5.5 astrophysics and cosmology

planets

objects with mass sufficient for their own gravity to force them to take a spherical shape (in hydrostatic equilibrium) where no nuclear fusion occurs and the object has cleared its orbit of other objects

dwarf planets

like planets but the orbit has not been cleared of other objects

planetary satellites

bodies that orbit a planet

asteroids

objects that have a near circular orbit around the sun, but are too small and uneven in shape to be planets (not in hydrostatic equilibrium)

comets

small, ittegularly sized balls of rock, dust and ice which orbit the sun in eccentric ellipses

solar systems

systems containing stars and their orbiting objects

galaxies

very large collections of solar systems, dust and gas

nebulae

very large clouds of dust and gas in which stars form

formation of protostars

-the gravitational attraction between dust and gas particles in nebulae slowly pulls them closer together causing denser regions to form
-the GPE converts to thermal energy and these regions become protostars

formation of stars from protostars

-hydrogen gas nuclei overcome the electrostatic forces of repulsion and undergo nuclear fusion
-this produces helium, producing a star
-the star remains in stable equilibrium during its main phase
-once all of the hydrogen is used up, the star’s next phase is determined by the mass of its core

stable equilibrium

the force of the star’s gravity is equal to that of the radiation pressure from the photons emitted from nuclear fusion and the gas pressure in the core, keeping the star at a constant size

star core

the central region of a star where nuclear fusion occurs

solar mass (inc symbol)

1.99x10^30kg

evolution of a low mass star

-these stars remain in the main sequence for longer as they have a smaller, cooler core
-once their hydrogen runs low they will collapse inwards, forming a red giant
-the core is too cool for fusion, but helium will fuse in the outer shell as it has sufficient pressure
-once helium runs low it will collapse further inwards and become a white dwarf, and the outer shell will separate and form planetary nebulae

white dwarfs

fusion does not take place in white dwarfs, and they have a temperature of around 3000K, photons produced during fusion earlier in its lifetime leak out, dissipating heat
electron degeneracy pressure (caused as two electrons cannot exist in the same state) prevents the core from fully collapsing, and once the core’s mass is below 1.44(SM) (Chandrasekhar Limit) the white dwarf is stable

evolution of a massive star

-as hydrogen depletes, the temperature is sufficient for helium fusion to occur and form heavier elements, forming a red supergiant
-once an iron core is produced, the star becomes unstable and a type 2 supernova occurs: a shockwave ejects the materials in the outer shells and the core collapses, elements heavier than iron form
-if the remaining core’s mass is above 1.44(SM) (Chandrasekhar Limit) protons and electrons combine to form neutrons producing an extremely small, dense neutron star
-if the remaining core’s mass is above 3(SM), gravity becomes so strong that the escape velocity becomes higher than the speed of light, creating a black hole

red supergiant

has many layers of increasingly heavy elements produced from fusion with an inert iron core (iron doesn’t fuse further as its fusion doesn’t release energy)

star mass boundaries

low mass stars have masses of 0.5 - 10 (SM) and anything above is a massive star

Hertzsprung-Russell diagram (HR diagram)

shows the stellar luminosity of a star versus its temperature, stars of the same spectral class tend to be clustered together (inc image)

energy levels of electrons

electrons bound to an atom can only exist in certain discrete energy levels, they cannot have an energy value between two levels
each element has its own set of energy levels

excitation and de-excitation

when an electron gains energy and moves to a higher energy level (further from the nucleus) it is excited
when it loses energy and moves to a lower energy level (closer to the nucleus) it is de-excited, and the energy is released as a photon of a certain wavelength

energy level values

all energy level values are negative (as energy is required to free the electron from the atom)with the ground state being the most negative, an electron that is completely free from an atom has energy equal to zero

continuous line spectra

contains all visible wavelengths of light

emission line spectra

a series of coloured lines on a black background where each line corresponds to a wavelength of light emitted when atoms are de-excited
each element produces a unique emission line spectrum because of its unique set of energy levels

absorption line spectra

a series of dark lines against the continuous spectrum with each line corresponding to a wavelength of light used to excite atoms of that element

emission vs absorption line spectra

the dark lines on the als are at the same wavelengths as the coloured lines on the els (meaning they are inverted) as the energy needed to excite an electron between two energy levels is the same as the energy released in de-exciting an electron between those same two energy levels

energy released in de-excitation

given by E = hc/λ

diffraction gratings

components with regularly spaced slits that can diffract light

diffraction angles

different colours have different wavelengths so are diffracted at different angles, given by dsin(theta) = n(lambda)
where d is the diffraction slit separation, theta is the angle, n is the order of maxima and lambda is the wavelength

atars and surface temperature

all objects with thermal energy emit electromagnetic radiation of varying wavelength and intensity, thus the surface temperature of a star affects its colour
stars can be modelled as idealised black bodies that emit radiation across a range of wavelengths, with a peak in intensity at a specific wavelength corresponding to the colour of the star

wein's law

"the black body radiation curve for different temperatures peaks at a wavelength intensity inversely proportional to the temperature of the object"
λmax ∝ 1/T
λmaxT = Wein's Constant
where λmax is the peak wavelength of the light and T is the absolute surface temperature of the object

wein's constant

2.9 x 10^-3mK

Stefan's law

"for a black body, the total radiant heat energy emitted from a surface (luminosity) is proportional to the fourth power of its absolute temperature"
L ∝ 4πr^2T^4
L = 4πr^2T^4σ
where L is the luminosity, T is the absolute surface temperature and σ is Stefan's Constant

Stefan's constant

σ, 5.67 x 10^-8 Wm^-2k^-4

absolute temperature

temperature in Kelvin, important to remember to not lose marks

astronomical units (AUs)

1.5 x 10^11m
the average distance from the Earth to the sun, often used to express distances of planets from the sun

light years

9.46 x 10^15m
the amount light travels in a year, often used to express distances to stars and other galaxies

angles in cosmology

can be measures in arcminutes (60ths of a degree) and arcseconds (3600ths of a degree)

parsecs (pc)

3.1 x 10^16m
can also be written as 1AU/arcsecond
the distance at which a radius of 1 astronomical unit subtends an angle of 1 arcsecond (i.e. draw a right-angled triangle with θ as 1 arcsecond- a will be 1 parsec and o will be 1 AU)
(inc diagram)

stellar paralax

the apparent shift in position of an object against a backdrop of extremely distant objects (that are so far away they don't move a noticeable amount) can be used to measure the distance to nearby stars up to distances of 100 parsecs, past that point the angles are too small to be measured without significant error

using SP to calculate distance

d = 1/p
where d is the distance between the observer and the object in parsecs, and p is the parallax angle in arcseconds

cosmological principle

"the universe is isotropic (the same in all directions) and homogenous (uniformly distributed)"

doppler effect

the apparent shift in wavelength that occurs when the source of the waves is moving
if the source is moving towards the detector, the wavelength appears to decrease, and if it is moving away the wavelength appears to increase

doppler effect and stars

the doppler effect shifts the positions of stars' spectral lines, and the doppler equation can be used to determine the relative speed of a star using the shift in wavelength from a hydrogen emission spectrum
Δλ/λ = v/c
where v is the velocity of the star relative to earth, λ is the original wavelength of the hydrogen spectral line, and Δλ is the change in wavelength of the hydrogen spectral line from light emitted by the star

hubble's law

"the recessional velocity v of a galaxy is proportional to its distance from earth"
V = H0d where H0 is the hubble constant

hubble constant

67.8kms^-1Mpc^-1

expanding universe

hubble's law suggests that the universe is constantly expanding, as almost all light from distant galaxies is red-shifted showing that the galaxies are moving away from Earth
this suggests the fabric of space and time is expanding, and any point in the universe is moving away from any other point

estimating the age of the universe using hubble's law

in the big bang theory all points in the universe were together, thus any galaxy's distance from earth and velocity relative to earth should be able to be used to calculate time since the big bang where it initially began moving away
V = H0d
t = d/V = d/H0d = 1/H0 = ~14 billion years
this is only a rough estimate as the velocity of objects moving away from earth is not constant

big bang theory

theory attempting to describe the origin of the universe
everything in the universe was originally contained in a singularity (an infinitely small point of infinite density where known laws of physics do not apply) which suddenly expanded outwards, and continues to expand to this day

evidence for the big bang theory

-hubble's law
-microwave background radiation

microwave background radiation

constant interference present everywhere in space

cosmic MBR and the BBT

microwave background radiation supports the big bang theory as it states that originally there were high-energy gamma photons, whose wavelengths became stretched into the microwave region as the universe expanded, and is the only known explanation for this phenomenon
however there is no experimental evidence for this as we can't recreate the initial conditions of the big bang

…

history of the universe and big bng, add later

expansion of the universe

this is happening at an increasing rate (accelerating) but this is not fully understood
dark energy is a hypothetical energy form used to explain the expansion and dark matter is a hypothetical matter form used to explain the acceleration

dark energy

a hypothetical form of energy which fills up space and accelerates expansion, should make uo 68% of energy but experiments have not been able to find its form

dark matter

a hypothetical form of matter which explains observations suggesting mass is not concentrated in the centre of galaxies but is instead spread out

dark matter explanation

all observable mass in galaxies is concentrated in the centre so there must be another un-observable type, it should make up 27% of the mass in the universe
it doesn't interact with light but potential particle types have been suggested

future of the universe

three options depending on the density of the universe:
-open, will continue expanding
-closed, will stop expanding, contract and collapse on itself
-flat, will stop expanding and remain a fixed size