Our solar system is an orderly place, making it unlikely that the planets were simply captured by the Sun. The overall organization points toward formation as the product of an ancient, one-time event, 4.6 billion years ago. An ideal theory of the solar system should provide strong reasons for the observed characteristics of the planets yet be flexible enough to allow for deviations.
In the nebular theory of the formation of the solar system, a large cloud of dust and gasthe solar nebulabegan to collapse under its own gravity. As it did so, it began to spin faster, to conserve angular momentum, eventually forming a disk. Protoplanets formed in the disk and became planets, and the central protosun eventually evolved into the Sun.
The nebular theory is an example of an evolutionary theory, in which the properties of the solar system evolved smoothly into their present state. In a catastrophic theory, changes occur abruptly, as the result of accident or chance.
The condensation theory builds on the nebular theory by incorporating the effects of particles of interstellar dust, which helped cool the nebula and acted as condensation nuclei, allowing the planet-building process to begin.
Small clumps of matter grew by accretion, gradually sticking together and growing into moon-sized planetesimals, whose gravitational fields were strong enough to accelerate the accretion process. Competing with accretion in the solar nebula was fragmentation, the breaking up of small bodies following collisions with larger ones. Eventually, only a few planet-sized objects remained. The planets in the outer solar system became so large that they could capture the hydrogen and helium gas in the solar nebula, forming the jovian worlds.
The condensation theory can explain the basic differences between the jovian and terrestrial planets because the temperature of the solar nebula would be expected to decrease with increasing distance from the Sun. At any given location, the temperature would determine which materials could condense out of the nebula and so control the composition of any planets forming there. The terrestrial planets are rocky because they formed in the hot inner regions of the solar nebula, near the Sun, where only rocky and metallic materials condensed out. Farther out, the nebula was cooler, and ices of water and ammonia could also form, leading to the observed differences in composition between the inner and outer solar system.
When the Sun became a star, its strong winds blew away any remaining gas in the solar nebula. Many leftover planetesimals were ejected into the Oort cloud by the gravitational fields of the outer planets. They now occasionally revisit our part of the solar system as comets. In the inner solar system, light elements such as hydrogen and helium would have escaped into space. Much, if not all, of Earth's water was carried to our world by comets deflected from the outer solar system.
The asteroid belt is a collection of planetesimals that never managed to form a planet, probably because of Jupiter's gravitational influence. Many "odd" aspects of the solar system may conceivably be explained in terms of collisions late in the formation stages of the protoplanetary system.
The angular momentum problem is that although the Sun contains virtually all the solar system's mass, it accounts for almost none of the angular momentum. It is believed that the solar wind or ejected planetesimals carried off the Sun's initially high angular momentum, allowing its spin to slow to the rate observed today.
The following nine questions present properties of the solar system that any model of solar system formation must explain. Which are correctly stated and which are not?
1. Each planet is relatively isolated in space. (Hint)
2. The orbits of the planets are not circular but significantly elliptical. (Hint)
3. The orbits of the planets all lie near the ecliptic plane. (Hint)
4. The direction of planetary revolution is in the same direction as the Sun's rotation. (Hint)
5. Planetary rotation is always in the same direction as the Sun's rotation. (Hint)
6. Moons do not usually revolve in the same direction as their parent planet rotates. (Hint)
7. The planetary system is highly differentiated. (Hint)
8. Asteroids were recently formed from the collision and breakup of an object orbiting within the asteroid belt. (Hint)
9. Most comets have short periods and orbit close to the ecliptic plane. (Hint)
10. Water could not have condensed out any closer than 3 or 4 A.U. from the Sun. (Hint)
11. The accretion process occurred faster in the inner part of the solar system than it did in the outer regions. (Hint)
12. The condensation theory does not offer an explanation of the highly tilted rotation axis of Uranus. (Hint)
13. The condensation theory does not offer an explanation of the formation of the Moon. (Hint)
14. Random collisions, inherently a part of the condensation theory, can explain many of the odd properties found among some solar system objects. (Hint)
15. Astronomers know of no planetary systems other than our own. (Hint)
1. The condensation theory, which currently is used to explain the formation of the solar system, is actually just a refined version of the older _____ theory. (Hint)
2. In the condensation theory, astronomers realized the critical role played by _____ in starting the formation of small clumps of matter. (Hint)
3. Initially, the accretion of matter into larger bodies occurred through _____ between particles in the solar nebula. (Hint)
4. By the time planetesimals had formed, the accretion process was accelerated by the effect of _____. (Hint)
5. In the final stage of accretion, the largest protoplanets were able to attract large quantities of _____ from the solar nebula. (Hint)
6. The temperature of the inner part (out to 1 or 2 A.U.) of the solar nebula was well above the boiling point of _____. (Hint)
7. Unlike the terrestrial planets, the planetesimals that formed the jovian planets were made up of _____ material. (Hint)
8. High-speed collisions between planetesimals often led to _____ rather than accretion. (Hint)
9. The large number of leftover planetesimals formed beyond about 5 A.U. were destined to become _____. (Hint)
10. The water now found on Earth was probably brought here by _____. (Hint)
11. The reason the planetesimals of the asteroid belt did not form a larger object was probably the gravitational influence of _____. (Hint)
12. The _____ phase of the early Sun cleared out excess gas not used in planet formation. (Hint)
13. Angular momentum depends on the mass, speed, and _____ of an object. (Hint)
14. The Sun's angular momentum is now much _____ than it was when the Sun was a protostar and is now much _____ than the total orbital angular momentum of all the planets. (Hint)
15. _____ played an important role in determining many of the irregularities in the solar system. (Hint)
1. List six properties of the solar system that any model of its formation must be able to explain. (Hint)
2. Explain the difference between evolutionary theories and catastrophic theories of the solar system's origin. (Hint)
3. Describe the basic features of the nebular theory of solar system formation. (Hint)
4. Give three examples of how the nebular theory explains some observed features of the present-day solar system. (Hint)
5. Explain the difference between angular momentum and linear momentum. (Hint)
6. What is the key ingredient in the modern condensation theory of the solar system's origin that was missing or unknown in the nebular theory? (Hint)
7. Why are the jovian planets so much larger than the terrestrial planets? (Hint)
8. What solar system objects, still observable today, resulted from the process of fragmentation? (Hint)
9. What influence did Earth's location in the solar nebula have on its final composition? (Hint)
10. How did the temperature structure of the solar nebula determine planetary composition? (Hint)
11. Why could Earth not have formed out of material containing water? How might Earth's water have gotten here? (Hint)
12. What happened in the early solar system when the Sun became a T Tauri star? (Hint)
13. What is the modern explanation for the formation of the Kuiper belt and the Oort cloud? (Hint)
14. How do modern astronomers attempt to explain the angular momentum problem in light of modern theories of solar system formation? (Hint)
15. Describe a possible history of a single comet now visible from Earth, starting with its birth in the solar nebula somewhere near the planet Jupiter. (Hint)
1. The orbital angular momentum of a planet in a circular orbit is simply the product of its mass, its orbital speed, and its distance from the Sun. (a) Compare the orbital angular momenta of Jupiter, Saturn, and Earth. (b) Calculate the orbital angular momentum of an Oort cloud comet, of mass 1013 kg, moving in a circular orbit 50,000 A.U. from the Sun. (Hint)
2. The rotational angular momentum of a spinning body is proportional to the product of its mass, its angular speed (in revolutions per day, say), and the square of its radius. An interstellar cloud fragment of 0.1 light year diameter is rotating slowly, at a rate of 1 revolution per million years, as it begins to collapse. Assuming that the mass remains constant, estimate what the rotation period will be when the cloud has shrunk to the size of the solar nebula, 100 A.U. across. (Hint)
3. By what factor would Earth's rotational angular momentum change if the planet's spin rate were to double? By what factor would Earth's orbital angular momentum change if the planet's distance from the Sun were to double (assuming that the orbit remained circular)? (Hint)
4. We can make a rough model of accretion in the inner solar nebula by imagining a 1-km-diameter body moving at a relative speed of 500 m/s through a collection of similar bodies having a roughly uniform spatial density of 10-10 bodies per cubic kilometer. Neglecting any gravitational forces (and hence assuming that the body moves in a straight line until it collides with something), estimate how long, on average, will be needed for it to experience a collision.
5. Consider a planet growing by accretion of material from the solar nebula. As it grows, its density remains roughly constant. Does the force of gravity at its surface increase, decrease, or stay the same? Specifically, what would happen to the surface gravity and escape speed as the radius of the planet doubled? Give reasons for your answer. (Hint)
6. How many 100-km-diameter rocky (3500 kg/m3) planetesimals would have been needed to form Earth? (Hint)
7. Two asteroids, each of mass 1018 kg, orbit near the center of the asteroid belt in the plane of the ecliptic on circular paths of radii 2.8 and 2.9 A.U., respectively. Calculate the gravitational force between them at closest approach, and compare it with the tidal force that would be exerted by Jupiter if that planet happened also to be at closest approach at that time. (Hint)
8. According to Figure 15.6, the temperature in the early solar nebula at a distance of 1 A.U. from the Sun was about 1100 K. Based on the discussion of surface temperature in Section 7.2, estimate the factor by which the Sun's current energy output would have to increase in order for Earth's present temperature to have this value. (Hint)
9. A typical comet contains some 1013 kg of water ice. How many comets would have to strike Earth in order to account for the roughly 2 1021 kg of water presently found on our planet? If this amount of water accumulated over a period of 0.5 billion years, how frequently must Earth have been hit by comets during that time? (Hint)
10. How many comet-sized planetesimals would have been needed to form Pluto? (Hint)