Formation of the Solar System
Questions to Answer:
How does a star form?
How does a planetary nebula form?
How do planets form?
How did we get the current distribution of planets...
- in a disk?
- with the observed sizes, densitiest compositions?
- with elliptical orbits?
How do satellite systems form?
I. Star formation:
A. Universe started with a "Big Bang" ~18 Ga. The main pieces of evidence for the occurrence of the Big Bang are:
1. All of the visible galaxies are receding from ours, indicating the universe is expanding.
2. The remnant energy from the big bang is observable as 3oK background radiation.
3. Recently, perturbations in the background radiation have been found, indicative of early clumping of the universe necessary for galaxy formation.
B. Interstellar dust collapses to form galaxies, star clusters, and ultimately stars.
1. Stars form from very large interstellar clouds of gas (99% by mass) and dust (1% by mass). This gas is composed mostly of H (~75%), He (~25%), plus trace amounts of C, N, O, Ca, Na, etc. The dust is composed of silicates, Fe, C-rich organics, etc. The interstellar dust is the stuff that will ultimately form the rocky planets, and that the interstellar gas will contribute to the planetary atmospheres, oceans, etc.
2. The "virial theorem", of "Jeans theorem" dictates that a cloud of gas will collapse if its gravitational potential energy is more than twice its thermal energy.
Required density for collapse:
Mass Density
Galaxy 1011 Suns 10-27 kg m-3
Open Star Clusters 104 10-9
Our Sun 1 10-2
Jupiter 10-3 10-2
3. The Hertzberg-Russel (HR) diagram shows several different star types:
a. Main sequence, normal star-sustained thermonuclear fusion of H2->He
b. Pre-main sequence
Starts off main sequence because of cocoon of material around stars
Cocoon is blown off in T-Tauri phase that may post-date planet formation
c. Post-main sequence
When stars die they turn into white dwarfs, neutron stars, or black holes with increasing size. Smaller of these go through red giant phase.
Larger stars blow out huge amounts of bright material as nova or supernova.
A nearby supernova may have triggered the collapse of a clod to form our solar system.
d. Note that larger stars have shorter lifetimes (lifetime proportional to mass -2)
II. Planet formation.
A. Evolution of the solar nebula:
1. Collapse into a disk.
2. Collapse vaporizes almost all material.
3. High-temperature elements condense.
4. Collisions at low velocity cause adhesion of particles. This coagulation process steadily produces fewer numbers of larger bodies: R~micrometer grains to R~1cm pebbles to R~1km planetesimals in t~103 years at r=1 AU from the Sun. Note that grain-growth proceeds slower at greater distances from the Sun, so the dust may still be settling to the midplane at, say, r~20 AU while planetesimals form at r~1 AU.
5. Gravity takes over and planetesimals form. Further growth of R>1 km bodies is assisted by their gravities, which allows them to accrete each other, ultimately forming R~1000 km protoplanets of mass M~0.01Mearth. This is a runaway growth process since the largest body tends to accrete faster than its smaller neighbors. By time t~105 years, runaway growth will produce a few hundred protoplanets in the terrestrial zone (eg, interior to Jupiter's orbit).
6. Planetesimals accrete into planets.
B. Some important details of the solar system:
1. Temperature of disk decreases away from the Sun, thus volatile-rich outer planets and rock inner planets.
2. More material in the disk for each planet as one goes outward, resulting in the general small-to-large trend in planets in the solar system.
3. Stellar wind, and the T-Tauri phase blows away dust and uncondensed material in disk, resulting in few volatiles in the inner solar system.
4. Gravitational perturbations prevent asteroids from accreting into a planet.
5. Giant planets have perturbed many icy planetesimals to the edge of the solar system where they form the Oort Cloud.
6. From 2 above and competition for planetesimals theoretical modeling shows that solar system should generally have something like Bode's Rule:
an = 0.4 + (0.3 x 2n), n = -infinity,0,1,2,...
where an is the distance of the nth planet in Astronomical Units (AU)
C. Formation of planetary satellite systems
1. Many satellites, such as the Galillean moons of Jupiter, form in an accretionary disk just like the solar nebula.
2. Some satellites are captured planetesimals, such as Phobos and Deimos, the moons of Mars.
3. Our moon my have formed from the debris from a Mars-sized planetesimal smashing into the Earth.
III. Some important celestial mechanics:
A. Kepler's Laws:
1. A planet moves in an ellipse with the Sun at its focus.
2. The line between the sun and a planet sweeps out an equal area in equal amounts of time.
3. The ratio of the cube of the semimajor axis to the square of the orbital period is the same for each planet.
B. Some implications of Kepler's Laws:
1. Comets move very fast close to the Sun.
2. Orbital period of a planet is largely independent of the planet's mass.
C. Seven orbital elements are needed to describe a planet's orbit:
1. semimajor axis of the ellipse (a above).
2. eccentricity, or noncircularity, of the orbit (e above).
3. inclination of the plane of the ellipse relative to the ecliptic.
4. the longitude in the ecliptic plane where the orbital plane crosses (the node).
5. the periapsis latitude relative to the ecliptic.
6. time of periapsis.
7. the orbital period.
D. Velocity equations:
1. orbital velocity
for
near-circular orbit
2. escape velocity
E. With 2 large bodies orbiting each other (like the Earth & Moon) there are 5 LaGrangian points where a satellite can be placed and remain motionless with respect to the planets.
F. Some important tidal effects:
1. Our moon is receding from the Earth.
2. Roche's limit - point at which a point mass is more attracted to a planet than another point mass.