1. Lecture 9 The Solar System
Our Place in the Cosmos
Lecture 9
The Solar System

2. Definition
The Solar System comprises the Sun and all objects gravitationally bound to it
It includes the planets, their moons, asteroids, comets, gas and dust

3. Formation
Clues:
Orbits of the planets lie close to a single plane
All planets orbit the Sun in the same direction
Meteorites are formed from from small fragments
These clues suggest that the Solar System began as a rotating disk of gas and dust, with larger bodies forming from aggregation of smaller bodies

4. Formation HST images of newly formed stars show accretion disks
The Solar system probably formed from the Sun’s accretion disk
Thus study of the formation of the Solar System is closely linked with the formation of the Sun, and with star formation in general

6. Sun’s Formation
Around 5 billion years ago, newly-formed Sun was still a protostar - a large ball of gas whose collapse converts gravitational energy to thermal energy
Surrounding the protostar was a flat, orbiting disk of gas and dust - a protoplanetary accretion disk, containing about 1% of the mass of the protostar

8. Why Disks?
A rotating object possesses a quantity called angular momentum
Angular momentum depends on:
rotation speed
mass
mass distribution
Just as the linear momentum p = mv of an object moving in a straight lines is conserved (ie will remain unchanged until an external force acts upon it, Newton’s 1st law of motion), angular momentum is also conserved

9. Spherical Collapse
Suppose that an approximately spherical cloud of interstellar gas is collapsing due to self-gravity
Cloud would maintain its spherical shape except for its angular momentum
Interstellar clouds are several light-years in size
Tidal forces from other objects “stir” them up and give them some rotation
Due to large extent of cloud, even very slow rotation corresponds to huge angular momentum
As cloud shrinks, in order for angular momentum to be conserved, rotation rate must speed up [cf a spinning ice skater pulling in their outstretched arms]

10. Spherical Collapse
Suppose that a cloud about 1 light-year (1016 m) across takes one million years to complete one rotation
By the time such a cloud has collapsed to the size of the Sun (109 m across, or one ten-millionth of the size of the original cloud), it will be rotating 50 trillion times faster, rotating once every 0.6 seconds
This is 3 million times faster than Sun’s actual rotation speed
Why isn’t the Sun rotating faster?

11. Non-Spherical Collapse
Cloud’s angular momentum opposes collapse towards rotation axis but allows collapse parallel to axis
An initially spherical, rotating cloud will thus collapse not into a ball, but into a flattened “pancake” structure which becomes the accretion disk
Infalling (accreting) material arrives first at the accretion disk before becoming part of the central star

13. Accretion Disk Formation
As material falls towards forming star it travels on elliptical orbits as predicted by Newton’s law of gravity
However when material reaches the centre of the cloud, it runs into material falling in from the opposite direction
The material piles up in the centre
Vertical motions cancel but rotational motion remains, resulting in a rotating accretion disk
Angular momentum of infalling material is transferred to the disk

14. Material rains down from collapsing, rotating cloud
Vertical motion of material from above and below cancels…
…leaving net rotational motion

15. Forming Structures
Small dust particles within a protoplanetary disk will be blown around by gas motion
Occasionally they will be blown into larger particles and stick - a process known as aggregation
Eventually some aggregates will grow into structures around 100 m across
Two such boulder-sized structures may stick together if they bump into each other very gently - at around 10 cm/s or less

16. Small particles are blown into larger ones by gas motions forming larger and larger aggregations

17. Planetessimals
Clumps that reach a size of 1 km are known as planetessimals (“tiny planets”)
These are massive enough that their gravity starts to attract other nearby bodies and their growth is no longer limited by chance encounters
Larger planetessimals quickly sweep up most remaining bodies in the vicinities of their orbits
The final survivors of this process are the planets

18. Disk Heating
As material falls into accretion disk it will be heated up
This heating results from the conversion of the systematic motion of the infalling particles to random motions as they collide with particles falling in from opposite side
It is the random motion of the particles that make up a body that make it hot
Equivalently, one can think of the gravitational potential energy of the outlying material being converted into kinetic energy

19. Marbles released together fall with little relative motion but have large relative motions after bouncing off a rough surface
Similarly, a cold cloud of infalling gas is heated when it collides with the accretion disk

20. Types of Energy Energy can take several forms
Anything moving possesses kinetic energy
Heat is a form of kinetic energy due to random motions of the constituent particles
Anything that feels a gravitational force possesses gravitational potential energy (GPE)
GPE is increased by separating two massive objects; it is lost as objects fall towards each other and is converted into kinetic energy
Total energy is conserved, but may be freely converted from one form to another

21. Disk Temperature
The inner part of the disk (that part closer to the protostar) will be hotter than the outer disk since:
Material has had further to fall and so has lost more GPE and gained more kinetic energy
Inner disk is radiated by hot protostar
Here only solids that can withstand high temperatures before melting or being vapourized (refractory materials, eg. rocks and metals) can exist
Volatile materials (eg. water and organic molecules) can only exist in solid form in the outer parts of the disk

22. Planet composition
The composition of planets at different radii is expected to reflect these differences
The inner planets will be made up mostly of rocks and metals
Outer planets can also contain refractory materials, but also contain large quantities of ices and organic materials
This trend in composition with distance from the Sun is found in our Solar System

23. Atmospheres and Moons
A solid planet can capture gas from the accretion disk but must act quickly as young stars are sources of “winds” and intense radiation that can disperse gaseous remains of accretion disk
Giant planets such as Jupiter have an advantage in attracting and keeping a primary atmosphere - a mini-accretion disk will form around them
Moon’s can then form from this mini-disk
In the case of small planets such as Earth, the primary atmosphere is lost, but a secondary atmosphere forms from the later release of carbon dioxide and other gases from volcanic activity

24. Brief Solar System History
Around 5 billion years ago the Sun was a protostar surrounded by a protoplanetary disk of gas and dust
Over a few hundred thousand years dust collected into planetessimals comprising rocks and metals close to the Sun with the addition of ice and organic compounds further away
About six planetessimals within a few AU of the Sun grew to become dominant masses
Their growing gravitational fields either captured the remaining planetessimals or ejected them from the inner part of the disk

25. Terrestrial Planets
These dominant planetessimals became the terrestrial planets: Mercury, Venus, Earth and Mars
Remaining debris continued to rain down on these young planets, as evidenced by the large impact craters seen on Mercury

26. Outer Planets
Beyond about 5 AU from the Sun, planetessimals coalesced to form a number of bodies with masses times that of the Earth
Being in a cooler region of the disk, they contained ices and organic compounds as well as rock and metal
Four of these became the cores of the giant planets: Jupiter, Saturn, Uranus and Neptune
All possessed mini-accretion disks funneling in hydrogen and helium gas and from which moons eventually formed
Jupiter’s solid core captured around 300 M of gas, Saturn around 100 M

27. Asteroids and Comets These are planetessimals that survive to this day
Gravitational field of Jupiter prevented planets from forming in the region between it and Mars - the asteroid belt
Icy planetessimals from outer Solar System remain as comets
Some are on very eccentric orbits and so occasionally travel very close by the Sun and Earth

28. Other Solar Systems?
Models of star formation generically predict the existence of proto-planetary disks around protostars and so we expect other planetary systems like the Solar System to be quite common
Planets around other stars (extra-solar planets) are extremely hard to see due to glare from the host star
However, since stars and massive planets are in orbit about each other we can detect a “wobble” in the position of stars with nearby massive planets
The existence of many extra-solar planets is now inferred from such observations