1
Q
What is in the solar system?
A
Eight major planets orbit the sun in the same direction, the Earth’s orbit is approximately circular.
2
Q
How are stars organized within the Milky Way galaxy? [3]
A
- Stars form stellar clusters, large groupings of stars gravitationally attracted to each other formed from the collapse of a single nebula
- Globular clusters have large numbers of mainly old, evolved stars
- Open clusters have smaller numbers of younger stars further apart
3
Q
What does it look like when you zoom out of the galaxy? [3]
A
- Galaxies form “clusters” - the Milky Way is in the Local Group along with the Andromeda galaxy
- Clusters of galaxies form superclusters
- On a very large scale, the universe looks almost uniform.
4
Q
What are binary stars?
A
Two stars orbiting a common centre
5
Q
What is a Cepheid variable?
A
A star of variable luminosity whose luminosity has a well-defined period. The period is related to the absolute luminosity, and so can be used to estimate the distance to the star.
6
Q
What is a comet?
A
A small body of mainly ice and dust orbiting the Sun in an elliptical orbit.
7
Q
What is a constellation?
A
A group of stars in a recognizable pattern that appear to be near to each other in space.
8
Q
What is the main sequence?
A
It is a star undergoing nuclear fusion of hydrogen into helium (eg. the sun). Found in the middle of the HR diagram.
9
Q
What is a nebula?
A
Clouds of dust: carbon, oxygen, silicon, metals, hydrogen in the space between stars.
10
Q
What is a neutron star?
A
The product of the explosion of a red supergiant. Very small and very dense - made almost entirely of neutrons.
11
Q
How do stars carry out nuclear fusion? [3]
A
- The high temperatures inside the core allows the protons to overcome electrostatic repulsion, so nuclei can get close enough to fuse.
- High pressure means that nuclear are close enough to to give high probability of collision and fusion.
- Net result: 4 hydrogen nuclei turn into 1 helium nucleus. Energy is carried away by the photons and neutrinos produced in the reactions.
12
Q
What are the two main forces inside a star?
A
- Gravitation tends to collapse the star inwards
- Radiation pressure opposes the gravitational pressure, keeping the star in equilibrium.
13
Q
What are the following astronomical distances? How can you convert between them?
- A light year
- An astronomical unit
- A parsec
A
- The distance light travels in 1 year (ly)
- The average radius of Earth’s orbit (AU)
- FINISH
14
Q
How can stellar parallax be used to measure astronomical distances? [3]
A
- Two measurements of the angular position of a star are made six months apart.
- The star appears to be displaced relative to the fixed background of distant stars.
- d (parsecs) = 1/p (in arc seconds)
15
Q
What is the parallax angle?
A
(p) is the angle, at the position of a star, that is subtended by a distance equal to the radius of the Earths orbit around the sun.
16
Q
What are the limitations of the parallax method?
A
If a star is too far away, the parallax angle is too small to be measured.
On Earth, distortions caused by the atmosphere also limit measurements.
17
Q
What is the surface area of a sphere?
A
A = 4πR² for a sphere of radius R
18
Q
What is luminosity? How can it be calculated?
A
The power radiated by a star, measured in watts. L = σAT^4 T = surface temperature A = surface area σ = Stephan-Boltzmann const
19
Q
What is apparent brightness? How can it be calculated?
A
The received power per unit area (Wm^-2)
b = L/4πd²
Where d is the distance to the star.
20
Q
What are stellar spectra?
A
Stars are assumed to radiate like a black body, over an infinite range of wavelengths.
21
Q
What is Wien’s displacement law?
A
- The peak wavelength, λ₀ is related to surface temperature T by:
λ₀T = constant = 2.9 x 10^-3
The higher the temperature of a star, the shorter the peak wavelength of radiation will be.
22
Q
What do absorption spectra show about a star? CHECK IN TEXTBOOK SAYS COOLER STARS WILL NOT RESULT IN MORE DARK BARS
A
- Dark bars represent the absorption of light of a specific wavelength by a specific chemical in the star’s atmosphere.
- The hydrogen in hotter stars is ionized, so atoms cannot absorb any light passing through them. Cooler stars have more electrons and can absorb more wavelengths
23
Q
What does the Hertzsprung-Russell diagram illustrate? Where can different types of star be found? [6]
A
- The correlation between surface temperature (hot to cold on the x axis) and luminosity (very bright at the top)
- The main sequence shows stars that fuse hydrogen into helium.
- The sun is right in the middle of the main sequence
- Red supergiants are above red supergiants in the top right
- White dwarfs are in the bottom left.
- Red dwarves and blue giants occupy the ends of the main sequence.
24
Q
What are some of the characteristics of red giants and supergiants?
A
- Large, cool stars with reddish appearance, tenuous (not very dense)
25
What are some of the characteristics of white dwarfs?
- dim, small, hot, whitish and dense. They are the naked core of red giants.
26
How is the mass of a star related to its luminosity?
L ∝ M^3.5
| - Only applies to main sequence stars
27
What causes Cepheid variables to fluctuate in luminosity?
- There is a periodic expansion and contraction in the outer layers of the star, caused by radiation ionizing helium, it heating up and expanding, then cooling, contracting, and helium nuclei recombining with electrons.
28
What is a standard candle?
A star of a known luminosity
29
What happens during the early part of a stars life? [3]
- Protostars begin to the right of the main sequence.
- As they contract under their own weight, GPE is converted to thermal energy and eventually it is hot and pressured enough for fusion to begin.
- More massive stars take less time to move to the main sequence.
30
What is the main factor that determines the evolution off the main sequence?
The mass of the star
31
What happens to high mass stars once they have used up roughly 12% of their hydrogen? [3]
- They move off the main sequence.
- The pressure caused by gravity is enough to raise the temperature sufficiently to fuse heavier elements: Ne, O, Mg, Si, Fe. These are layered shells of progressively higher temperature and heavier elements.
- Fusion ends with the production of iron, since it is near the peak on the binding-energy curve. No further fusion reactions can be made that release energy.
32
What happens to low mass stars off once they have used up roughly 12% of their hydrogen? [6]
- They move off the main sequence
- Helium collects in the core
- The hydrogen directly surrounding the core hoses into helium
- The temp builds up, and helium in the core begins to fuse into carbon then oxygen.
- The huge release of energy blows away the outer layers of the star in a planetary nebula, leaving behind the carbon and oxygen core (a white dwarf).
- Temperature never gets high enough for more fusion reactions. White dwarfs have no reactions.
33
What happens to white dwarfs once they are formed?
- They cool slowly, no fusion reactions take place, and eventually become a black dwarf. (none exist yet because it takes so long).
34
What prevents the collapse of white dwarfs?
- Electron degeneracy
35
What is the Chandrasekhar limit?
The maximum mass of a white dwarf is 1.4 solar masses (M☉)
36
What happens when iron is finally produced in a red supergiant? [4]
- When fusion stops in the core, the GPE overcomes the radiation pressure and the star collapses.
- The star is very hot in the core, and photons have enough energy to split nuclei apart into individual protons and neutrons.
- Electrons are forced into protons, turning them into neutrons and producing neutrinos. The star is nearly all neutrons.
- Because of the Pauli Exclusion principle, the collapsing star rebounds on the core, creating a supernova explosion that rips apart the outer layers of the star.
37
What is the Oppenheimer-Volkoff limit?
- When the mass of the core of a red supergiant is less than 2-3 solar masses (M☉), it will form a neutron star after a supernova.
- Above the limit, the core left behind by a supernova may collapse further and become a black hole.
38
What is a neutron star?
- The end result of a red supergiant.
- Very small, very dense, and made almost entirely of neutrons.
- Neutron pressure keeps the star from collapsing further
39
What causes the redshift of distant galaxies?
- The absorption spectrum of light from distant galaxies is red shifted, which according to the Doppler effect, implies that they are moving away.
- This suggests that the space between galaxies is stretching and the universe is expanding.
40
What is the velocity of recession?
- The speed at which a distant galaxy is moving away from us.
41
What is Hubble's law?
- The velocity of recession is directly proportional to the distance away from a distant galaxy.
- v = H₀d
v = velocity of recession
H₀ = Hubble constant, the gradient of v against d graph
d = distance away
The more distant, the faster it is moving away.
42
How can you calculate redshift?
- z = (λ - λ₀)/λ₀
z is the redshift
λ is the wavelength received on Earth
λ₀ is the wavelength of a spectral line
43
What evidence is there for the Big Bang? [2]
- The redshift of light from distant galaxies shows that the universe is expanding, and that the universe must have begun from a very small point.
- The cosmic microwave background is the residual radiation from the Big Bang explosion. Temperature has fallen with the expansion of the universe.
CHECK THESE AGAINST A MARKSCHEME
44
What is the cosmic scale factor?
R describes the expansion of the universe.
d = RΔx
where d is the physical distance between two points
Δx is the difference in coordinates.
45
How can redshift be expressed in terms of the cosmic scale factor? How is this derived?
λ₀ = R₀Δx and λ = RΔx
gives λ/λ₀ = R/R₀
Combine with redshift formula z = (λ - λ₀)/λ₀ = λ/λ₀ - 1
z = R/R₀ - 1
46
What was the Big Bang?
The universe began as an infinitesimally small point of enormous temperature. Time space and energy were created in an explosion which set matter moving outwards
47
How can you estimate the age of the universe?
T(small H) = 1/H₀
Using the Hubble constant.
This is an upper bound on the age of the universe because it assumes that the universe has been expanding at a constant rate.
48
What are the characteristics of the cosmic microwave background?
- a spectrum corresponding to black-body radiation at a temperature of 2.7 K
- The peak radiation is in the microwave region
- The radiation is isotropic with no apparent source
49
How was the rate of expansion of the universe found?
Scientists measured the redshift for very distant galaxies using type Ia supernovae as standard candles.
They used a formula for distance in terms of z and the deceleration parameter q₀.
q₀ turned out negative, indicating that the expansion of the universe is accelerating.
50
How can type Ia supernovae be used to find distance?
All type Ia supernovae have the same peak luminosity and so can be used as standard candles
51
What is the Jeans criterion?
Whenever the gravitational energy of a given mass of gas exceeds the average kinetic energy of the random thermal motion of its molecules, the gas becomes unstable and tends to collapse.
GM²/R > 3/2 NkT
R = radius of the gas cloud
M = mass of the gas cloud
N = number of particles
T = temperature
Ie. if a gas cloud is massive or cool enough it will collapse to form protostar(s).
52
How are heavy elements formed? [4]
Neutron capture - nuclei absorb neutrons, become unstable, and decay, becoming a heavier element.
- The s-process happens when there are not many neutrons present. After absorbing neutrons, nuclei decay before absorbing more neutrons.
- The r-process happens during a supernova: nuclei keep absorbing neutrons before decaying and the atomic number increasing.
- Neutrons can absorb neutrinos in supernovas, and become a proton and an electron.
53
What are the main features of type Ia supernovae? [3]
- They do not have hydrogen lines in their spectra
- They are produced when mass from a companion star accretes onto a white dwarf, forcing it to exceed the Chandrasekhar limit.
- They have a luminosity that falls off sharply after explosion
54
What are the main features of type II supernovae? [3]
- They have hydrogen lines in their spectra
- They are produced when a red supergiant explodes
- They have a luminosity which falls off gently after the explosion.
55
What is the cosmological principle?
- The universe is both homogenous and isotropic
| - Ie. The universe appears uniform on a very large scale and it looks the same in all different directions.
56
How does the cosmological principle imply that the universe has no edge?
- An edge would violate the homogeneity principle as the place near the edge would look different from the middle
- It would violate the isotropy principle because an observation from the centre would be different from one near the edge.
57
What is the significance of fluctuations in the CMB?
- Small variations in temperature are related to variations in density, which explains the formation of structures such as stars and galaxies. A perfectly uniform universe would not allow these structures to form.
58
How can you find the speed of rotation of a particle orbiting inside a spherical mass cloud of uniform density?
use v = √(GM/r) where M is the mass of the spherical volume inside the orbit radius r.
Find a substitution for M using density p = M/V and the volume of a sphere.
Gets v = √(G4π^3p/3r)
So v ∝ r
59
What does the rotation curve of the Milky Way suggest? [3]
- Speed (y) against radial distance from galactic centre
- The flat part of the galaxy's rotation curve indicates substantial mass far from the centre: dark matter.
- The relationship v ∝ r predicts that otherwise the rotation curve would be a straight line graph.
60
What is dark matter? [3]
- Matter that is too cold to radiate and cannot be seen, known mainly because of its gravitational effects on nearby bodies.
- Could be partially baryonic matter (made of protons and neutrons)
- Could be undiscovered elementary particles based on the idea of supersymmetry.
61
How can you show that the universe is cooling down using the formula λ/λ₀ = R/R₀ ?
The wavelength λ₀ corresponds to a CMB temperature T₀. By Wien's displacement law,
λ₀T₀ = λT = constant
Rearrange λ/λ₀ = T₀/T
Therefore T₀/T = R/R₀
And T ∝ 1/R
As the universe expands (R gets bigger), the temperature drops.
62
What is the critical density and how can you derive it?
It is the density which,
The total energy of a mass traveling outward at the edge of a spherical dust cloud velocity v: Et = Ek + Ep = 1/2mv² - GMm/r
Substitute in the density Mass of the cloud in terms of density, and the velocity in terms of Hubble's law: M = ρ4/3πr^3 and v = H₀r
Rearrange to show E = 1/2mv²(H₀ - 8πρG/3)
Set (H₀ - 8πρG/3) and rearrange to find critical density ρc
63
What does the total energy of the a mass travelling outward at the edge of a spherical mass cloud show? [3]
- If the total energy is positive, it will expand forever. ρ < ρc
- If the total energy is zero, expansion will halt at infinity. This corresponds to the critical density. ρ = ρc
- If the total energy is negative, contraction will follow expansion. ρ > ρc
64
What are density parameters Ωm and ΩΛ ?
```
Ωm = ρm/ρc = actual density of matter in the universe/critical density
ΩΛ = ρΛ/ρc = density of dark matter/critical density
```
65
What do the density parameters show?
- Whether the universe will expand forever, stop at infinity, or collapse. Eg. if ΩΛ = 0, Ωm > 1 ie. ρm > ρc then the universe will collapse
66
What does the sum of the density parameters show?
| Ωm + ΩΛ
The geometry of the universe: expands forever or collapses?
Ωm + ΩΛ = (ρm + ρΛ)/ρc
ρm + ρΛ < ρc open universe / open model
ρm + ρΛ = ρc flat universe / critical model
ρm + ρΛ > ρc closed universe / closed model
67
What is dark energy?
Energy that creates a repulsive force to counteract the effects of gravity on a large scale and cause the universe to accelerate outwards.
68
What is the CNO cycle?
A series of fusion reactions in more massive main sequence stars, in which carbon, nitrogen and oxygen are produced.
The net effect is to turn four hydrogen nuclei into one hydrogen nucleus.
69
What is the triple alpha process?
A series of fusion reactions that occurs in red giants.
| The net effect is that three helium nuclei turn into a carbon nucleus.
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