ASTR 1010 – Homework Assignment 8 – Spring 2009

Question 1 - #3. The Solar Nebula is the term given to the protoplanetary disk around the Sun as the Sun was forming from a clump in a molecular cloud. The Solar Nebula, like the Sun or proto-Sun, was composed of the same material as the parent molecular cloud: about ¾ hydrogen, about ¼ helium, and about 2% of the heavier elements.

Question 2 - #4. The three processes are heating, spinning, and flattening (look at figure 8.3). As the original clump that goes on to form the Sun collapses, it heats up by the conversion of gravitational potential energy into kinetic enegy (them atoms and molecules are moving around faster) and, thus, thermal energy (the faster a collection of atoms or molecules moves, the higher is its temperature). The evidence for this comes from observing dense clumps in other molecular clouds. Many of these clumps harbor protostellar cores as seen with infrared instrumentation.

The spinning process is just conservation of angular momentum, as the clump shrinks, conservation of angular momentum dictates that it rotate faster (remember the figure skater?) Evidence for this feature of the collapse comes from computer simulations which model the collapse of molecular cloud clumps.

The flattening process is produced by friction in the spinning disk. Particles collide and lose energy thereby settling into a disk. The evidence for this comes from computer simulations and looking at a multitude of structures in the Universe that resemble flattened disks with central spherical condensations (i.e., any spiral galaxy, see Figure 1.4).

Question 3. - #5. See Table 8.1 for the four types of material. The terrestrial planets are composed primarily of metals and rock, the jovian planets primarily of hydrogen compounds, hydrogen gas, and helium, asteroids in the Asteroid belt are like the terrestrial planets while those in the Kuiper belt are composed primarily of icy hydrogen compounds. Comets are also composed primarily of icy hydrogen compounds. All this has to do with where in the Solar Nebula each type of object formed.

Question 4. - #6. The frost line is the boundary in the Solar System beyond which ices can condense, while only metals and rocky particles can condense inside of it. It is located between 3-4 AU from the Sun. Terrestrial planets form from the accretion of rocky and metallic particles. Jovian planets start out with such a core and then accrete lots and lots of icy particles. They can get 5-10 times more massive than the terrestrial planets in this way. When they get to that size, their gravity is strong enough to pull in additional hydrogen and helium gas from the Solar Nebula.

Question 5. - #7. The terrestrial planets formed from the sticking together of the rocky and metallic tiny particles that condensed out from the Solar Nebula. This process is called accretion. Once planetesimals (bodies ~ 1 km in size) were formed, further accretion resulted in the formation of Earth-sized objects except that gravity now played a large role in keeping the accreting planets together.

Question 6. - #8. The jovian planets likely started out as the terrestrial planets did but then added significant layers of icy material (which was present in their region of the Solar nebula but not inside the frost line). When they got large enough to pull in and gravitationally retain hydrogen and helium from the Nebula, they grew to their final sizes.

Question 7. - #9. The solar wind is a stream of charged particles emanating from the Sun and moving out in all directions at relativistic speeds. The combination of radiation pressure (from light) and the solar wind eventually swept the Solar Nebula free of most of the remnant hydrogen and helium.

Question 8. - #11. The period of heavy bombardment was the era during the formation of the Solar System when the vast numbers of planetesimals in the young Solar System were colliding with each other and with the proto-planetary bodies. This occurred from the beginning of the Solar System till about 4 billion years ago.

Question 9. - #12. We believe that the Moon formed as the result of a giant impact between a Mars-sized body and the young Earth (see Figure 8-12). Your book quotes as evidence the similarity between the composition of moon rocks and the composition of rocks in the Earth’s outer layers. While there is some similarity, there are also differences. These differences basically rule out that the Moon was just “ejected” from the Earth with no external colliding partner. So, a more significant line of evidence for the Giant Impact theory is the lack of volatiles on the Moon. Volatiles are materials with low boiling points. The lack of volatiles on the Moon implies that lunar material was heated to an extraordinary degree (as would happen during a giant impact). The lack of a large iron core within the Moon has also been invoked to support the Giant Impact theory (the moon formed from the left-over debris of the original impactor and from the debris strewn out from the Earth’s surface. The surface of the Earth is relatively metal-poor compared to the core regions (which would have been untouched by the collision). We should not be surprised that a giant impact affected our planet given the rate of impacts during the period of heavy bombardment.

Question 10. - #14. The Solar System is 4.55 billion years old as determined from the radioactive dating of isotopes in meteorites found on the Earth’s surface.

Question 11. - #48.

t = t_half {log₁₀[current amount/original amount]}/(-0.301)

if you have equal amount of parent (potassium-40) and daughter (argon-40) product, then current amount/original amount = 1/(1+1) = 0.5

t = 1.25 x 10⁹ yr{log₁₀[0.5]}/(-0.301) = 1.25 x 10⁹ years

You could have done this without using the formula; in one half-life, the original parent radioactive isotope decays into half of the original and half of the daughter element. So, that gives you equal amounts of potassium-40 and argon-40.

If you have a ratio of daughter/parent of 3, then the current amount of parent is ¼ of the original amount (because if the original amount of parent was 1 “unit”, and now you have ¼ unit of parent isotope, that means you must have ¾ unit of daughter material. The ratio of ¾ to ¼ is 3).

t = 1.25 x 10⁹ yr{log₁₀[0.25]}/(-0.301) = 2.50 x 10⁹ years

You can do the same thing as a table:

Time Parent Daughter Ratio (Daughter/Parent)

0 yrs 100% 0% 0

1.25 billion yrs. 50% 50% 1

2.50 billion yrs. 25% 75% 3

3.75 billion yrs. 12.5% 87.5% 7

5 billion yrs. 6.25% 93.75% 15

etc., etc.

Question 12. - #52.

Metals/Rock/hydrogen compounds = 0.2/0.4/1.4

So Metals + Rock / hydrogen compounds = 0.6/1.4 = 0.42

So if the Earth was able to have a layer of hydrogen compounds accreted onto it, its new mass would be:

Current Mass/Mass with hydrogen compounds = 0.42

Mass with hydrogen compounds = Current Mass/0.42 = 6 x 10²⁴/0.42 = 1.4 x 10²⁵ kg

Metals + Rock + hydrogen compounds / H + He = 2/98 = 0.02

Mass with hydrogen compounds / Mass with H + He = 0.02

Mass with H + He = Mass with hydrogen compounds/0.02 = 7 x 10²⁶ kg

Compare this mass to that of Jupiter: 2 x 10²⁷ kg