# P9-Astrophysics(Optional topic)

Telescopes

Ray diagrams

Converging lens (convex)                                  Diverging lens (concave)

Formation of a real image by a converging lens

Formation of a vertical image by a converging lens

There is a simple relationship between the distances of the object from the lens, u the distance of the image from the lens, v, and the focal length f.

If v is the positive the image is real, if v is negative the image is virtual.

Units must be the same.

Refracting telescope

A simple refracting telescope consists of 2 converging lenses, the objective lens and the eye piece.

Normal adjustment is when the telescope is adjusted so the image seen by the viewer is at infinity.

fo and fe coincide so the distance between the two lenses is the sum of their focal lengths.

Ray diagram for refracting telescope

The angular magnification M or magnifying power of a refracting telescope is given by:

Chromatic and spherical aberration – reflecting telescope suffer aberrations (faults). There are two main ones:

• Chromatic aberration
• Spherical aberration

Chromatic aberration – one problem with refracting telescopes is that there is a frequency dependence for refraction, so the amount of refraction at each surface of the lens depends on the wavelength.

Chromatic aberration can be corrected by using a second carefully designed lens placed behind the objective lens, to compensate for the chromatic aberration and cause the wavelengths to focus at the same point however this does not completely dominate the problem.

Achromatic doublet an additional convex cave attached to defract focus back so that they focus at one point.

Spherical aberration– this is due to the manufacture of the lenses being produced as sections of spheres, rays of light away from the centre are brought to focus closer to the lens than those that have passed through the centre.

This again leads to blurring of the image, which can be minimized but not eliminated. A variable aperture can be used.
Reflecting telescopes – In a reflecting telescope, a concave mirror is used instead of a converging lens. There is the objective (or primary) mirror that reflects into a smaller secondary mirror that then reflects into the eye piece.

The light gathering power of the mirror is proportional to the mirrors area, so the bigger the mirror, the more light will be gathered and the more of space you will see.

Spherical aberration also happens in reflecting telescopes but you can use parabolic mirrors to counter it.

The magnification of a reflecting telescope is found using the same formula as for a refracting telescope. The ratio of focal length of objective mirror to eye piece.

Cas segrain arrangement– a common design for the reflecting telescopes is the Cas segrain arrangement. The large primary mirror has a parabolic shape. A convex secondary mirror with a hyperbolic shape is used, which sends the rays down an opening in the primary mirror, where the image is brought to focus using an eyepiece or a magnifying camera.

 Disadvantages of refracting Advantages of reflecting Mounting of the lens and support can only be made using the edge of the lens. Large single mirrors can be made which are light and easily supported from behind. Using glass of sufficient clarity and purity and free from defects to make large diameter telescopes is extremely difficult. Mirror surfaces can be made first a few mms thick giving excellent image properties. Large diameters lenses are heavy and can distort under own weight. Mirrors only use front surface. Suffer chromatic + spherical aberration. No chromatic and spherical aberration         when using parabolic mirrors. Heavy and difficult to            quickly. Relatively light mirrors allow rapid response to achrononical events. Difficult to mount heavy observing equipment and electronics. Smaller segmented mirrors can be used to form a large composite objective mirror. Large magnifications require large objective lenses and very long focal lengths.

Limitations of ground -based optical telescopes – For ground based optical telescopes atmospheric absorption and distortion in the visible region of the electromagnetic spectrum are limiting factors in image quality.

Ozone, oxygen, water vapor, carbon dioxide all contribute to the absorption of light from the ultraviolet through visible to infrared.

Dust within the atmosphere also absorbs and scatters light on its way to the telescope and atmospheric turbulence reduced image quality.

Such problems can be avoided by building observations in dry, pollution-free areas, at high altitude or better by putting telescopes in orbit around the earth.

Atmospheric opacity – is a measure of the absorption of electromagnetic radiation by the atmosphere.

Resolution and the Ray lergh Cntenon – Avery important performance parameter for any kind of telescope is its resolving power. This is its ability to produce separate images of closely spaced objects.

When light enters the opening (or aperture) or the telescope it diffracts (similar to a single slit diffraction) to produce a circular diffraction pattern.

The central spot is called an Airy disc and is blurred due to high spreading out as it diffracted.

The Ray lergh Cntenon states that two point objects can be resolved if their angular separation is at least.

Therefore the angle  is known as the minimum angular resolution of the instrument at a particular wavelength λ.

Collecting power – the collecting power is the ability of the telescope to collect incident electro-magnetic radiation.

It is directly proportional to the square of the diameter of the objective lens/ mirror.

This is because the surface is proportional to 1/4 a2.

Collecting power α (objective diameter)2

A large diameter telescope has improved collecting power + resolving power.

Radio telescopes – The simplest radio telescope consist of a simple parabolic ‘dish antenna’ (the ‘objective’) by which the radio energy is collected and brought to focus in a recover where it is amplified and displayed as an intensity trace.

Compared to an optical telescope, radio telescopes have a low angular resolution as λ is large this is why they have such large dishes.

• Can be used at night and day.
• Can detect distribution of gas in galaxy that is obscured at an optimal wave length.
• Can be used from earth as ozone does not absorb radio actives.

• Very large and costly
• Can get interface from mobile phones and such which is bad.

Infrared telescopes

Infrared astronomers study parts of the infrared spectrum which consist of electro-magnetic wavelengths ranging from just longer than visible light, to thousand times longer than visible light. Earth’s atmosphere absorbs infrared radiation, so astronomers must collect infrared radiation from places where the atmosphere is very thin or from above the atmosphere. Observators for these wavelengths are located on certain high mountain tops or in space.

Every warm object emits some infrared radiation. Infrared astronomy is useful because objects that are not enough to emit visible or UV light may still emit infrared radiation. Infrared radiation also passes through interstellar and intergalactic gas and dust more easily.

• Infrared waves are shorter than radio waves, so telescopes can be smaller and achieve the resolution.
• They are sensitive to thermal ‘noise’ so they are cryogenically cooled, often to temperature just above absolute zero.

Ultraviolet telescopes

Ultraviolet telescopes are used to examine objects in the UV part of the electromagnetic spectrum.

The ozone layer in the earth’s atmosphere blocks all UV wavelengths shorter than 300nm from reaching the ground, so rocket launched satellites are needed for UV astronomy.

Like optical and IR telescopes a W telescope uses a cassegrain mirror system which brings the UV radiation to a focus, where it is detected by a special solid-state devices. These detectors use the photoelectric effect to convert Uv photons to electrons.

It can help give us the chemical composition of stars as young stars shine very brightly in UV light.

X- Ray telescopes

X-rays comes from extremely hot gas.They have such high energies that reflecting mirrors such as those in an optical telescope cannot be used because the x- ray would penetrate into the mirror, Instead the mirror has to be extremely smooth and be specially shaped as a combination of parabolic and hyperbolic surfaces.They then slum off the surface of the mirror and are brought to focus to be detected using charged- coupled devices.

These telescopes must be placed in space as x- rays are absorbed by the ozone.

Charged Coupled Devices (CCDs)- A charged coupled device is a semiconductor  device in which light is converted directly into digital information .CCDs are divided into small regions called pixels.

One advantage of CCD is that it is directly stored meaning it can be sent across the world and archived for easy removal.

Quantum Efficiency (CE)

QE is the measure of how well a detector can capture photons and make them available for imaging. The human eye has a QE of 4.5% whereas CCDs have a QE of 80% making them very efficient. A high QE means that the time needed to acquire an image of the same intensity is smaller, so it needs less exposure time.

Resolution- The resolving power of a CCD is defined differently from that of an optical system. It is dependent on the number of pixels and their size.

The resolution of an eye using Rayleigh’s intention is about 1-2 arc minutes.

Classification of Stars

Luminosity – the luminosity of a star is the amount of energy in Jules a star radiates per second-power-watts –W.
Intensity- the intensity of radiation of a star is called the brightness of it (Wms-2).

Relative brightness from earth is expressed on the Hipparchus scale. Hipparchus was a great astronomer who placed stars into different classes. Classified by their apparent magnitude.

Apparent magnitude- how bright a star looks from earth?

The Hipparchus scale has 6 magnitudes, 6 being the dim most and 1 being the brightest.However due to the development of technologieswe can see more stars, so the Hipparchus scale has been extended, even into negative numbers.

The more negative on Hipparchus scale = The brighter it appears from earth.

Brightness when used this way is a subjective scale as we need to know how far away a star is to know its +ve luminosity.

The human eye perceives equal ratios of brightness at equal intervals.

On the Hipparchus scale the brightness coming from stars of magnitude 1 is 100x greater than that of magnitude 6. This means that over 5 scales the stars get 100x brighter. Therefore 1 magnitude will get (100)1/5 brighter or 2.51x brighter.

Units

Astronomical unit (Au)- the mean distance from the earth to the sun.

1Au = 1.5×1011 m

A Parsec (Pc)- the distance at which theobserved  parallax angle of the star is equal to 1 arc second.

1Pc = 3.08×1016 m

1◦ (degree) = 60 arc minutes

1 arc minute = 60 arc seconds

Therefore 1 arc second = 1/3600 of a degree.

A lightyear- the distance that a photon of light travel sthrough space in one year.

1 lightyear = 9.46×1015 m

Absolute magnitude- is the brightness of the star if it were 10 parsec away. This is the more absolute scale as it is at a fixed distance, so the distance no longer plays into this magnitude and therefore stars can be effectively compared.

It is calculated using

Stefan’s law- As well as stars being classified by their luminosity, they can also be classified by  temperature.The luminosity (rate at which thermal energy is emitted) depends on the temperature and its size.

Intensity α (temperature)4

Stefan’s law holds time for an object in thermal equilibrium.

Kirchoff’s law of thermal radiation – states “for any given temperature, the ratio of emitting a radiation to absorbing it is constant and independent of the composition of the body.”

This means that if an object is an efficient absorber of a wavelength, then  it must be an efficient emitter of that wavelength.

A black body is a perfect absorber of energy as it does not reflect any light.

All stars are assumed to be black bodies.

Wien’s displacement law- when an object is heated it emits light of a shorter wavelength(why metal burns yellow then red then white) wien discovered that –

The wavelength of the peak emmission intensity is inversly proportional to the absolute temperature of the object.

λ wavelength (m)

T temperature (k)

Constant Wien’s constant

Black body curves

Using these laws we can estimate temperature if we know what peak wavelength of light it emits. We can then use Stefan’s law to find power is v.

Inverse square law- the inverse square law states that the luminosity is inversely propotional to the square of distance from the center of the star.

Assuming light radiates in a sphere and perfectly evenly.

Stella spectral classes

The classes assigned to the stars to classify them by theier temperature. The classes are O, B, A, F, G, K,M.

Hertzspring-Russel (HR) diagram

Supernova– a star that suddenly increase in the brightness because of catastrophic explosion that effects most of its mass.

Type 1 supernova

white dwarf draws mass from a red giant until it becomes compressed and runaway nuclear reaction are set off blasting its matter into space.

Type 2 supernova

is the single star that runs out of the nuclear fuel. gravity is the resultant force causing it to collapse rapidly effecting its outer layer with enormous energy.

Neutron stars

the energy released by the supernova expulsion is huge.After supernova expulsion, what is left is supernova remnant at the senter known as a neutron star.

A neutron star is formed when the gravitational contraction is so strong that the electrons are pulled off outer shells and electrons and electron capture occurs. It is a rigid neutron rich core surrounded by the outer iron outer crust. The gravitational field of a neutron star. The gravitational field of a neutron star is so strong that it would regain a escape velocity, nearly the speed of light to escape star.

Black Holes

For extremely large stars, the neutron star continues to compress itself until the gravitational field is so strong that no electromagnetic light or  particle can escape it. This means that escape velocity must be larger than the speed of light.

To calculate, how big a black hole is, we can assume a minimum Vesc= c

The maximum radius forms a boundary called the event horizon.

Event Horizon- the maximum radius for the light to escape black hole.

As the speed of particle can increase only to escape a black hole wheras

if the speed increases, R will increase.

This means Rc is the maximum when c= 3*108.

Gamma Rays Bursts

Gamma ray bursts originates from supernova, when super giant stars collapse to form neutron star and black holes. Gamma ray bursts are dangerous, formed by the narrow beam of gamma photon, if they were directed at us, it would wipe out most life.

Super-massive black holes

Observations have shown that stars and gas orbiting near the center of galaxies are being accelerated to very high velocities. This can be explained if a super massive object with strong gravitational field in small region of space is attracting them. The most likely candidate is the super massive black hole.

Standard Candles

A standard candle is the object whose absolute magnitude and luminosity is known.

Astronomer measure large distances by using bright objects with a known luminosity and absolute magnitude.

Which act as a standard candle. large distances in space are called cosmological distances.

We can use a type one supernova as a standard candle to help us to measure the distance from one glaxy to us. using

where d is the distance of supernova from the earth in per-second.

Dark energy

typically we would expect matter to be moving towards each-other in the universe-due to gravity, however whats actually happen, against exceptions, the usiverse is expanding and the matter is accelerating away from eachother. for this to happen, there must be resultant force acting on matter, one which we can’t see or detect. we call this clark energy.

Cosmology

Cosmology – The study of structure and development of the universe as whole.

The dropper effect

The dropper effect is change in the frequency of the object due to relative movement of an object (distance from the obsorver).

This is because there are move waves reaching you when the object is moving toward you so, the wavelength  is shortened.when is object is moving away from you, there are less waves per second reaching you

so, as a result the wavelength is increased.

Moving toward observer

• Wavelength decreases
• frequency increases
• Blue shifted

Wavelength away from the observer

• Wavelength increases
• frequency decreases
• red shifted

Binary Star

The doppler effect can be used to determine the rotational velocity and distance between the two stars in the binary system.

Binary stars – when 2 star orbit around i center.

and then use the rotational time period and speed to find the radius of the orbit.

adding the radii together gives distance, the star are from each other.

Hubble’s law

hubble’s law states that the recession velocity of the galaxy is directly proportional to its distance from us.

This can be used to estimate the age of the universe.

if for time t, the galaxy has moved outward, a distance d at a velocity v then

Evidence of the Big Bang

The Big Bang theory predicts that high energy gamma rays from t ≈ 300000 years ago should be seen today. However because of the red shift, they should now be red shifted down to microwaves. there is a cosmological microwave background (CMB) radiation coming from all directions of the universe. also the relative abundance of hydrogen and helium provide thestrong evidence as hydrogen produces helium in 3:1.

The current composition of the universe is 25% helium ,73% hydrogen and 2% other, supporting the big bang theory.

Quasars

quasars are the most distant measurable objects.these are the star like objects, however with unusually strong radio emission. they are also incredibily bright as shown by the inverse square law to show that thequasars luminosity is about 1038 to 1042 W. Quasars have very large red shifts showing that they are far away..

Quasars are thought to have formed from the huge disc of particles falling into a supermassive black hole, this would explain its brightness.

Detection of the exoplanets

Exoplanet- A planet that orbits the star which is not sun. exoplanet are hard to detect as they lost in the glare of stars.

Exoplanet exerts gravitational force on star causing it to orbit about a center of mass. using the doppler effect, we can find the radial velocity of the star.

Time period of the star = Time period of planet

These measurement allow the size and motion of the planet to be known.

2. Transit method

how much a star dims as planet covers it.

Decrease in brightness = Area of planet over star.