Full PHYC10008 Notes (solar system to cosmos) PDF

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Complete lecture notes for the semester. Everything you need for the final exam and mid semester test...

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PHYC10008: From the Solar System to the Cosmos

1: Our Place in the Universe -

Earth à Solar System à Milky Way Galaxy à Local Group à Local supercluster

-

There are 8 planets (first 4 are terrestrial, last 4 are gaseous), 210 moons and dwarf planets (like Pluto or Eris) o

There are many more trans-Neptunian objects similar in size/bigger than Pluto, so instead of changing the number of planets, they changed the definition of planet to exclude Pluto and make it easier

o

Planet must orbit the Sun, have enough mass to be round AND has cleared the surrounding neighbourhood of debris

-

Milky Way, Andromeda and M32 are part of the Local Group, which in turn is part of the Virgo Cluster

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Distance in the Universe is measured in:

-

o

Astronomical Unit (AU) = average distance between Earth and Sun (1.5 x 108 km)

o

Light year = distance light travels in a year (9.5 x 1012 km)

o

Parsec = roughly 3 light years

Because light velocity is finite, and it takes it a certain amount of time to cross large distances, the light we receive from very distant objects let us look back in time, i.e. we are seeing the object as it was when those photons were emitted

2. History of the Universe -

The universe had a beginning: o

Within a second, rapid expansion occurred

o

Within 100-1000 seconds the nuclei of H, He, Li and others began to form

o

We can detect cosmic radiation from as far back as 300 000 years, before this the universe was opaque

o

At a few hundred million years matter began clumping under their own weight to create the first proto-galaxies and stars

o

After a few billion years the expansion of the universe began to accelerate, after initially decelerating (this acceleration is due to dark energy)

o

At 9 billion years our solar system forms, and a billion years later life appeared on Earth

o

Today we are 13.7 billion years into the lifetime of the universe

o

In another 20 billion years from now our Sun will turn into a red giant and life on Earth will no longer be possible

o

In 10100 years, all matter will be trapped inside black holes, protons will decay, and black holes will evaporate, leaving the cold and dead universe as empty space with only radiation

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The universe has been expanding from the beginning, with the expansion now accelerating o

The size and volume of empty space is increasing, but the objects themselves aren’t growing farther apart 1

PHYC10008: From the Solar System to the Cosmos

o

This causes redshift (z); the light we capture from distant galaxies, has a lower frequency than the one we capture from our sun because the distant galaxies are “moving away” from us (Doppler effect) §

-

z=1100 means the universe when it was 1100 times smaller

Everything in space has a velocity and there are 6 major “motions” that govern this velocity o

1. Rotation of the Earth from west to east; largest velocity at equator (1670 km/hr), and lowest at the poles (0 km/hr); Earth rotates as an angle of 23.5º towards Polaris (this causes seasons)

o

2. Orbit of Earth around the Sun with an average speed of 107 000 km/hr in the same direction as the rotational motion

o

3. Random motion of the Sun with respect to the other local stars at 70 000 km/hr

o

4. Rotation of Sun (along with the solar system) around the Milky Way at 800 000 km/hr

o

5. Milky Way moving in the Local Group of galaxies

o

6. The Local Group moving towards the Virgo Cluster

3. Human Side of Science -

Early recordings of the sky and supernovas go as far as 4500 BC in India

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The first attempt to measure the circumference of the Earth was by Eratosthenes in c. 240 BC, who used the sun and shadows to calculate a circumference of roughly 42 000 km (real value 40 100 km)

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Ptolemy (100-170 AD) came up with the geocentric model of the universe, which Aristotle adopted and was taken for truth for 1500 years

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Copernicus proposed the heliocentric model, but still used perfect circles in his models, so it wasn’t more accurate than the geocentric model

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Kepler used Tycho’s observation to come up with the elliptical heliocentric model, which got rid of all discrepancies in previous calculations

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Galileo was one of the firsts to use the scientific method by collecting data without making it fit a preconceived conclusion o

He built the first telescope and discovered the moons of Jupiter and the phases of Venus which was evidence for the heliocentric model

4. Kepler’s 3 laws -

1st law: o

The orbit of a planet is an ellipse with the Sun at the focus by the perihelion (“close to Sun”); the other end of the major axis is called aphelion

o

Ellipticity à 1 – B/A

o

Eccentricity à !1 −

! ( )# "

Both describe the shape of the ellipse, B = minor axis A = major axis

2

PHYC10008: From the Solar System to the Cosmos

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2nd law: o

A planet moving in an orbit will sweep out equal areas for a time t

o

This means it will travel faster closer to the Sun

o

Proven by the conservation of angular momentum (i.e. if a planet has smaller radius/distance to the Sun, it must speed up to conserve angular momentum)

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3rd law: o

P2 = a3

o

P = period of orbit (in years) and a = semi-major axis length (in AU); average distance from the Sun

o

From this law we can calculate speed from period/semi-major axis à 𝑣 = ( = ( % $

#&' (

= ('!/# = (√' #&'

#&

5. Motion and Newton’s laws -

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Galileo’s Theory of Relativity: o

Free motion is constant in speed and direction

o

A free-falling body has constant acceleration

o

It is not possible to tell if an object is in constant motion

o

There is no such thing as an “observer at rest”

Types of motion: o

Speed à rate at which an object moves (m/s)

o

Velocity à speed with particular direction (vector quantity m/s)

o

Acceleration à change in velocity (m/s2) in either value OR direction

o

Momentum à mass x velocity (kg m/s) §

o

Angular momentum à mass x velocity x radius

o

Weight à net force acting on your body §

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An object moves at constant velocity (a = 0) unless a net force acts on it

Newton’s 2nd law: o

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Free-falling object has 0 weight

Newton’s 1st law: o

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Changes with force because force causes acceleration (change in velocity)

F = ma OR F = m∆v (change in momentum)

Newton’s 3rd law: o

For every action (force) there is an equal and opposite reaction (force)

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PHYC10008: From the Solar System to the Cosmos

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Conservation laws: o

Mass-energy, momentum, angular momentum and energy are always conserved

o

Higher principle than Newton’s laws

o

Objects move at constant velocities if no force acts on them due to the conservation of momentum

o

Planets are constantly orbiting the sun due to the conservation of angular momentum §

Angular momentum also proves Kepler’s 2nd law à smaller radius around the sun means velocity must increase to conserve angular momentum

o

Energy can be exchanged or transformed, but never created nor destroyed §

Temperature is the average kinetic energy of particles

§

Thermal energy is the total kinetic energy of particles (temperature + density), i.e. a solution of higher density will have more thermal energy than a less dense solution even if their temperatures are the same

-

Newton’s universal law of Gravitation: o

𝐹* = 𝐺

+$+# $#

G = 6.67 x 10-11 m3 kg-1 s-2

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Newton’s version of Kepler’s 3rd law (can be used to measure mass of distant objects orbiting each other)

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o Orbits cannot change spontaneously (2-body problem) o

Total orbital energy always stays constant if there is no external force acting on it (which is why you can’t fall into a black hole if you are constantly orbiting it)

o

They need an external force acting on them e.g. atmospheric drag, friction or a gravitational encounter with a 3rd body

o

If the object in orbit gains enough orbital energy, it may increase their velocity enough to escape the gravitational pull (escape velocity) §

Escape velocity does NOT depend on the mass of the object trying to escape, only on the mass of the object it is trying to escape, and the radius

§

Gravitational acceleration also does not depend on the mass of the falling object, only on the mass of the more massive object, and its radius

-

The Moon’s gravity pulls on the oceans causing tides o

Highest tides along the direction towards the Moon, lowest along the perpendicular

o

The tides also depend on where the Sun and the Moon are with respect to one another (Solar tidal force is 46% that of the Lunar)

o

Tidal friction (against the ground) gradually slows the Earth’s rotation and makes the moon move farther away 4

PHYC10008: From the Solar System to the Cosmos

6. Our Solar System -

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Sun: o

Over 99.9% of the mass of the solar system

o

Mostly made out of H/He and converts 4 million tons of mass into energy every second

Terrestrial planets are made of rock and metal (high density), are small and closer to the Sun (higher surface temps): o

Mercury à large iron core; the side that faces the sun (day) is very hot (425ºC) and the other side (night) is very cold (-170ºC)

o

Venus à similar in size to Earth but very dense atmosphere that hides the surface; very extreme conditions due to extreme greenhouse effect which also makes it very hot (470ºC day and night)

o

Earth à only planet with surface liquid water to accommodate life and a surprisingly large moon

o

Mars à similar to Earth with giant volcanoes, huge canyons and polar caps; thought to have had flowing water in the distant past

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Jovian planets are gaseous giants (lower density than terrestrials) with many moons and rings that sit farther away from the Sun (lower surface temps) and are considered “miniature solar systems”: o

Jupiter à mostly H/He with no solid surface; its Galilean moons (Io, Callisto, Europa and Ganymede) have solid surfaces and have similarities to planets

o

Saturn à known for its rings which are NOT solid, they are made of countless very small chunks of ice and rock; the Cassini satellite went through them with practically no damage which shows their non-solidity

o

Uranus à made of H/He but also larger quantities of other hydrogen compounds and it has a very unusual axis tilt almost parallel to its orbit

o

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Neptune à similar to Uranus but a much more perpendicular tilt

Dwarf planets are much smaller than normal planets, with icy and rocky composition and also have moons e.g. Pluto and Eris (5 dwarf planets known to date)

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Smaller bodies like asteroids and comets also populate the Solar System: o

Asteroid Belt à flat shape and found between the orbits of Mars and Jupiter §

There are small gaps in the Belt due to orbital resonance with Jupiter, i.e. asteroids’ orbits in the gaps lined up with Jupiter’s orbit creating gravitational tugs that pulled them closer, creating gaps

§ o

It is hypothesised that Jupiter’s tidal forces impeded the formation of a planet there

Kuiper Belt à flat shape and found on the outskirts of the Solar System, after the orbit of Neptune

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PHYC10008: From the Solar System to the Cosmos

o

Oort Cloud à spherically shaped and found in the far end of the Solar System; can’t be seen but we can see comets moving with unbound orbits coming from all directions so its hypothesised to be spherical in shape

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Formation of the Solar System: o

The nebular theory states that a solar system is formed from the gravitational collapse of a massive interstellar gas cloud (solar nebula)

o

Interstellar gas is recycled throughout a star’s lifetime: they are born from the collapse of the gas, form heavier elements during its lifetime thanks to fusion and they return the material (gas) to space when they die in an explosion §

The next star to be born from the new gas cloud now has even heavier elements

§

From the heavy elements found on Earth, it is thought that our Solar System was formed after a number of these cycles

o

As a nebular cloud begins to collapse the conservation of angular momentum and energy cause it to speed up (potential energy à kinetic energy) §

The kinetic energy is then converted to thermal energy, so it also heats up (with the inner parts spinning faster i.e. getting hotter than the outer parts)

§ o

Collision between newly formed particles in the cloud also causes it to flatten

Due to the different temperatures in the disk, the frost line becomes important (to understand the differences between Terrestrial and Jovian planets) §

Inside the frost line of the disk the temperature is too high for ices to stay solid (i.e. they melt) •

This is where Terrestrial planets form from small particles of rock and metal (which are solid even at high temps) stick together getting bigger and heavier and transforming from planetesimals to planets

§

Outside the frost line the temperature is much lower, so ices stay solid •

This is where Jovian planets form because ice is now a solid too, so they can become larger and heavier, obtaining a large gravity which is able to draw in gases like H/He to their surface, becoming even bigger (process of accretion)

o

Once the star/Sun is formed, light and ‘solar wind’ (charged particles exhaled by the new star travelling at very high speeds) blew away most particles which were not accreted onto a planet due to gravity §

According to the nebular theory, the young Sun was much faster than it is now

§

This is due to the ‘loss’ of angular momentum from the exhale of solar wind à the small charged particles latched onto the magnetic field of the sun, rotating with it but getting further away until they are far enough to be out of the field’s influence •

With their increasing radius from the Sun, they increased their angular momentum which means the Sun’s angular momentum must have gone down (conservation laws)

o

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Formation of planets in any solar system would be inevitable (although they would differ widely)

Surprising exceptions to the norms: 6

PHYC10008: From the Solar System to the Cosmos

o

Not all the junk from the nebula cloud latched onto the planetesimals, some was leftover creating rocky asteroids (inside frost line) and icy comets (outside the frost line) §

Water may even have come to Earth from icy planetesimals

§

Most comets are found in “deep freeze” outside the frost line but when they come inside it (and closer to the Sun) they develop 2 tails: •

1st is the dust tail which is the material on it evaporating as it comes into contact with photons

•

The 2nd one is the ion tail is formed as a result of the solar wind ejecting charged particles off the comet’s head (or coma)

o

Mars’s moons are captured, i.e. they are planetesimals which came close enough to Mars to get trapped in its gravitational field and start an orbit (they are not round)

o

Earth’s Moon has some material similar to Earth’s and some which isn’t §

This can mean that the Moon formed as a result of a massive collision between the Earth and Mars-sized planetesimal early in the solar system

§

This collision created a lot of debris, some of which came back to Earth, but some of it accreted together to form our large Moon

o

Big collisions may also explain: §

Uranus’ almost parallel rotation to its orbit •

Although the collision must’ve happened LATE in its formation to have become tipped as it is

§ -

Venus’ opposite rotation to that of the orbit and the rest of the planets

Dating the Solar System can be done in 2 ways: o

1. Looking at the evolution of the Sun

o

2. Radioactive dating of the oldest rocks on Earth (most useful method although both methods give similar results) §

This method is based on all elements in a rock having formed at the same time and knowing the half-life of its elements

§

From there you can count the number of ‘parent’ and ‘daughter’ atoms and find out when the rock was formed

o

Our best estimate for the age of the universe is 4.54 +/- 0.5 billion years (but the Murchison meteorite was dated back to 7 billion years!)

7. Geology of the Solar System -

Terrestrial planets o

Have a heavy metal core of high density, mostly Ni and Fe

o

The outside of the planet is crust which has the lowest density, mostly granite, basalt, etc

o

Between the core and the crust lies the mantle, of medium density, made of Si, O, etc 7

PHYC10008: From the Solar System to the Cosmos

o

The lithosphere is the rigid part of the outer mantle + the crust à divided into tectonic plates §

o

Lithosphere “floats” on the warmer and thus softer rocks of the mantle

The different layers were formed by differentiation early in the planets’ formation §

Higher density material was pulled to the centre by gravity while lower density material was left at the surface

§

For this to happen the planet need to have been “liquid” or molten, when the temperatures were still incredibly high early in the formation of the Solar System

o

Seismic waves can be used to determine the inside of the Earth §

P (primary) waves are longitudinal and fast, and can travel through the Earth’s core