

K

A

AT

IR

V

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

Internal Heat SourcesInternal Heat Sources

•Gravitational energy?

R

GMEg

2

5

3

•For Ceres, what is the maximum temperature increase possible from gravitational assembly?

• The heat capacity of typical rock is

KkgJcV //840

Impact HeatingImpact Heating• Two asteroids orbit the Sun in virtually identical

orbits. One has a radius of 40 km and a density of 3300 kg/m3. The other has a radius of only 100 m, and the same density. Due to a small difference in initial velocity, the two asteroids approach each other and are attracted gravitationally.

• How much heating might be expected from this collision?

Internal heat sourcesInternal heat sources

• Radioactive heating? Unstable isotopes present in solar or carbonaceous chondrite

mixture can be powerful sources of energy Especially at earlier times when more of the radioactive isotope

was available.

Isotope Half-life(109 yr)

Isotope fraction in

present-day chondrites

Element abundanc

e

Heating rate

Isotope(J/yr/kg)

Chondrite (J/Gyr/kg)

40K 1.25 0.00011 5.6x10-4 920 5.7x104

87Rb 50.0 0.293 2.2x10-6 0.544 3.51x102

232Th 13.9 1.00 2.9x10-8 837 2.4x104

235U 0.71 0.0072 8.2x10-9 18000 1.1x103

238U 4.5 0.993 8.2x10-9 2970 2.4x104

Total: 1.1x105

ConductionConduction

where A is the surface area, dx is the distance over which the heat is transmitted, kc is the thermal conductivity of the material.

dx

dTAk

t

Qc

For a spherical asteroid, radius R, assume the surface temperature is T=0, and the T gradient is linear. How long will it take to radiate away all its internal energy?

In solid rock, the main method of heat transport is conduction. The rate of heat loss (dQ/dt) is related to the conduction efficiency and temperature gradient:

Cooling timesCooling times

•For rocky material, the thermal diffusivity kc/ρcv=1x10-6m2/s so τyr~1x104Rkm

2 A body the size of an asteroid (R~500 km) will lose any internal

energy in less than ~2.5 Gyr.

c

v

k

cR

tQ

U

3~)/(

~2

Note that while the heat acquired in various ways is proportional to mass (and thus R3), the heat radiated away is proportional to surface area (thus R2). smaller bodies preferentially cool faster.

BreakBreak

HeatingHeating

•Consider the equilibrium case where the internal heating rate changes slowly, relative to the cooling rate.

•Assuming a roughly linear temperature gradient:

R

TT

dx

dT surfacecore

• The rate of heat loss is given by:

R

TTRk

t

Q surfacecorec

24

• If l=L/M is the heat production per mass (W/kg) then setting the total heating rate lM equal to the cooling rate gives:

Rk

MlTT

TTRkt

QlM

csurfacecore

surfacecorec

4

4

E.g. CeresE.g. Ceres

Estimate the core temperature of Ceres, assuming it is in equilibrium with the flux of radiation from the Sun.

You will need the following information:

The mass is M=9.5x1020 kgThe diameter is D=1000 km.For typical carbonaceous chondrites, the energy produced by

radioactivity is L/M~4x10-12 W/kg, and the thermal conductivity is kc=3W/K/m

CometsComets•Comet Hale-Bopp in 1997, photographed at Mono Lake, CA

The nature of cometsThe nature of comets

•Comets are distinguished from all other SS bodies by their appearance which includes a bright coma and long tails

•The appearance of a comet changes as it moves through its orbit, becoming brighter as it approaches the Sun and fainter again as it moves away.

Asteroid or Comet?Asteroid or Comet?

• The only distinction between asteroids and comets is the presence of a Coma and tail

These features get dimmer as a comet moves farther away from the Sun. E.g. comet Wilson-Harrington, discovered in 1949, was “rediscoverd” in

1979 as an asteroid. Similarly, the asteroid 2060 Chiron moves in a cometlike orbit, and in

1988 it came closer to the Sun and became brighter and more cometlike.

• Coma and tail are caused by sublimation of ice. Thus distinction is simply one of ice content.