Transcript Chapter 3: the Sun

Chapter 5: Formation of planets
Disk shapes
We can see that many
disks are thinner in the
centre than the edges.
Why is this?
General properties of the Solar System
1. Patterns of motion: The theory must successfully explain the
orderly patterns of motion that we observe in the solar system.
 all planets orbit the Sun in the same direction and with nearly
circular orbits in nearly the same plane
 the Sun and most planets rotate in the same direction that they
orbit
 most large moons also orbit their planets in the same direction.
2. Two types of planets. Need to explain why planets fall into two main
categories: the small, rocky terrestrial planets near the Sun and the
large, hydrogen-rich jovian planets farther out.
3. Asteroids and comets. The theory must be able to explain the
existence of huge numbers of asteroids and comets and why these small
objects reside primarily in the regions we call the asteroid belt, the
Kuiper belt, and the Oort cloud.
4. Exceptions to the patterns. Finally, the theory must explain all the
general patterns while at the same time making allowances for the
exceptions to the general rules, such as the odd axis tilt of Uranus and
the existence of Earth's large Moon.
Solar nebula
Composition:
• Hot gas
• Dust grains: microscopic
rock or ice particles
• Planetesimals: small bodies
from which the planets are
made up.
• Protoplanet: large
precursor to a planet
Recall:
• There is a temperature gradient in the solar nebula
 Hotter near the centre, where the gas is denser, so gravitational
potential energy is not radiated away efficiently
Condensation
Metals
Rock
Hydrogen
compounds
H and He
gas
Examples
Iron, nickel,
aluminum
Various minerals
Water, methane,
ammonia
Typical
condensation
temperature
1000-1600 K
500-1300 K
<150 K
<< 50 K
Relative
abundance ( by
mass)
0.2%
0.4%
1.4%
98%
Comments
In all but hottest regions of the
nebula, these will be present in solid
form (mostly olivine and pyroxene)
Much of the
C,N,O get locked
up in these
compounds.
Always in the gas
phase in the solar
nebula.
CNO Ices
T (K)
>1000 K
Compound
Much of the O will be combined in
water molecules
>700 K
Most of the C will be in CO, while N will
be in N2.
300-700 K
C forms methane (CH4) rather than CO
<300 K
N may form some NH3 (this is a slow
conversion).
Theoretically computed variation
of temperature across the
primitive solar nebula:
• In the hot central regions, only metals
could condense out of the gaseous
state to form grains.
• At greater distances from the central
protosun, the temperature was lower,
so rocky and icy grains could also form.
Planet compositions
• Metal-rich rock has a typical density of ~5000 kg/m3.
• An estimate of the relative amount of rocky and icy material in
planets (excluding the gas giants) and moons can be obtained from
their average densities:
Planet or Moon
Approximate rocky
fraction?
Mean density
(kg m-3)
Mercury
5440
1
Venus
5250
1
Earth
5515
1
Moon
3340
0.58
Mars
3933
0.73
Europa (Jupiter)
2990
0.5
Dione (Saturn)
1440
0.1
Umbriel (Uranus)
1490
0.1
Pluto
2000
0.25
Mass of the Solar nebula
• We can estimate the minimum mass of the solar nebula, from the existing
planets.
 Assume solar nebula composition was initially the same as the present day solar
atmosphere.
 Need to estimate how many volatiles have been “lost” from each planet
• Minimum mass of the protoplanetary disk is about 0.03 MSun.
 Much of the mass may have been expelled during the T-Tauri phase
of the Sun’s formation
 Total mass was likely something like 0.15-0.4 MSun.
High-temperature refractories
• Carbonaceous chondrites formed 4.6 Gyr ago and have never been
heated since
 They include minerals from the time of their formation
• The Allende meteorite (fell 1969) includes (5-10%) irregular
inclusions of Ca-, Ti-, and Al-rich minerals.
 These high-T refractory materials are pieces of the first matter to
condense from the solar nebula, at ~1500K.
Major condensates
• At about 1400K, more abundant materials could condense
 Iron and nickel alloy
 Magnesium silicates (e.g. enstatite MgSiO3).
 Enstatite chondrites have much of this mineral, and most of their
iron is in the form of metal or sulfide rather than taken up as oxides
in silicates.
• As the temperature dropped,
feldspars formed
 Iron began to be oxidized
 Other reactions formed
olivine
 These reactions completed
when the nebula reached
~500 K.
 These make up most of the
material in ordinary
chondrites
Carbonaceous condensates
• In the most distant parts of the nebula, the temperatures
dropped even lower
 A graphite-like carbonaceous compound formed.
 This compound is found (spectroscopically) on the surfaces of many
asteroids in the outer belt and in the Kuiper belt.
 This material is the source of the carbonaceous chondrites
Break
Planet formation
• There are two main ways a planetesimal can
grow
 Solid body accretion: collisions between solid
particles often result in them sticking together.
This is a slow but sure process.
 Gravitational collapse: a sufficiently dense
protoplanet can accrete surrounding material (in
any state) quite rapidly (on the free-fall timescale).
Planetesimal formation
 Initially, planetesimals
form through:
a) Collisions of dust grains
due to differential
velocities through the gas
b) Collisions where the
cross-section is increased
due to gravitational
attraction.
Accretion
For particles of radius R, the time between
collisions is
  4R vn
2
1
Example
At a certain time in the development of the solar nebula, dust
particles have grown to a typical diameter of 0.1 mm. Their
relative velocities are ~0.1 m/s.
If the average mass density of dust in the nebula is ~10-3 kg/m3 and
individual grains have mass densities of r~100kg/m3 calculate the
mean time between collisions, and the typical mean free path.
Gravitational accretion
When the particles are massive enough, they can alter the paths of
other particles making a collision more likely.
• In this case a collision will occur if the initial path separation (or
impact parameter), a, is reduced so that A = r in drawing – and
this will depend on a combination of factors such as the relative
velocity of the two objects and the mass of the larger one.
• It can be shown that the collisional cross-section radius a is
given by
2 RGM
2
aimp  R 2 
2
v
Gravitational accretion
A meteor approaches Earth with a velocity of 0.75vesc. How much
greater is the gravitational cross-section, compared with the
geometrical cross section?
aimp  R 2 
2
2 RGM
v
2
Major collisions
• After planetesimals have swept up most of the surrounding
material, collisions can only occur if orbits change from being
nearly circular to being more eccentric
 This can occur as the collisions get larger and more violent.
 This is the final step in the formation of terrestrial planets. Some
of the final impacts were quite large:
 Such an impact may have ejected the material from which the Moon
formed
 Enormous impact sites (Caloris Basin on Mercury, Hellas & Argyle on
Mars) likely also resulted from massive collisions at this time.
• But: why are orbits today nearly circular??
Phobos
Mimas
Tethys
Asteroid Mathilda
Accretion or breakup?
Collisions will tend to break up a planetesimal if the kinetic energy
of the collision exceeds the gravitational binding energy of the
planetesimal.
For a uniform-density sphere, the gravitational binding energy is
3 GM 2
Eg 
5 R
So the body will break up if
1 2 3 GM 2
mv 
2
5 R
Breakup of Earth?
The largest relative velocity that could occur between Earth and a
bound member of the solar system is about 70 km/s.
How large a mass would have to hit Earth at this velocity, to
destroy it?
What is the impact parameter of this collision?
Giant planets
• After a rock-ice core with
mass about 10 times the mass
of earth formed, it could
accrete gas and dust from the
surrounding nebula by gravity.
• The accreting material would
form a disk around the planet,
out of which moons and rings
could form.
• Gravitational planet formation
takes place on approximately
the free-fall timescale, which
can be as short as a few
hundred years.
Captured moons
• Although many moons probably formed from a debris disk, some were likely
captured well after the epoch of planet formation.
• Often on inclined, retrograde orbits.
• Dark composition typical of carbonaceous asteroids/comets of outer solar
system
Phobos and Deimos:
moons of Mars
Phobos (small dark object) has a very different
albedo from Mars. Carbonaceous asteroid?
Origin of Moon
• Earth’s moon is very large,
0.012 times the mass of the
Earth.
 This ratio is 60 times larger
than for other satellites in
the SS
• Moon has much lower density
than Earth
 Earth has iron and nickel in its
core, which the moon lacks.
 Moon is richer in refractories,
lacks volatiles
• Best explanation is that a large
collision with a Mars-sized
planetesimal ejected (and
heated) mass from Earth’s
outer regions
 This formed debris disk which
coagulated to form the moon.
Fate of Planetesimals
1. Ejection from the SS
•
Many icy bodies from the outer
solar system expelled to the Oort
cloud
2. Collision with Planets
•
Densely cratered surfaces show
evidence for heavy bombardment
3. Capture into Satellite or resonant
orbits
•
Extended atmospheres or
satellites of protoplanets can be
effective at capturing material
4. Fragmentation
•
As collisions get more energetic,
fragmentation becomes more
common than aggregation