AstrophysicsAstrophysics

ContentsContents

Lenses & Optical TelescopesLenses & Optical Telescopes Radio AstronomyRadio Astronomy Classification of StarsClassification of Stars CosmologyCosmology

Lenses & Optical TelescopesLenses & Optical Telescopes Convex LensConvex Lens: light rays converge: light rays converge

Power (Dioptres, D) = 1 / focal length (m)Power (Dioptres, D) = 1 / focal length (m)

Lenses & Optical TelescopesLenses & Optical Telescopes Lens FormulaLens Formula::

1/f = 1/v + 1/u1/f = 1/v + 1/u v = image distance, u = object v = image distance, u = object distancedistance

M = v/uM = v/u M = magnification (no units)M = magnification (no units)

Lenses & Optical TelescopesLenses & Optical Telescopes Refracting TelescopeRefracting Telescope: bends light with lenses: bends light with lenses

- objective lens: produces small real image- objective lens: produces small real image- eyepiece: magnifies image- eyepiece: magnifies image

Angular MagnificationAngular Magnification:: M = M = αα//ββ

αα: angle (rads) subtended by the object to the unaided : angle (rads) subtended by the object to the unaided eyeeye

ββ:: angle (rads) subtended by the image to the eye angle (rads) subtended by the image to the eye

Reflecting TelescopesReflecting Telescopes DisadvantagesDisadvantages::

- refract light of different colours by different - refract light of different colours by different distorted imagedistorted image- do not transmit 100 % of the light; some is lost- do not transmit 100 % of the light; some is lost- large lenses are complex to make- large lenses are complex to make- for good magnification, the objective lens must have a - for good magnification, the objective lens must have a very long focal length very long focal length telescope becomes very long telescope becomes very long

Reflecting TelescopesReflecting Telescopes Resolving PowerResolving Power: how good a telescope is at distinguishing : how good a telescope is at distinguishing

between two objects that are close to one anotherbetween two objects that are close to one another

Resolving power of eye: angle = 3x10Resolving power of eye: angle = 3x10-4-4 radiansradians

Observations from EarthObservations from Earth: are poor because of atmosphere : are poor because of atmosphere turbulence (light is scattered) and light pollutionturbulence (light is scattered) and light pollution

DiffractionDiffraction: As light enters the telescope, a small gap diffracts : As light enters the telescope, a small gap diffracts the light wave the light wave Fraunhofer Diffraction Pattern Fraunhofer Diffraction Pattern

Overlapping of fringes can occur: Overlapping of fringes can occur: θθ = = λλ/D/Dθθ = angular separation (rads), D = aperture width (m) = angular separation (rads), D = aperture width (m)

Reflecting TelescopesReflecting Telescopes Recording the ImageRecording the Image: Charged Coupled Device (CCD): Charged Coupled Device (CCD)

- films have fine grain for high resolution- films have fine grain for high resolution- CCD (size of a stamp) connects to computer- CCD (size of a stamp) connects to computer- CCD has millions of pixels on it- CCD has millions of pixels on it

The eye has a quantum efficiency of 1%; CCD is approx. The eye has a quantum efficiency of 1%; CCD is approx. 70%:70%:

Radio TelescopesRadio Telescopes Radio AstronomyRadio Astronomy::

- revealed the existence of radio sources, such as - revealed the existence of radio sources, such as quasars and pulsarsquasars and pulsars- analyses chemical elements in stellar objects- analyses chemical elements in stellar objects- tracks the movement of planets using the Doppler - tracks the movement of planets using the Doppler effecteffect- looked at microwave radiation which gives evidence - looked at microwave radiation which gives evidence for the Big Bangfor the Big Bang

Radio waves penetrate dust (nebulae etc.) so radio Radio waves penetrate dust (nebulae etc.) so radio telescopes allow us to view inwards, into the centre of telescopes allow us to view inwards, into the centre of the galaxythe galaxy

Radio telescopes have poor resolution and are absorbed Radio telescopes have poor resolution and are absorbed by light pollution on Earthby light pollution on Earth

Classification of StarsClassification of Stars Astronomical Unit (AU):Astronomical Unit (AU):

- Distance between Earth and Sun: 1AU = 1.5 x 10- Distance between Earth and Sun: 1AU = 1.5 x 101111mm

Light Year (ly):Light Year (ly):- Distance travelled by light in 1 year: 1ly = 9.46 x 10- Distance travelled by light in 1 year: 1ly = 9.46 x 101515 mm

Parsec (pc):Parsec (pc):- An object at 1pc subtends an angle of 1 arc second for - An object at 1pc subtends an angle of 1 arc second for a distance of 1AU: 1pc = 3.086 x 10a distance of 1AU: 1pc = 3.086 x 101616mm- 1 pc = 3.26 ly- 1 pc = 3.26 ly

Classification of StarsClassification of Stars Apparent MagnitudeApparent Magnitude: apparent brightness of stars on a : apparent brightness of stars on a

scalescale Very bright stars have negative magnitudesVery bright stars have negative magnitudes Magnitude 1 star = 100 times brighter than magnitude 6 Magnitude 1 star = 100 times brighter than magnitude 6

starstar

Difference in magnitudes = nDifference in magnitudes = n- ratio of brightnesses = 2.512- ratio of brightnesses = 2.512nn

Absolute MagnitudeAbsolute Magnitude: stars at an: stars at anarbitrary distance of 10pcarbitrary distance of 10pc

m: apparent magnitudem: apparent magnitudeM: absolute magnitudeM: absolute magnituded: distance (pc)d: distance (pc)

Classification of StarsClassification of Stars Classification by TemperatureClassification by Temperature: spectroscopy: spectroscopy

- Balmer lines arise from electron transitions in - Balmer lines arise from electron transitions in hydrogen atomshydrogen atoms- As the electron drops from high levels to the - As the electron drops from high levels to the second energy level, photons are emittedsecond energy level, photons are emitted- Emissions of photons appear black - Emissions of photons appear black absorption absorption spectrumspectrum

EmissionSpectrum

AbsorptionSpectrum

Classification of StarsClassification of Stars Low Temperatures:Low Temperatures:

- energy levels are rare as electrons remain in ground - energy levels are rare as electrons remain in ground statestate

High Temperatures:High Temperatures:- Electron transitions occur at higher levels so there are - Electron transitions occur at higher levels so there are comparatively few Balmer transitionscomparatively few Balmer transitions

Intermediate Temperatures:Intermediate Temperatures:- Many electrons perform Balmer transitions, so there - Many electrons perform Balmer transitions, so there are strong absorption linesare strong absorption lines

Classification of StarsClassification of Stars Black BodyBlack Body: an object that absorbs all radiation: an object that absorbs all radiation

Perfect absorber = perfect emitter (of all radiation… Perfect absorber = perfect emitter (of all radiation… including visible)including visible)

Stars are approximated to black bodies:Stars are approximated to black bodies:- hot object emits radiation across range of - hot object emits radiation across range of λλ- peak in intensity at a given - peak in intensity at a given λλ- hotter object = higher peak - hotter object = higher peak

- hotter object = shorter peak - hotter object = shorter peak λλ ((λλmaxmax))

Wien’s Displacement LawWien’s Displacement Law::

λλmaxmaxT = constant = 0.00289 mKT = constant = 0.00289 mK

Classification of StarsClassification of Stars Luminosity of StarsLuminosity of Stars: power; energy given out per second: power; energy given out per second

Stefan’s Law: P = Stefan’s Law: P = σσATAT44 σσ = = 5.67x105.67x10-8-8WmWm-2-2KK-4-4

star = sphere… star = sphere… A = 4 A = 4ππrr22

For a star…For a star… P = 4P = 4ππrr22σσTT22

Observing Stars is difficult due toObserving Stars is difficult due to::- light pollution which is problematic for viewing dim stars- light pollution which is problematic for viewing dim stars- poor weather such as clouds- poor weather such as clouds- dust (from pollutants)- dust (from pollutants)- turbulent atmosphere (which is why stars “twinkle”- turbulent atmosphere (which is why stars “twinkle”

put telescope in orbit, or failing that, on a very high put telescope in orbit, or failing that, on a very high mountainmountain

Life & Death of a StarLife & Death of a Star Hertzsprung-Russell DiagramHertzsprung-Russell Diagram::

Life & Death of a StarLife & Death of a Star Hertzsprung-Russell DiagramHertzsprung-Russell Diagram::

- most stars lie along the main sequence- most stars lie along the main sequence- very bright = blue; very dim = red- very bright = blue; very dim = red- Luminosities: Sun = 1, Betelgeuse = 20 000, Sirius = - Luminosities: Sun = 1, Betelgeuse = 20 000, Sirius = 0.0020.002- Surface Temp: Sun = 5800K, Sirius = 20 000K- Surface Temp: Sun = 5800K, Sirius = 20 000K

Life & Death of a StarLife & Death of a Star Stage 1Stage 1: Stars are born in a region of high density : Stars are born in a region of high density

Nebula, which condenses into a huge globule of gas Nebula, which condenses into a huge globule of gas and dust and contracts under its own gravity. Huge and dust and contracts under its own gravity. Huge amounts of thermal energy and IR radiation are amounts of thermal energy and IR radiation are emittedemitted

Life & Death of a StarLife & Death of a Star Stage 2Stage 2: A region of condensing matter will begin to : A region of condensing matter will begin to

heat up and start to glow forming Protostars. If a heat up and start to glow forming Protostars. If a protostar contains enough matter, the internal protostar contains enough matter, the internal temperature can reach 15 million degrees Celsiustemperature can reach 15 million degrees Celsius

Life & Death of a StarLife & Death of a Star Stage 3Stage 3: Ignition temperature is reached… fusion : Ignition temperature is reached… fusion

begins. Hydrogen fuses into Heliumbegins. Hydrogen fuses into Helium

Stage 4Stage 4: Energy is released which prevents the star : Energy is released which prevents the star from collapsing further. Star stabilises and shinesfrom collapsing further. Star stabilises and shines main sequence lasts approx. 10 billion yearsmain sequence lasts approx. 10 billion years

Life & Death of a StarLife & Death of a Star Stage 5Stage 5: Helium core contracts and reactions occur in a : Helium core contracts and reactions occur in a

shell around the coreshell around the core

Stage 6Stage 6: Core is hot enough for the Helium to fuse to : Core is hot enough for the Helium to fuse to form Carbon. Outer layers begin to expand, cool and form Carbon. Outer layers begin to expand, cool and shine less brightly. Expanding star is now called a Red shine less brightly. Expanding star is now called a Red GiantGiant

Life & Death of a StarLife & Death of a Star Stage 7Stage 7: Helium core runs out, and the outer layers : Helium core runs out, and the outer layers

drift away from the core as a gaseous shell. This gas drift away from the core as a gaseous shell. This gas that surrounds the core is called a Planetary Nebulathat surrounds the core is called a Planetary Nebula

Life & Death of a StarLife & Death of a Star Stage 8Stage 8: Approx. 20% of original star mass has been : Approx. 20% of original star mass has been

lost. Remaining mass (core) becomes a White Dwarf as lost. Remaining mass (core) becomes a White Dwarf as the star cools and dims. Once it ceases shining the star cools and dims. Once it ceases shining Black Dwarf. It is believed that up to ½ the mass of the Black Dwarf. It is believed that up to ½ the mass of the galaxy is due to Black Dwarfsgalaxy is due to Black Dwarfs

White DwarfWhite Dwarf Black Black DwarfDwarf

Life & Death of a StarLife & Death of a Star Novae & SupernovaeNovae & Supernovae: With massive stars, electrons & : With massive stars, electrons &

protons will combine to form neutrons. The inner core protons will combine to form neutrons. The inner core will spontaneously collapse (approx. 1 sec duration) as will spontaneously collapse (approx. 1 sec duration) as neutrinos are ejected at which point neutrinos are ejected at which point Neutron Star. Neutron Star. The outer layers then collapse onto the core, which The outer layers then collapse onto the core, which cannot be compressed further. The pressure of this cannot be compressed further. The pressure of this outer layer collapse causes the wave of movement to outer layer collapse causes the wave of movement to reverberate and a violent shock wave outwards occurs. reverberate and a violent shock wave outwards occurs. This explosion is called a SupernovaThis explosion is called a Supernova

Life & Death of a StarLife & Death of a Star Black HoleBlack Hole: With very massive stars, the inner core : With very massive stars, the inner core

collapses but continues to do so until it becomes collapses but continues to do so until it becomes nothing more than a point mass. Point mass nothing more than a point mass. Point mass singularity, and this breaks the laws of Physics. The singularity, and this breaks the laws of Physics. The strength of gravity inside a black hole is so massive strength of gravity inside a black hole is so massive that nothing can escape, not even light (which is why that nothing can escape, not even light (which is why they are not visible). The perimeter at which light they are not visible). The perimeter at which light can/cannot escape is called the Event Horizon, but far can/cannot escape is called the Event Horizon, but far away from this point, everything else is sucked in. away from this point, everything else is sucked in. Black holes are invisible, but they can be found, as Black holes are invisible, but they can be found, as nearby stars will be sucked innearby stars will be sucked in

CosmologyCosmology Doppler EffectDoppler Effect: shift in frequency and wavelength of waves : shift in frequency and wavelength of waves

that causes its properties to changethat causes its properties to change

Objects that travel with v<<c obey this law:Objects that travel with v<<c obey this law:

andand

- Moving towards observer = positive speed; away = - Moving towards observer = positive speed; away = negativenegative

- Moving away - Moving away frequency decreases frequency decreases wavelength wavelength increasesincreases

- Moving towards - Moving towards frequency increases frequency increases wavelength wavelength decreasesdecreases

Moving away = red shiftMoving away = red shift Moving towards = blue shiftMoving towards = blue shift

CosmologyCosmology Big BangBig Bang: age of universe = 1/H: age of universe = 1/H00

If galaxies are moving away from us, they must have If galaxies are moving away from us, they must have been closer together millions of years ago. If Hubble’s been closer together millions of years ago. If Hubble’s graph is used, the origin of this movement = approx. graph is used, the origin of this movement = approx. 10 000 million years old10 000 million years old

Earth = approx. ½ age of universe (5 000 millions Earth = approx. ½ age of universe (5 000 millions years old)years old)

The universe will either:The universe will either:

1)1) Continue to expand foreverContinue to expand forever

2)2) Return in on itself back to its origin (Big Crunch)Return in on itself back to its origin (Big Crunch)

CosmologyCosmology QuasarsQuasars: Extremely bright objects that are most : Extremely bright objects that are most

distant from us that we know of. Smaller than a distant from us that we know of. Smaller than a galaxy, they are more luminous and contain elements galaxy, they are more luminous and contain elements we do not know exist. They have a huge red shiftwe do not know exist. They have a huge red shift

They could be:They could be:

1)1) massive black holes?massive black holes?

2)2) responsible for consuming 10 solar masses per yearresponsible for consuming 10 solar masses per year

3)3) responsible for ejecting jets of matter at high velocityresponsible for ejecting jets of matter at high velocity

(Several hundred light years is probably a safe distance!)(Several hundred light years is probably a safe distance!)

SummarySummary Lenses & refracting telescopesLenses & refracting telescopes Reflecting telescopesReflecting telescopes Radio telescopesRadio telescopes Classification of starsClassification of stars Life & death of a starLife & death of a star CosmologyCosmology