The Formation of the Solar System

How do we know that the solar system had an origin?

The sun is  a star, and stars have life cycles.

We know stars are born,
they are sources of energy and those energy sources are limited,
and therefore they must die.
We assume that since planets are associated with stars, planets form when stars form.

What do we know about the solar system?

1. Gravity inexorably pulls things in the universe together. Clumps of mass only stay apart if something else opposes the inward pull of gravity. In between the stars, in interstellar space, we find enormous clouds of gas (98% H + He, just like the Sun) and dust (solid stuff, sub-micron sized).  Some of these clouds are hot and the pressure generated by the hot gas is sufficient to push outwards against the self-gravity of these clouds that otherwise would squeeze the clouds.  However, the cores of some of these clouds are cold; their internal pressure is too small to resist gravity.  In these cold cloud cores, new stars are being born [Orion Nebula, for example].  The law of gravity says that as the cloud becomes smaller, it's own self-gravity [the attraction of any one particle in the cloud for all of the rest of the cloud] becomes stronger (why? the cloud doesn't change mass.  What changes?)  So the cloud should collapse faster and faster and faster, an accelerating collapse.

2. A cloud that is collapsing due to gravity is undergoing gravitational collapse.  If the cloud were sitting absolutely still when gravitational collapse began, what shape would it take?  Since all the material is drawn equally toward the center of the distribution of mass, the object will be spherical (like stars and planets, whose shapes are dominated by gravity - remember our attempt to define a planet?).  However, nothing in the universe is sitting absolutely still. Planets spin.  Moons orbit planets.  Planets orbit stars.  Stars spin.  Stars orbit the center of galaxies.  Galaxies orbit other galaxies.  All of these motions are "spinning" motions, the movement of some mass around a common center.  This is what we term angular momentum. Angular momentum cannot be destroyed, although it can be transferred from one object to another.  This is known as conservation of angular momentum.

Go to  mathematics of angular momentum for more information about angular momentum.

For planets, you recall Kepler's Second Law was his discovery that angular momentum is conserved.  For the planets, as they go around the Sun, their masses don't change but their distances from the Sun do.  As they get closer to the Sun (distance gets smaller) they orbit faster (higher velocity).  The product of these two quantities remains unchanged, thus angular momentum is conserved.

3.  You are very familiar with angular momentum conservation: ice skaters spinning (arms pulled in closer, spin gets faster), divers diving (arms and legs pulled in tighter, spin gets faster).  These clouds are not sitting still.  They are rotating.  So what happens to a rotating, collapsing cloud?  It flattens, or pancakes.  While gravity pulls everything inwards, angular momentum conservation prevents the material from all collapsing to the center.  Instead, gravity is very effective at pulling everything toward the midplane, which is the plane of the system perpendicular to the rotation axis.

4.  If we apply this knowledge to our collapsing cloud, we realize that it must collapse gravitationally inwards, forming a star at the center.  Material with small amounts of angular momentum (i.e., low velocities, small distances) collapse all the way to the center.  But much of the cloud is unable to move inwards.  However, such material can maintain a constant angular momentum if it moves only "downwards" toward the midplane, thus creating a central star surrounding by a flat disk of gas and dust orbiting the central star.  If planets can form within this disk, we have a natural mechanism generated by the combined effects of gravity and angular momentum conservation acting on a collapsing, rotating cloud that will produce planets in a single plane, orbiting in a single direction around a star.

5. So how do the planets form in this revolving disk of dust and gas? [For a longer discussion of this process, see How Do Planets Form? by yours truly, in Mercury magazine, v. 29, No.6, pp. 10-17 (Nov-Dec 2000 issue).]  We must return to the law of gravity and understand how gases behave.  Gases are not mechanically bound to other material.  Gas molecules fly in random directions unless forced to change directions, either through collisions with other molecules or by gravity.  On a massive body like the Sun or Jupiter, hydrogen gas is held down by gravity.  Recall that the weight of a 100 kg person would be 220 lb on the Earth but more than 8000 lb at the surface of the Sun.  Thus, the Sun's gravity holds on to gases with much greater strength than does the Earth.  In fact, the Earth is not gravitationally strong enough to hold onto H or He molecules in the atmosphere.  If placed there, they would escape to space.  One can calculate very directly that H and He gas will not be bound to a planet unless the planet has a total mass of about 10 times the mass of the Earth.

6. As the disk material revolved around the forming Sun, some of the solid stuff, the dust, collided with other dust grains.  Some of those collisions would be destructive but some collisions would be constructive, making bigger grains.  Those bigger grains would experience more collisions, primarily with smaller solids, and would be more likely to grow than to be destroyed.  We call this process accretion.  Gradually, those little grains of dust became pebbles, then boulders, then km-sized tiny planetesimals, then larger and larger planetesimals, gradually growing into moon-sized and Earth-sized planets or planet cores.  As the planetesimals grew, there were fewer of them and those that remained were mostly large.  The final collisions among these remaining objects would be quite violent, leaving large crater scars in the biggest one, the protoplanet. Thus, we have a reasonable mechanism for making solid planets and for producing large craters on their surfaces near the end of the formation epoch.

7. In parts of the solar system where there was an abundance of solid stuff, the solid objects grew faster.  In the inner solar system, where the temperature was hottest closest to the forming star, the only solids were rocky and metal materials.  However, at distances beyond the asteroid belt, we cross the snow line. Beyond the snow line, water could condense into ice.  Since water is made of H and O, two of the three most abundant elements in the universe (He is #2), at the distance of Jupiter the accretion process has much more solid stuff to work with.  Thus, in the Jupiter zone, accretion quickly made a protoplanet whose mass grew to 1 to 2 to 5 and to 10 Earth masses.  At this point, the protoplanet's gravity was strong enough to grab the H and He gas that it was orbiting within (the gas disk), making a giant, gaseous planet.  We now know from our observations of the giant planets that all four of them - Jupiter, Saturn, Uranus and Neptune - all have solid cores of about 10 Earth masses.  Thus, a theoretical prediction of the planet building process has been confirmed by our robotic spacecraft observations of the planets.  In the inner solar system, the forming planets never became big enough to grab the H and He gas.  At some point, the Sun turned on an outward blowing wind, something we find that all young stars do, and this wind blew all the remaining gas out of the solar system.  Once the gas is blown away, no more gaseous planets can form.

 8. All that remained were the solid planets, some remaining planetesimals, and some giant, gaseous planets.  Over time, most of those remaining planetesimals collided with the remaining planets, leaving the solar system largely cleared of debris and the solid surfaces scarred by the final cleanup.  This final cleanup period is the early bombardment.

   When we are dealing with the impacts of many small objects on one larger protoplanet, we would expect the collisions to be fairly randomly distributed, coming from many different directions.  Some collisions might be near the poles, some near the equators. On average, since all the planetesimals are orbiting the Sun in the same direction, the randomness would average out such that the average impactor would be near the equator in the same direction as the planets orbit and rotation.  However, since the last impacts were of large bodies hitting larger, nearly fully formed planets, and there were very few of these, the statistics don't work any longer. And it becomes possible, though not provable, that the final impact could have been a glancing blow near the north pole which would flip the planet upside down (Venus) or knock the planet over a little bit (perhaps 23.5 degrees, like the Earth).

     In the outer solar system, the planets became so massive, they may have collected material into their own circumplanetary disks. Within these disks, the accretion process could have repeated itself on a smaller scale, making moon systems around these planets.

Stars are born:
Orion Nebulaproplyds, more proplyds
M16 - The Eagle Nebula
photoevaporation in the Pleiades
Trifid Nebula
R136 in 30 Doradus
NGC 3603  - a supernova explosion and star formation in the same place
Rho Ophiuchi
the Horsehead Nebula in Orion

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Stars die:
 Planetary Nebula IC 418  - a star that has blown off shells of material as it dies
 Planetary Nebula NGC 6751
 The Hourglass Nebula
 Helix Nebulacometary knots  (close up)
 Crab Nebula  - site of a supernova explosion 1000 years ago

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What is a star?

Why Does a Star Shine? It's HOT!

How hot is the Sun?
surface: 6 x 103  K
core: 107 K
How long can it shine, simply by cooling off?
the total thermal energy content of the Sun (the amount of heat stored in the Sun because it is hot) is equal to
Ethermal = 5 x 1041 Joules (kg m2 s-2) = 5 x 1048 ergs (gm cm2 s-2)

since the sun releases

Lsun  = 3.9 x 1026 J s-1 = 3.9 x 1033 ergs s-1

the lifetime of the Sun (if it has no sources of energy) is only

Lifetime = Ethermal / Lsun =  5 x 1041 Joules / 3.9 x 1026 J s-1
Lifetime = 1.3 x 1015 s * (1 yr / 3.15 107 s) =  4 x 107 yr
What if the Sun was hotter in the past because it was born hot and has cooled off?
The Sun did gain energy intially from gravitational collapse (gravitational potential energy) during the protostar phase.

We can calculate how much energy the Sun gained from gravitational collapse by doing the imaginary experiment in which we move one gram of the Sun at a time from the surface of the Sun out to an infinite distance. If we do this for the whole star, we find

Egravity = 4 x 1041 J

Therefore, the sun's lifetime would be limited to

Lifetime = Egravity / Lsun =  3 x 107 yr
What if the Sun's energy source is nuclear fusion?
particles must approach to within one nuclear diameter (D = 1 Fermi = 10-13 cm)

work required to overcome Coulomb repulsion barrier is

Ecoulomb = (Z1 e)(Z2e)/D = 1.5 Z1 Z2 MeV
compared to the thermal energy of two particles:
Ethermal = 1.5 kT = 1.5T MeV (with T in units of 1010 K)

where 1 MeV = 1.602 x 10-13 J
and k = Boltzman's constant = 1.38 x 10-23 J/K

thus, for two protons (Z1 = Z2 = 1) at 10 billion degrees, we have a match!
fortunately, quantum mechanical tunneling permits some protons to "tunnel" through this coulomb barrier and collide.
Estimate of Nuclear Energy Stores in the Sun:
Enuclear = alpha x mc2
where c = speed of light = 3 x 108 m/s
alpha = mass defect: in converting H -> He, alpha = 0.007, in converting He -> Fe, alpha = 0.001
so most of a star's energy is obtained by fusing H to He
almost all of mass of stars is H
only the core (10%) of a star is normally hot enough for fusion, thus
Enuclear = 0.008 x 0.1 Msunc2= 1.5 x 1044 J
this would allow the sun to shine for Lifetime = Enuclear / Lsun = 12 x 109 yr
Conclusion: the sun has an energy source that permits it to shine for several billion years, but we must conclude that the Sun can't shine forever, that it had a beginning and will have an end.