Chapter 5: Formation of planetsChapter 5: Formation of planets

Disk shapesDisk shapes

We can see that many disks are thinner in the centre than the edges. Why is this?

General properties of the Solar SystemGeneral 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 nebulaSolar 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

CondensationCondensation

 

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 IcesCNO Ices

T (K) Compound

>1000 K 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 compositionsPlanet 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

Mean density (kg m-3)

Approximate rocky fraction?

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 nebulaMass 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 refractoriesHigh-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 condensatesMajor 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 condensatesCarbonaceous 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

BreakBreak

Planet formationPlanet 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 formationPlanetesimal 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.

AccretionAccretion

For particles of radius R, the time between collisions is

124

vnR

ExampleExample

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 ~100kg/m3 calculate the mean time between collisions, and the typical mean free path.

Gravitational accretionGravitational 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

222 2

v

RGMRaimp

Gravitational accretionGravitational 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?

222 2

v

RGMRaimp

Major collisionsMajor 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??

Asteroid MathildaMimasPhobos Tethys

Accretion or breakup?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

R

GMEg

2

5

3

So the body will break up if

R

GMmv

22

5

3

2

1

Breakup of Earth?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 planetsGiant 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 moonsCaptured moons

Phobos and Deimos: moons of Mars

• 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 (small dark object) has a very different albedo from Mars. Carbonaceous asteroid?

Origin of MoonOrigin 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 PlanetesimalsFate 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