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Dec 6, 2023
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Why will a star, rather than a black hole, form in a collapsing cloud?
Answer: much more mass is required to compress the available matter into a tiny area.
What force is responsible for holding small particles together in the collapsing cloud?
Answer: the electric force. The electric force is much stronger than the force of gravity. The electric force can easily hold two particles together while gravity is too weak to do so. However, gravity is responsible for the attractive force between massive objects acting over great distances.
After matter has coalesced in kilometer-sized boulders, the process of accretion increases significantly. Why is this?
Answer: the process will go faster because at this stage the chunks of matter are big enough to exert a gravitational force on each other.
Why are Neptune and Uranus much smaller than Jupiter and Saturn?
Answer: being farther from the Sun, they were the last to begin their formation and therefore they did not have enough time to grow to larger sizes.
According to our current understanding of the Solar System, we believe that in a billion years planetary
orbits will not be the same as they are today. Why would they change?
Answer: planets exert gravitational tugs on each other, slightly altering their orbital paths around the Sun. These changes can have a noticeable effect over long periods of time .
Why were there more collisions in the Solar System in the past?
Answer: there were numerous amounts of clumps of matter that orbited the Sun in chaotic orbits. These objects constantly collided and changed their trajectories.
What is the origin of water on our planet?
Answer: it is very likely that water was brought to our planet by comets during the late heavy bombardment (500-800 million years after Earth’s formation).
Common misconceptions
1. Small particles stick together in the collapsing cloud as the result of gravity
This is incorrect notion. Gravity is too weak to hold these tiny particles together. It is the electric force that is responsible for creating the initial clumps of matter in a spinning cloud, it is only after they reach a much larger
size that gravity starts to play a role.
2. Terrestrial planets formed closer to the Sun because heavier particles were
attracted more strongly to the center
The cloud that gave birth to the Sun and every single speck of dust and ice in
the Solar System had a homogeneous composition. Also, we have to bear in mind that the speed at which something falls (toward the center) does not depend on its mass: a chunk of iron falls just as fast as a chunk of ice. This can be verified here on Earth by dropping two objects of different weight,
and watch them reach the ground at the same time. Rather, the difference in
composition reflects the condensation sequence as dictated by the temperature at various points in the nebula.
3. The Solar System is the same as the Universe or the galaxy
Some people confuse our Solar System with a galaxy or the Universe. Our Solar System is a system of planets and small bodies orbiting a star (the Sun)
which is one among 200 to 400 billion stars in our galaxy (the Milky Way) which is one among 100 billion galaxies in the visible Universe.
4. The formation of planets stopped when the Sun ignited (when nuclear fusion started up inside its core)
Stars like our Sun are more active (have stronger stellar winds) during their pre-nuclear fusion stages: essentially all gas and dust is removed after 3 to 10 million years, whereas fusion does not start up until 50 million years after the collapse of the cloud.
KEy terms
Astronomical Unit (AU) – the average distance (semi-major axis) between the Sun and the Earth
Nebula – any fuzzy object of undetermined shape
Accretion – a process by which small particles combine to form larger objects
Condensation sequence – the order in which chemical compounds transition from the gas into the solid phase, following the condensation
temperature of each compound
Volatile materials – gaseous and icy materials that easily evaporate at elevated temperatures
Refractory materials – solid materials that can withstand very high temperatures (they have high melting points)
Star – a ball of ionized gas (plasma) that converts lighter elements into heavier elements in its core; in other words, it converts matter into energy by the means of thermonuclear fusion
Planetesimal – a large chunk of primordial rock and a building block of a planet
Proto-planet – a forming planet that is still growing
Inner Solar System – the region from the Sun to the asteroid belt
Outer Solar System –the region in the Solar System beyond the asteroid belt Meteoroids, asteroids and comets are leftovers from the formation of the Solar System. They are rocky and icy planetesimals – huge chunks of rock
and ice (those that formed farther away from the Sun) – that did not have chance to accrete into sizable planets. The largest asteroid in the Solar System is Ceres which you can find in the Asteroid Belt. When Ceres was discovered in 1801, it was first classified as a planet. When more asteroids were discovered in the same area, Ceres was demoted to an asteroid status but we discovered the asteroid belt! Recently, Ceres has been promoted to the status of dwarf planet. Ceres is currently being orbited by a spacecraft, you can follow the latest updates hereLinks to an external site.
.
The largest dwarf planet known to us today is Eris. This object is located in the scattered disk. One of Eris’s neighbors is Pluto that used to be classified as a planet just like Ceres used to be until more similar objects were discovered in the same vicinity. Pluto was demoted to a dwarf planet but we discovered the Kuiper belt and the scattered disk! Well, we already knew about the Kuiper Belt before but we did not know how many huge planetesimals were hiding there. The scattered disk is the home of the short-
term comets (orbital period under 200 years). Long-term comets with orbital periods of between 200 years and millions of years are coming from the Oort
cloud. There are about one trillion comets in our Solar System.
The planets completed the process of condensation and accretion within 50 million years. During this process, the radiation emitted by the forming star was slowly removing gasses and dust from the proto-planetary disk. In the end, there were no more materials left in the disk and the formation of the planets came to a halt.
The Solar Nebula Theory provides a single consistent explanation for the dynamics and chemical composition of our Solar System. In particular:
a) The Dynamics of the Solar System
All planets revolve around the Sun counterclockwise
All planets orbit in the same ecliptic plane
All planets have almost circular orbits
(Nearly) all planets rotate counterclockwise and so does the Sun
Planets' orbital distances are regularly spaced
Most satellites (moons) revolve counterclockwise
Comets come from all directions and angles
b) Composition:
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There are two distinct classes of planets with two distinct chemical makeups:
Terrestrial planets made up mostly of metals and rocks
Jovian planets made up mostly of hydrogen compounds and gases
Farther out
Another, wider band of icy bodies in the Solar System is located past Neptune – the Kuiper Belt. This is home to many comets and dwarf planets that are also leftovers from the formation of the main planets. Pluto is now considered to be one of these objects. Past the Kuiper belt lies the Oort cloud
– the most distant region of the Solar System, home to a trillion comets. While the flat Kuiper belt is somewhat thicker than the asteroid belt, the spherical Oort cloud completely envelops our Solar System. Comets that travel to the Inner Solar System from different directions at different angles are coming from these regions.
If we look at our Solar System from above, from above the imaginary North Pole, we will see that all the planets revolve (orbit) around the Sun in the counterclockwise direction. This is because the cloud spun in this direction and therefore everything in it inherited this motion. Nearly all of the planets are rotating (spinning) around their axes in the counterclockwise direction. Venus and Uranus are exceptions to this rule. Venus spins upside down and Uranus is orbiting the Sun while spinning on its side. The Solar Nebula Hypothesis ascribed these oddities to the result of collisions that took place during the early stages of planetary formation. Most of the moons orbit their
parent planets in the counterclockwise direction. Nearly all the planets are orbiting the Sun in the ecliptic plane (the plane that corresponds to the orbit of the Earth). Pluto, a dwarf planet, has the largest inclination (the angle to the ecliptic) of 17 degrees while the planets have inclinations of no more than seven degrees. Conservation of angular momentum explains why the cloud became flat, and therefore why the planets formed in the same plane. It also must be mentioned that according to the conservation of angular momentum, the Sun, since it is in the center, must spin very fast. In reality, it
rotates once in 25 days.
While planets were forming in their orbits they were accreting specks of dust and different kinds of rocks. The more mass the planets accreted, the stronger their gravity became, attracting more materials on the way and clearing their orbit. Planets could not form too close to each other – otherwise, they would constantly pull on each other and stunt their growth. Perhaps, one doomed planet tried to form between Mars and Jupiter but the constant gravitational tugs from the two neighboring planets would never
allow for any big body to coalesce in the region; thus, the asteroid belt, a band of rocky rubble of unused building blocks was left behind in its place.
According to the Solar Nebula Hypothesis, our system started out as a big and very cold (10K-30K) molecular cloud that was slowly drifting and spinning in the Orion-Cygnus arm of the Milky Way galaxy. However, 4.568 billion years ago this cloud was disturbed by a shockwave from a supernova explosion. This disturbance began the compression of atoms and molecules making the cloud shrink (gravity pulled the collapsing matter towards the center of the cloud). As it span faster and faster it flattened (conservation of angular momentum made sure of this to happen). This is the same process that is behind the formation of flat galaxies.
The center of the cloud, where most of the particles ended up, became the densest and hottest part of the cloud. It is here where a future star began its formation. The rest of the particles were condensing from the cloud based on
their distances from the forming star (a glowing warm proto-star). Close to the proto-star, temperatures were above the melting point of tungsten (3,700 K) and thus nothing could condense.
At a distance of about 0.3 AU (Mercury’s orbit), the temperature dropped to 1,000 K, and here atoms could condense into metals and some silicates (rocks). At the distance where our planet is today, the temperature was low enough (500K) to allow for the formation of more types of silicates. At about 3 AU (past Mars’s orbit), the temperature was so low that various hydrogen compounds (ices) could form and survive the solar heat. Not surprisingly, we call this borderline the frost line. Gas giants (Jupiter, Saturn, Uranus and Neptune) formed beyond this line. This drastic drop in temperature with increasing distance from the Sun explains the chemical composition of our Solar System: four terrestrial (Earth-like) rocky planets closer to the Sun followed by four gaseous Jovian planets (Jupiter-like) located farther away from the star.
Star systems (the Solar System is one of them) form through the processes of (1) the gravitational collapse of a cloud of gas and dust, (2) the condensation of elements from gases into solids, and (3) the accretion of the elements into proto-planets.
Our Solar System consists of a star named Sol. Most people in North-America
know this star as the Sun. Sol sits at the center of its own Solar System and
governs the motions of eight planets (we miss you Pluto), a number of dwarf (minor) planets, over 200 moons, and countless numbers of asteroids and comets. Perhaps something surprising, 99.86 percent of the mass of the Solar System is contained within the Sun. The Sun is the only star in our system.
The Solar Nebula Hypothesis (or more often it is being referred to as a theory) represents our current understanding of how our Solar System was formed. This hypothesis is based on observational data of our own Solar System, on mathematical models and on our current understanding of the laws of physics. Additional observations of stellar and planetary formations in
other systems, such as in the Orion Nebula, have allowed us to elevate this hypothesis to the rank of a theory.
Diameter of the Solar System: 100,000 AU
Mass of the Solar System: 1.0014 solar masses
Number of planets: 8
Number of dwarf (minor) planets: 5 (2013 census)
Number of asteroids: tens of billions
Number of comets: about one trillion
5 billion years: the time that the Sun will continue hydrogen fusion for
4 million tons: how much mass the Sun converts into light every single second
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0: the number of organisms on Earth that do not rely (directly or indirectly) on the Sun’s energy
This period we visit the stars. The reading assignment consists of part IV in its entirety. During this period we look at everything that makes a star tick. All of this is part of the midterm at the end of this period, so do not wait until Friday to digest this part of the book.
Stars form, live, and die. There are small stars, and there are really big stars. They all adhere to the same laws of physics, namely the forces of gravity, electricity, strong, and weak nuclear forces. Out of these forces, a large variety of stars emerges with different colors, as well as a variety of stellar corpses: white dwarfs, neutron stars, and black holes. It was the great discovery of the early 20
th
century that all this diversity can be ascribed to a single underlying cause: the mass of the star.
How do stars work
In order to understand stars, we need to look into what makes stars shine: how do they generate the energy that they release in such copious amounts?
The answer is that stars fuse protons together to make larger nuclei. The force that binds the protons together is called the strong nuclear force, and it
is about 100 times stronger than the electric force that repels two protons. However, there is a catch. The nuclear force can only bind together protons that are touching each other. Therefore, the electric force, that tries to keep protons separate, needs to be overcome.
In order to overcome the electric force, protons need to be flying at each other at very high speeds. In order for them to have very high speeds, the star needs to have a very high temperature. When a star is born, the temperature is raised as a result of the gravitational contraction of the forming star (proto-star). The more mass that is contracting, the faster this process will be, and the higher the (final) temperature of the core. Once the temperature is high enough for fusion to start, the star stops being a proto-
star and becomes a full-fledged star. The star reaches its gravitational (sometimes you hear another term “hydrostatic”) equilibrium. In this state gravity is balanced by pressure and the same amount of energy that is being
generated in the core of a star is being emitted from stellar surface. Stars spend about 90% of their lives in the state of gravitational equilibrium. How fast fusion events happen in the core of a star once fusion has been ignited depends on the temperature of the star. The more massive the star, the higher the core temperature, and the faster fusion events will follow each
other. In very low mass stars (above 0.08 solar masses) that barely could ignite fusion in the first place, fusion events follow each other so slowly that
the hydrogen fuel can last for a trillion years. In very massive stars (over 100
solar masses) fusion events take place so fast that the star will fuse all the hydrogen in the core in less than a million years. Once we realize the implications of mass on temperature, and of temperature on lifespan, then we can understand almost everything about the births, lives, and deaths of stars. The details of all these processes are given in part IV of the book, and this video captures some of the essentials
Links to an external site.
. But do not rely on the video alone, you need to read and study the book.
The deaths of stars also represent a struggle, namely the competition between the force of gravity trying to crush all matter into one point and matter trying to resist the crush. Depending how well matter — without being aided by the heat and internal pressure generated by fusion — is able to withstand the force of gravity we can have different outcomes for the stellar corpse left behind after fusion stops.
We can end up with white dwarfs, representing stars where the force of gravity could be balanced by the pressure generated by the electrons inside a cooling core made of carbon nuclei. But when gravity is stronger, the electrons can no longer generate enough pressure and a new state of matter
forms: electrons and protons combine into neutrons, and the pressure generated by the neutrons can keep the force of gravity in check. These stellar corpses are called neutron stars. However, if gravity is even stronger — something which occurs in stellar corpses at least three times the mass of the Sun — then neutrons cannot resist the crushing force of gravity and all matter collapses into a single point and the star becomes a black hole. As with the birth and life of the stars, their ultimate fates are determined entirely by their masse
Black hole — the corpse left behind by a very massive star. The force of gravity is so strong because of the density of the matter contained within the black hole that nothing can escape it, not even light.
Hertzsprung –Russell (H-R) diagram — a diagram that shows the relationship between temperature and luminosity (amount of energy radiated) of stars.
Neutron star — the corpse left by a massive star consisting of neutrons
that formed when the star ran out of fuel and protons and electrons combined to forge neutrons.
Main sequence — the region of the H-R diagram where all hydrogen-
fusing stars spent most of their lives
Nuclear fusion — a manifestation of the strong nuclear force whereby smaller nuclei are fused together to form a larger nucleus, releasing energy in the process.
Planetary Nebula — rings or strings of material seen to be fleeing away
from a white dwarf. This material consists of the outer layers of stars in
their giant phases that were shed through strong stellar winds.
Red giant — a luminosity class, describing an expanding dying low-
mass or intermediate-mass star (between 0.08 to 8 solar masses) that fuses hydrogen into helium in the shell surrounding its core; typical sizes are 50-100 solar radii.
Supergiant — a luminosity class, describing an expanding dying high-
mass star (over 8 solar masses) that simultaneously fuses a number of chemical elements in concentric shells surrounding its core; typical sizes are 100-1000 solar radii.
White dwarf — the corpse left by a low, or intermediate mass star after
it ran out of helium to fuse into carbon.
1. The farther away from the surface of the Sun, the cooler it gets
o
This is incorrect notion, but almost correct. It is true that it is warmer on Earth than on Mars because of this distance effect, but very close to the Sun it is in fact the opposite. The photosphere, the visible ‘surface’ of the Sun, is 6,000 K, but the corona is a few million degrees.
2. The Sun is not changing
o
This is incorrect notion, both on a billions-of-years basis and on an hourly basis. Over time, the Sun gets a little brighter because the temperature in its core slowly rises. Over a period of 22 years
the Sun’s magnetic field undergoes a full reversal cycle, with consequences for the solar activity (most notably the number of sunspots). On a daily, or even hourly basis, the convection cells that guide the Sun’s interior heat to the surface will change shape.And on the shortest times scales, solar flares can happen, followed by mass ejections.
3. Planetary nebulae have something to do with planets, or galaxies
o
Planetary nebulae are caused by dying low- and intermediate-
mass stars when they shed their outer layers during their helium-
burning phases.
4. Black holes are invisible
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o
This actually is correct, but nevertheless they reveal their presence indirectly when gas and dust fall into them, and they can also be observed when companion stars orbit around them.
5. All elements essential to life are forged in supernova explosions
o
Many elements are, and certainly all of the very heavy elements (heavier than iron). However, many of the lighter elements are forged in Sun-like stars and dispersed throughout the Universe via the strong stellar wind of dying stars.
6. Global warming is caused by the increased activity of the Sun
o
This is incorrect. The Sun increases its brightness very slowly, over a period of many millions of years. Global warming — an increase in the average temperature of the Earth during the last two hundred years with a marked upward trend during the last decades — has occurred on a much shorter timescale. 7. A star moves along the main sequence during its life
o
Stars join the main sequence as soon as fusion takes place in the
core. But during their lives, stars barely move along the main sequence. When they run out of hydrogen, they follow tracks almost perpendicular to the main sequence.Global warming is caused by the increased activity of the Sun
uppose the Sun had double the mass it actually has. How would this affect the Sun’s temperature, luminosity and lifespan?
Answer: it would be hotter (9,000 K), more luminous (20 times), and only shine for a much shorter time (1 billion years).
Population III stars consisting of only hydrogen and helium all were hundreds of solar masses. Why could they not be smaller?
Answer: Lacking CO molecules, they could not cool off to below 100 K, therefore, their spawning clouds
had to be more massive to still contract according to the Jeans criterion.
Why does fusion, when it takes place following the CNO-cycle, operate so much quicker than fusion based on the proton-proton chain?
Answer: the CNO-cycle only requires collisions between larger nuclei and protons, but not between two rare helium-3 nuclei.
Describe the role that magnetic fields play in the formation of sun spots
Answer: Magnetic fields can trap the charged plasma particles, interrupting the convective heat transfer from the inner parts of the Sun to the photosphere. As a result, the trapped particles will cool off and show up as darker spots in the photosphere.
Why does a more massive star have a shorter lifespan than a less massive star?
Answer: the life span is governed by how quickly fusion events follow each other. The likelihood that two particles can approach each other closely enough for the nuclear force to bind them together in the face of the repulsive electric force depends on how fast particles were moving. Since the measure of how fast particles are moving is the temperature, it implies that higher temperatures correspond to higher fusion rates. The temperatures in turn are dictated by the force of gravity since it is the gravitational contraction that raises the temperatures in the first place. Thus, more mass equals higher
temperatures, which equals higher fusion rates.
Is there any way for us to directly image what happens at the cores of stars, given that light from the core does not reach us?
Answer: Yes, rather than looking for photons we can look for neutrinos. Neutrinos can make it directly all the way from the core to us. Neutrinos cannot be focused like light, so we cannot see any details of what happens where in the core, just that events are happening in the core that produce neutrinos. We
have detected neutrinos that come from the heart of the Sun.