# Astrophysics

AQA unit 5

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## Clasification of stars

Type- colour- surface temp- origin of prominent features

O- blue- 28000 to 50000- Ionized helium

B- blue/white- 10000 to 28000- Neutral helium, H2

A- white- 7500 to 10000- Hydrogen

F-yellow/white- 6000 to 7500- calcium+ and ionized metals

G- yellow- 5000 to 6000- Calcium+ and neutral metals

K- orange/red- 3500 to 5000- molecules of calcium and neutral metals

M- red- 2500 to 3500- molecules and Ca

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## Stars

The luminosity of a star is the total amount of energy it emits form its surface, in all wavelengths. It is very difficult to to measure the intensity of light from a star especially when it must be done over all wavelengths including IR and UV.

F=L/4piedsquared

Absolute magnitude- The magnitude a star would have if it were seen at a standard distance of 10pc.

m-M= 5log10 (d/10)

Apparent magnitude- A measure of its brightness as seen from earth.

m1 - m2= 2.5log10 (I2/I1)

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## Wien's displacement law

The wavelength lambda max at which the maximum amount of energy is radiated decreases with temperature and is such taht:

lambdamaxT= a constant

Where T is the temperature of the black body in kelvin.

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## Stefan's law

The total energy radiated per unit time per unit surface area of a black body is proportional to the fourth power of the temperature of the body expressed in kelvin.

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Black body is a body which absorbs all the radiation that is incident on it. The concept is an idealized one, but it can be very nearly realized in practice.

Black-body radiation is the radiation emittd by a black body; its spectral distrubution depends only on the temperature of the body.

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## Inverse square law

A point source of light emits light in all directions about the source. It follows that the intensity of light decreases with disance from the sourcw because the rays are spread geater areas as the distance increases.

Rays of light at a distance d froma point source are spread over the surface of a sphere of radius d and area 4piedsquared. If E is the energy radiated per unit time, then the intensity at a distance d form th source is given by I where

I=E/4piedsquared

I is proportional to 1/dsquared

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## The astronomical telescope

diagram

Image- real, inverted and diminished

Eye-piece - acts as a magnifying glass and forms a magnified, virtual image.

Power of a lens

The shorter the fical length of a lens teh more it will converge or diverge light. The power F of a lens is defined as the reciprocal of ts focal length in metres.

F=1/f unit Dioptres

Refracting astronomical telescopes

Consist of 2 converging lenses:

1. Objective- long focal length

2. Eyepiece-short focal length

The objective L1 forms a real, diminished, inverted image. I of a distant object at its principle focus Fo(because rays assume to be parralel) The eyeiece L2 cts as a magnifying glas and forms, a magnified, virtual imae of I. I must be at the prinicile focusof L2 so Fe and Fo coincide. (when telescope is normal adjustment, virtual image of I is at infinity)

Magnifying power

Assume- all rays paraxial eye close to eyepiece. Telescope in normal adjustment.

Magnifying power= beta/alpha

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## Chromatic aberration

Occurs only with lenses and causes the image of a white object to be blurred with coloured edges.

It can be reduced by using an achromatic doublet.

Two lenses each made from a different type of glass and cemented together with canada balsam.

Crown glass- converging and the deviation it produces is in the opossite direction to that produced in the flnt glass.

Can only eliminate two colours.

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## Reflectors

• Can have large diameter mirrors, as it can be supported over the whole surface.
• No chromatic aberation in mirrors.
• Use of parabolic mirrors eiminating spherical aberations.
• Can be used to study long wavelengths that peneate earths atmosphere.

• More sensitive to temperature change.
• Mirrors have to be re-alluminized periodically- higher maintenance
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## Refractors

• Less sensitive to temperature change.
• Requires less maintenance.

• Lenses can only be supported at the ends. So may bend/break if too large.
• Suffers from chromatic aberations
• Suffers from spherical aberations
• Glass lenses absorbs UV competely
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## Resolving detail

Image resolution is limited by the diffraction that occurs at the collecting aperture.

Radio waves are much longer than light waves so are diffracted more significatly by the dish than light waves are when they enter the eye.

Resolving power- to see fine detail an instrument must form distinguishable images of objects that have a small angular seperation. The smaller the angular seperation for which it can do this, the greater the instruments resolving power.

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## Rayleigh criterion and the limit of resolution

An optical instrument can resolve to points if their images can be distinguished.

Diffraction at the appeture will spread the light from each point and for objects with a very small angular seperation the diffraction patterns may overlap so that they produce a single blob of light (they are not resolved)

Theoretcial limit of resolution is 'rougly' when the first maximum of one diffraction pattern falls on the first minimum of the other.

This occurs when the angular seperation of the objects= the angle from the centre to the first minimum of either pattern.

Limit of resolution

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## Supernovae

2 main types

Type 1: Occur in binary systems when one star goes into its red giant phase and the other is a white dwarf.

As the giant swells up gas is drawn from its surface onto the white dwarf increasing its CHADRASEKHAR limit (>1.4Mo)

The carbon core collapses- it reifnites and explodes.

Net effect- Burn 1Mo(solar masses) of C and O to produce Ni-56 (radioactive)

Brightness- decays exponebtially.

*Characteristic - 60 day half-life makes it easy to identify *

Type 2- Luminosity increases by a factor of about a billion (x23 magnitude) This increases the distance at which star can be seen by 30, 000

Can be used as standard candles to distances - 1000MPc

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## Black holes

Supernovae reminents greater than 2.5 solar masses. Collapse to a point of inifinte density (singularity) and the star ends its life as a black hole.

'Black'- because even light cannot escape its intense gravitational field.

Steven Hawking- has predicted a quantum mechnical proccess that allows black holes to radiate but so far no-one has detected it.

For something to become a black hole it must trap light. In Newton's theory this means the escape velocity from the surface of the object must be at least the speed of light.

Vesc=square root of 2GM/R

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Rs= 2GM/csquared

All the mass of the earth would have to be compressed into a sphere smaller than a golf ball. Once a star has collapsed inside its schwarzschild radius there is no hope for it. The core is now invisible to the outside universe and continues collapsing to become a singularity. From outside spherical shell of radius Rs is the final place from which messages from the collapsing star can escape to the outside.

This surface is called an EVENT HORIZON nothing inside gets out.

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## Time and black holes

Time run slows in a strong gravitational field. If you watch a clock falling into a black hole it will apear to tick slower and slower as it passes the event horizon.

It would get fainter and fainter as photons struggle against gravity and loose energy(shift out of the visible range)

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## Hubbles law- the expanding universe

Vesto Slipher- measured the doppler shifts, in spectral lines, from the arms of spiral galaxies in order to work it out their rotation rates. He discovered that 36 of the 41 galaxies had red shifts. It implied that the majority of the observed galaxies must be moving away from the earth, and some of the velocities were enormous.

Edwin Hubble- had been developing techniques to measure distances to galaxies. When Hubble's distances and Slipher's red shifts were put together :-

z= dlambda/lambda

z= v/c

Hubble's law- the recession velocity v of a distant galaxy is proportional to its distance d.

V is proportional to d.

V=Hod

The discovery of Hubble's law combined with Einsteins model of space and time indcates that we are living in an expanding universe.

A singularity- Infinite density, temperature at time zero.

Big bang- Universe explodes and begins to expand out to its present state. The study of the universe as a whole is called cosmology.

Closed universe- If gravitational forces are strong enough to halt the expansion and make the universe collapse.

Open universe- If the expansion cannot be stopped.

Cosmological principle

The universe should look the same from all points. Every place is equivalent and the universe looks the same in all directions and from any point.

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