Section 9: Astrophysics

Question 1

What is a convex or converging lens?

Answer 1

A lens which focuses incident light.

Question 2

What is a concave or diverging lens?

Answer 2

A lens which spreads out incident light.

Question 3

What is the principal axis?

Answer 3

The line passing through the centre of a lens at 90 degrees to its surface.

Question 4

What is the principal focus in a converging lens?

Answer 4

The point where incident beams passing parallel to the principle axis will converge.

Question 5

What is the principal focus in a diverging lens?

Answer 5

The point from which the light rays appear to come from. This is the same distance either side of the lens.

Question 6

What is the focal length?

Answer 6

The distance between the centre of a lens and the principal focus. The shorter the focal length, the stronger the lens.

Question 7

What is a real image?

Answer 7

The image formed when light rays cross after refraction. Real images can be formed on a screen.

Question 8

What is a virtual image?

Answer 8

The image formed on the same side of the lens. The light rays do not cross, and so a virtual image cannot be formed on a screen.

Question 9

What is the lens formula?

Answer 9

1/u + 1/v = 1/f

where u is the distance from the object to the centre of the lens, v is the distance of the image from the centre of the lens, and f is the focal length of the lens.

Question 10

What is the power of a lens?

Answer 10

A measure of how closely a lens can focus a beam that is parallel to the principal axis - in other words, how short the focal length is.

The shorter the focal length, the more powerful the lens.

In a converging lens this value is positive and in a diverging lens it is negative.

Measured in Dioptres (D).

Question 11

What is the formula for power of a lens?

Answer 11

P = 1/u + 1/v = 1/f
(the lens formula)

Question 12

What is the objective lens?

Answer 12

The lens that collects light and creates a real image of a very distant object.

Question 13

What features should the objective lens have?

Answer 13

A long focal length, and it should be large to collect as much light as possible.

Question 14

What is the eyepiece lens?

Answer 14

The lens that magnifies the image produced by the objective lens so that the observer can see it. It produces a virtual image at infinity since the light rays are parallel. This reduces eye strain for the observer as they do not have to refocus every time they look between the telescope image and the object in the sky.

Question 15

What is normal adjustment?

Answer 15

When the distance between the objective lens and eyepiece lens is the sum of their focal lengths (fo + fe). This means the principal focus for these two lenses is in the same place.

Question 16

When can M be said to equal fo/fe?

Answer 16

When the angle subtended by the image at the eye and the angle subtended by the object at the unaided eye are both less than 10 degrees.

Question 17

Describe the setup of a Cassegrain Reflecting Telescope

Answer 17

A concave parabolic primary mirror with a long focal length and a small convex secondary mirror in the centre. The light is collected through the combination of the primary and secondary mirrors and focused onto the eyepiece lens in the centre of the primary mirror.

Question 18

What is chromatic aberration?

Answer 18

For a given lens, the focal length of red light is greater than that of blue light, which means they are focused at different points (since blue is refracted more than red).

This can cause a white object to produced on image with coloured fringing, with the effect being most noticeable for light passing through the edges of the lens.

Question 19

What is spherical aberration?

Answer 19

The curvature of a lens or mirror can cause rays of light at the edge to be focused in a different position to those near the centre, which leads to image blurring and distortion.

This effect is most noticeable in lenses with a large diameter.

Question 20

How can spherical aberration be avoided in reflecting telescopes?

Answer 20

Using parabolic objective mirrors.

Question 21

How can both types of aberration be minimised in lenses?

Answer 21

Make use of an achromatic doublet: a convex lens made of crown glass and a concave lens made of flint glass cemented together. This brings all rays of light into focus in the same position.

Question 22

What are the disadvantages of refracting telescopes?

Answer 22

• Glass must be pure with no defects, which is difficult for a large diameter lens
• Large lenses can bend and distort under their own weight
• Chromatic and spherical aberration affect lenses
• They are incredibly heavy and difficult to manoeuvre
• Large magnifications require large diameter objective lenses
• Lenses can only be supported from the edges

Question 23

What are the advantages of reflecting telescopes?

Answer 23

• Few nanometre thick mirrors can be made, which give excellent image quality
• Mirrors unaffected by chromatic aberration and spherical aberration can be solved by using parabolic mirrors
• Mirrors not as heavy as lenses, so easier to handle and manoeuvre
• Chromatic aberration in eyepiece lens can be solved by using achromatic doublet
• Large composite primary mirrors can be made from lots of smaller mirror segments
• Large primary mirrors are easily supported from behind

Question 24

Describe and explain how a radio telescope works

Answer 24

They consist of a large diameter parabolic dish, which reflects radio waves onto a detector, that sends the signal to an amplifier that is then sent to a trace, in order to be able to see the intensity of radiation.

They can be ground-based since the atmosphere does not absorb most radio waves, however they must be in remote locations to avoid interference.

It also needs to move across an area in order to build up an image.

Question 25

Describe and explain how an infrared telescope works

Answer 25

They consist of large concave mirrors which focus radiation onto a detector. However, since infrared radiation is emitted as heat, these telescopes must be cooled using cryogenic fluids to almost absolute zero. They must also be shielded to avoid thermal contamination.

They are used to observe cooler regions in space. However, the atmosphere absorbs most infrared radiation, so these telescopes must be launched into space.

Question 26

Describe and explain how a UV telescope works

Answer 26

They utilise a cassegrain configuration to bring UV rays to a focus, which are then detected by solid state devices which use the photoelectric effect to convert UV photons into electrons, which then pass around the circuit.

They must be positioned in space since the ozone layer blocks all UV rays with a wavelength less than 300nm. They can be used to observe interstellar medium and star formation regions.

Question 27

Describe and explain how X-ray telescopes work

Answer 27

Since X-rays have such high energy and would pass through mirrors, X-ray telescopes are made up of a combination of extremely smooth parabolic and hyperbolic mirrors. The X-rays skim off these mirrors and are brought into focus on CCDs that convert them into electrical pulses.

They must be positioned in space as all X-rays are absorbed by the atmosphere. They are used to observe high-energy events and areas such as active galaxies, black holes and neutron stars.

Question 28

Describe and explain how gamma telescopes work

Answer 28

Gamma radiation would pass through all mirrors, so these telescopes instead use a detector made of layers of pixels, and as gamma photons pass through they cause signals into pixels they come in contact with.

They are used to observe gamma ray bursts, quasars, black holes and solar flares.

Question 29

Describe the two types of gamma ray bursts (GRBs)

Answer 29

Short-lived: Last 0.01 - 1 sec, associated with merging neutron stars (forming a black hole) or a neutron star falling into a black hole.
Long-lived: 100 - 1000 sec, associated with a Type II supernova.

Question 30

What is collecting power?

Answer 30

A measure of the ability of a lens or mirror to collect incident EM radiation.

It increases with the size of the objective lens/mirror. It is directly proportional to (objective diameter)^2.

The greater the collecting power, the brighter the images produced.

Question 31

What is resolving power?

Answer 31

The ability of a telescope to produce separate images of close-together objects.

Question 32

What is the Rayleigh Criterion?

Answer 32

The criterion that states that two objects will not be resolved if any part of the central maximum of either of the images falls within the first minimum diffraction ring of the other.

Also represented by the equation:

θ = λ/D , where θ is the minimum angular resolution, λ is the wavelength of radiation and D is the diameter of the objective.

Question 33

What are charge-coupled devices (CCDs)?

Answer 33

An array of light-sensitive pixels which become charged when they are exposed to light by the photoelectric effect.

Question 34

State and explain the features of a CCD that can be compared with the human eye

Answer 34

• Quantum efficiency: the percentage of incident photons which cause an electron to be released.
• Spectral range: the detectable range of wavelengths of light
• Pixel resolution: the total number of pixels used to form the image on a screen
• Spatial resolution: the minimum distance two objects must be apart to be distinguishable
• Convenience: how easy images are to form and use

Question 35

Compare the quantum efficiency and spectral range of a CCD and the human eye

Answer 35

CCD
- QE: ~80%
- SR: Infrared, UV, visible

Eye
- QE: 4-5%
- Only visible light

Question 36

Compare the pixel resolution and spatial resolution of a CCD and the human eye

Answer 36

CCD
- PR: Varies, but ~50 megapixels
- SR: 10 micrometres

Eye
- PR: ~500 megapixels
- SR: 100 micrometres

Question 37

What is luminosity?

Answer 37

Rate of light energy released by a star.

(The power output of a star)

Question 38

What is intensity?

Answer 38

The power received from a star (luminosity) per unit area, unit Wm^-2

It follows the inverse square law.

It is the effective brightness of an object, though brightness is a subjective scale of measurement.

Question 39

What is apparent magnitude?

Answer 39

How bright an object appears in the sky, therefore it depends on a star’s luminosity and distance from Earth.

Question 40

What is the Hipparcos scale?

Answer 40

A scale that classifies astronomical objects by their apparent magnitudes, with the brightest stars given an apparent magnitude of 1 and the faintest visible stars being given an apparent magnitude of 6.

The scale is logarithmic - as magnitude changes by 1, intensity changes with a ratio of 2.51. The intensity of a mag 1 star is 100x intensity of mag 6 star.

Question 41

What is absolute magnitude?

Answer 41

What the apparent magnitude of an object would be if it were placed 10 parsecs away from Earth.

Question 42

What does d stand for in the magnitude equation?

Answer 42

Distance from Earth in parsecs

Question 43

What is parallax?

Answer 43

The apparent change of position of a nearer star in comparison to distant stars in the background, as a result of the orbit of the Earth around the Sun.

It is measured by angle of parallax (θ) - the greater the angle of parallax, the closer the star is to the Earth.

Question 44

What is an Astronomical Unit (AU)?

Answer 44

The average distance between the centre of the Earth and the centre of the Sun.

Question 45

What is a parsec (pc)?

Answer 45

The distance at which the angle of parallax is 1 arcsecond (1/3600th of a degree)

..which can be described as:

The distance at which 1 AU subtends an angle of 1 arcsecond

Question 46

What is a light year (ly)?

Answer 46

The distance an EM wave travels in a year in a vacuum.

Question 47

What is a black body radiator?

Answer 47

A perfect emitter and absorber of all possible wavelengths of radiation.

(Stars can be approximated as black bodies)

Question 48

What is Stefan’s law?

Answer 48

The power output of a black body radiator is directly proportional to its surface area and its (absolute temperature)^4

P = σAT^4 , where σ is the Stefan constant.

Question 49

What can Stefan’s law be used for?

Answer 49

To compare the power output, temperature and size of stars.

Question 50

What is Wien’s displacement law?

Answer 50

The peak wavelength of emitted radiation is inversely proportional to the absolute temperature of the object. (The peak wavelength is the wavelength of light released at maximum intensity)

(λmax)T = 2.9 × 10^−3 m K , where m K is metres-Kelvin, not milliKelvin

Question 51

What does Wien’s law show?

Answer 51

That the peak wavelength of a black body decreases as it gets hotter, meaning the frequency increases so the energy of the wave increases. This law can be used to estimate the temperature of black-body sources.

Question 52

What is the formula for the inverse square law of intensity?

Answer 52

I = P/4πd^2 , where P is the power output of the star and d is the distance from the star in metres.

Question 53

What is the order of spectral classes from hottest to coolest?

Answer 53

O B A F G K M

Question 54

O-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 54

1. Blue
2. 25,000 - 50,000 K
3. He+, He, H
4. Weak

Question 55

B-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 55

1. Blue
2. 11,000 - 25,000 K
3. He, H
4. Slightly stronger than O-type

Question 56

A-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 56

1. Blue/white
2. 7,500 - 11,000 K
3. H, ionised metals
4. Strongest of all classes

Question 57

F-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 57

1. White
2. 6,000 - 7,500 K
3. Ionised metals
4. Weak

Question 58

G-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 58

1. Yellow/white
2. 5,000 - 6,000 K
3. Ionised and neutral metals
4. None

Question 59

K-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 59

1. Orange
2. 3,500 - 5,000 K
3. Neutral metals
4. None

Question 60

M-type stars:
1. Colour
2. Temp
3. Absorption lines
4. Prominence of hydrogen Balmer lines

Answer 60

1. Red
2. < 3,500 K
3. Neutral atoms, Titanium Oxide
4. None

Question 61

Describe the evolutionary path of a Sun-like star in reference to the HR diagram

Answer 61

Once a main sequence star uses up all hydrogen in its core, it will move up and to the right as it becomes a red giant, which is brighter and cooler than a main sequence star.

Once the red giant uses up all helium in its core, it ejects its outer layers and moves down and to the left, becoming a white dwarf, which is hotter and dimmer than a main sequence star.

Question 62

Describe the stages of stellar evolution

Answer 62

1. Protostar: Nebulae have fragments of varying masses that clump together under gravity, rotating and spinning inwards to form a dense centre, surrounded by a disc of material (circumstellar disc). When it gets hot enough it begins to fuse elements, producing a strong stellar wind that blows away surrounding material.
2. Main Sequence: Inward force of gravity and outward force of fusion in equilibrium - star is stable. Hydrogen fused into helium. Greater mass = shorter main sequence period because fuel used more quickly.
3. Red Giant (for < 3 solar masses) or Red Supergiant (for >3 solar masses): Once hydrogen runs out, temperature of core increases and starts fusing helium into heavier elements. The outer layers expand and cool. Process same for both, just on a larger scale in supergiants.
4. White Dwarf (for Red Giants <1.4 solar masses) or Supernova (for Red Giants 1.4 - 3 solar masses and Red Supergiants):
   White Dwarf - When red giant uses up all fuel, fusion stops and core contracts. Outer layers thrown off, forming planetary nebula around core. Core becomes very dense. Eventually cools to a black dwarf.
   Supernova - When all fuel runs out, fusion stops, core collapses inwards suddenly and becomes rigid. Outer layers of star fall inwards and rebound off core, launching them out in a shockwave. As shockwave passes through surrounding material, elements heavier than iron are fused and flung into space. Defining characteristic of a supernova is its rapidly increasing absolute magnitude.
5. Neutron Star (for 1.4 - 3 solar masses) or Black Hole (for >3 solar masses):
   Neutron Star - When core of large star collapses, gravity so strong it forces protons and electrons to form into neutrons. Incredibly dense, ~10^17 kgm^-3, the density of nuclear matter. Pulsars are spinning neutron stars that emit beams of radiation from poles as they spin.
   Black Hole - When core of giant star collapses neutrons are unable to withstand gravity forcing them together.

Question 63

What is the event horizon?

Answer 63

The point at which the escape velocity of a black hole becomes greater than the speed of light.

Question 64

What is the Schwarzchild radius?

Answer 64

The radius of the event horizon.

Question 65

What is a binary system?

Answer 65

One where two stars orbit a common mass.

Question 66

Describe the two types of supernovae

Answer 66

Type I : When a star accumulates matter from its companion star in a binary system and explodes after reaching a critical mass.

Type II : The death of a high-mass star after it runs out of fuel.

Question 67

What is a Type 1a supernova?

Answer 67

A Type I supernova involving a white dwarf. When the companion star runs out of hydrogen and expands the white dwarf begins to accumulate some of its mass. Eventually it reaches a critical mass, at which point fusion begins and becomes unstoppable as mass continues to increase, eventually causing the white dwarf to explode in a supernova.

Question 68

Why are supernovae useful to astronomers?

Answer 68

All types of supernovae occur at the same critical mass, so they all have a very similar peak absolute magnitude (about -19.3) and produce very consistent light curves. This allows astronomers to use them as standard candles to calculate distances to far-off galaxies (they can be seen up to 1000Mpc away)

Question 69

What do scientists believe is at the centre of every galaxy and why?

Answer 69

A supermassive black hole. This is because stars and gas at the centre of galaxies appear to be orbiting very quickly. Therefore they concluded that there must be a supermassive object at the centre with a very strong gravitational field attracting them.

Question 70

How can supermassive black holes form?

Answer 70

From the collapse of massive gas clouds while the galaxy was forming.
From a normal black hole that accumulated huge amounts of matter over millions of years.
From several normal black holes merging together.

Question 71

What is the evidence that the expansion of the universe is accelerating?

Answer 71

If it was slowing down, more distant objects would be observed to be receding more quickly. Objects would also appear brighter than predicted as they would be closer than expected. However, type 1a supernovae have been seen to be dimmer than expected, so are more distant than Hubble’s law predicted.

Question 72

What is dark energy?

Answer 72

What is thought to be the reason behind the universe accelerating. It is described as having an overall repulsive effect throughout the whole universe, and is constant throughout the universe, so has a grater effect than gravity.

It is controversial since there is evidence for its existence but no-one knows what it is or what is causing it.

Question 73

What is the Doppler effect?

Answer 73

The compression or spreading out of waves that are emitted or reflected by a moving source.

Question 74

Describe the Doppler effect in context of the line spectra of distant objects

Answer 74

The line spectra of objects are blue-shifted (shifted towards the blue end of the visible spectrum) when they move towards the Earth, and red-shifted (shifted towards the red end of the spectrum) when they move away from the Earth.

Question 75

When can the equations for red shift be used?

Answer 75

When the objects receding velocity is much smaller than the speed of light, since the formula was derived without taking into account relativistic effects that occur when objects move close to the speed of light.

Question 76

What are spectroscopic binaries?

Answer 76

Binary star systems in which the stars are too close to be resolved by a telescope, meaning the only way to identify them is by using the Doppler shifts of each star.

Question 77

Describe the light curve of eclipsing binaries?

Answer 77

With no eclipse, the brightness is a maximum. When the larger star in in front of the smaller star, there is a primary minimum (the point of lowest intensity). Then, again, there is no eclipse so brightness is a maximum. Finally, when the smaller star is in front of the larger star, there is a secondary minimum (lower than max but higher than primary min).

Question 78

What is Hubble’s law?

Answer 78

Hubble’s law states that a galaxy’s recessional velocity is directly proportional to its distance from the Earth. It essentially states that the universe is expanding from a common starting point.

Question 79

Explain how you can use Hubble’s law to estimate the age of the universe

Answer 79

1. Rearrange v = Hd into 1/H = d/v
2. Using distance = velocity x time, rearranged to t = d/v, time can be equated to the reciprocal of Hubble’s constant: t = 1/H
3. However for this to work, H needs to be in SI units:
   - Multiply by 1000 converting from km to m
   - Divide by Mpc in meters to convert from pc to m.
   - Metres cancel out so unit is just s^-1, hence 1/H gives time.
4. Sub in value of H in SI units, then convert from seconds to years.

Question 80

State two pieces of evidence for the Big Bang Theory

Answer 80

The presence of Cosmological Microwave Background Radiation

The relative abundance ratio of hydrogen and helium

Question 81

Explain Cosmological Microwave Background Radiation

Answer 81

When the Big Bang happened, it is thought that there was high-energy radiation everywhere, and as the universe expanded and cooled, this radiation would have lost energy and been red-shifted. The remains of this radiation is what we can Cosmological Microwave Background Radiation, which is microwave radiation that has been detected from all directions in space.

Question 82

Explain the relative abundance ratio of hydrogen and helium

Answer 82

During the early stages of the Big Bang, fusion converted hydrogen nuclei into helium nuclei. However, this only lasted for a very short period of time before the universe cooled too much and fusion stopped. Approximately 1/4 of all hydrogen nuclei were fused into helium, resulting in a relative abundance ratio of H:He of 3:1. The relative abundance by mass observed today is 73% hydrogen, 25% helium and 2% everything else.

Question 83

What is a quasar?

Answer 83

An active galactic nucleus - a supermassive black hole surrounded by a disc of matter which, as it falls into the black hole, causes jets of radiation to be emitted from the poles. They are characterised by having extremely large red-shifts, a very powerful light output, being not much bigger than a star, and being radio emitters.

They are the most distant measurable objects in the known universe.

Question 84

What is an exoplanet?

Answer 84

A planet that is not within our solar system - it orbits another star. They can be difficult to detect directly as they tend to be obscured by the light of their host stars.

Question 85

State the two methods for detecting exoplanets

Answer 85

Radial velocity method

Transit method

Question 86

Explain the radial velocity method

Answer 86

The star and planet orbit a common centre of mass, causing the star to ‘wobble’ slightly, which causes a Doppler shift in the light received from the star. The line spectrum of the star is blue-shifted as it moves towards the Earth, and red-shifted when it moves away. This shows that there is something else near the star exerting a gravitational force on it. The time period of the planet’s orbit is equal to the time period of the Doppler shift.

Question 87

Explain the transit method

Answer 87

Involves observing the intensity of the light output of a star. If a planet crosses in front of a star, the intensity dips slightly. If the intensity dips regularly, it could be a sign that there is an exoplanet orbiting it. If there are variations in the regularity of the dips, there may be several planets.

The size of the orbital period can be determined from the amount that the intensity falls by and the duration of the dip.

Question 88

What are the limitations of the transit method?

Answer 88

Only works if the line of sight to the star is in the plane of the planet’s orbit, which is more likely for planets with small orbits. This is because most orbits are inclined (do not pass in front of the star when observed from Earth), and smaller orbits mean that parts of the planet are more likely to cross in front of the star.