Astronomy Homeworks ( Astronomy Of The Universe AST 101) !!

When a galaxy forms, gravity pulls all of the material toward the center of the mass distribution.

Conservation of angular momentum – one consequence of this is that if a rotating object’s volume is decreased the object will rotate faster.

 

Remember the discussion about randomness. While the material that will make up the galaxy is collapsing, the individual molecules still have some random motion. The way to think about this is that there is a bulk motion (gravitational collapse) and a random motion (particles moving individually) and the combination of this determines the outcome.

 

In this random motion, it is expected that roughly (but not exactly) half of the material is rotating clockwise and half of the material is rotating counterclockwise. Combining these thoughts means that as the bulk motion causes the material to collapse, an overall rotation will become significant.

 

Now consider our solar system. The planets that are further from the Sun are in a weaker gravitational field. This means that they orbit around the Sun more slowly.

 

As the material collapses to form a galaxy, much of it will gain an orbital speed that is high enough to keep it from moving inward further. In other words, the gravity pulling the material together is not strong enough to pull in material with significant rotation. The result of this is that the majority of the material forms a supermassive black hole at the center and the remainder creates a debris field around it.

Initially, this debris field will have a spherical distribution. Eventually, it will flatten out into a disk. This forms our spiral galaxy. The debris in the disk eventually forms the stars, planets, etc.

 

 

Stars form basically the same way as a galaxy. Gravity pulls together material to form the star. There is a debris field around the star which becomes planets, asteroids, comets, etc.

 

Solar vs Stellar … Solar refers to our Sun while stellar refers to stars in general. The name of our sun is Sol.

 

Stars form from molecular clouds. Are the molecules within the molecular clouds moving or at rest? They must be moving fast enough to keep the cloud from collapsing due to gravity. They must also be moving slow enough to keep the cloud from dispersing.

 

What is an arbitrary volume? It is a defined region of space that does not have any physical boundaries and is used to describe the behavior in that region.

Consider an arbitrary volume in the molecular cloud. The motion of the individual molecules leads to density fluctuations within this volume.

How do the density fluctuations affect the gravitational field within the arbitrary volume? Remember that gravity is determined by mass and separation. This means that at low density the gravitational field is weaker. This is because there are fewer molecules (less mass) and on average the molecules are further apart. Conversely, at high density the gravitational field is stronger.

 

In order for a star to form, an arbitrary volume with enough mass (an amount of mass equal to the mass of a star) must reach a high enough density that the gravitational field is strong enough to collapse just the arbitrary volume in question.

 

After the first star forms, the outward flow of energy through the cavity left behind triggers more star formation. The majority of the material in the molecular cloud eventually becomes either part of a star or the stellar system around it.

 

As the material is collapsing the density, temperature, and pressure are all increasing. The increasing temperature leads to the formation of a plasma core. This plasma core will eventually sustain nuclear fusion and at this point you have a newly formed star.

 

At low enough temperature, water is a solid. The molecules are held together in a lattice structure and there is minimal motion. When enough energy is added that the water melts, it is now in liquid form and the molecules clump together due to surface tension.

Continuing to add energy will lead to the liquid evaporating to form a gas. Now the molecules are completely dissociated from one another.

What happens when the gas continues to be heated (more energy is continually added to the gas)? At significant temperature the molecular bonds begin to break and now there are isolated hydrogen and oxygen molecules instead of water molecules.

The final stage in the generation of the plasma is collisions that can strip the electrons away from their respective nuclei. The end result is protons (hydrogen nuclei), oxygen nuclei, and individual electrons. This means that the constituents are now ionized (electrons are negative and the nuclei are positive).

 

Assuming that the Big Bang Theory is correct, the universe began as roughly 75 percent hydrogen and 25 percent helium with trace amounts of other material. Observations today suggest that the universe is 70 percent hydrogen, 25 percent helium, and 5 percent other stuff.

 

A consequence of this is that molecular clouds will be roughly 70 percent hydrogen. This means that when a star forms inside a molecular cloud its plasma core will be roughly 70 percent protons (hydrogen nuclei). This means that once a star forms, it and all other stars will evolve through the same process.

What is nuclear fusion?

1) Nuclear – pertaining to the nucleus (mostly to the protons).

2) Fusion – to combine

3) Nuclear fusion is the combining of protons to form heavier elements.

Individual protons will repel one another. In order to have them fuse they need to be traveling at very high speeds (they need to be in a high temperature environment). After two protons fuse together they will be highly unstable due to the repulsive force between them.

 

One of two things is going to happen. Either the protons are going to rip back apart or something must happen to remove the repulsion. The answer is that one of the protons becomes a neutron and the repulsive force disappears.

The model for this is that protons and neutrons are made up of quarks. For now, the agitation in the protons after they fuse causes one of the quarks to change its properties. This causes the proton containing that quark to change from being a proton to being a neutron.

 

 

 

 

 

In physics we assume that the total amount of energy in the universe is constant. This means that energy can’t be created from nothing and it won’t just magically disappear.

 

In physics the work-energy theorem says that the change in energy is equal to the amount of work done.

 

 

The initial fusion process in any star (regardless of mass) is going to be hydrogen fusion. Specifically this is the proton-proton chain.

 

The first of three parts for the proton-proton chain is the fusion of two individual protons to form deuterium. Remember that deuterium is one of the isotopes of hydrogen. A deuterium nucleus has one proton and one neutron.

The second part is where a third proton is added and a helium-3 nucleus is made. Now this is an isotope of helium

The third part is where two helium-3 nuclei fuse together and form a helium-4 nucleus. This is the most stable isotope of helium.

The overall result is that after a star forms and develops a significant plasma core, hydrogen fusion begins and produces both helium-4 and excess energy (in the form of photons). The star holds on to the helium that was made and releases the excess energy into the environment.

 

Does the star have an infinite amount of hydrogen (fuel)? No

This means that eventually the core will no longer be able to sustain hydrogen fusion in this way. This means that one of three things must happen:

1) More hydrogen is added to the core

2) The fusion relocates to where there is more hydrogen

3) The fusion ceases

For the purposes of this class (and most astrophysics) a star is considered to be a sphere that is spherically symmetric.

 

An object that is spherically symmetric can be considered as a collection of infinitely thin spherical shells that are concentric.

A consequence of this is that the only variation in the star’s parameters are based on changes in distance from the center (radius).

 

Given this, once the core can no longer support hydrogen fusion, the fusion relocates to where there is more hydrogen. It moves outward because that is where the hydrogen fusion can take place efficiently.

 

 

 

Why does our sun stay the same size?

Gravity is always trying to make everything smaller. The energy being released by fusion is counteracting this and trying to make the star bigger. Think about this as a continuous outward flow of energy. The reason the star stays the same size is because these two effects are balanced and the star is in equilibrium.

 

Moving the hydrogen fusion outward means that it is taking place on a larger surface. The fusion process is the same, but there is more of the process occurring. This means that the outward pressure goes up. Gravity has not changed. The end result is that the star gets bigger because it is no longer in equilibrium and the outward pressure is greater than gravity’s ability to try and make the star smaller.

 

Now that the fusion is making energy and helium, but this fusion is no longer taking place at the core, where does the helium go? The helium is heavier than its surroundings so it migrates toward the core and begins to stockpile

 

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