# OCR 21C Physics P7

The Whole of P7 - Further Physics

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## Looking Into Space

The Earth rotates west to east on its axis once in just under 24 hours.

We can't feel the Earth spinning, but it is this rotation that makes the stars appear to move east-west across the sky in just under 24 hours.

The Sun, planets and Moon also appear to travel east-west across the sky. Their motion, and the time they take to cross the sky, is affected by their relevant orbits. The Sun appears to travel across the sky once every 24 hours.

Higher Tier:

Stars appear to travel east-west across the sky in 23 hours and 56 minutes.

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## The Earth and the Sun

A sidereal day is the time it takes for the Earth to rotate 360degrees on its axis. A solar day is the time from noon on one day to noon on the next day, i.e. 24 hours.

Whilst the Earth rotatesonce on its axis, it also orbits the sun. It is this orbiting movement that makes a sidereal day shorter than a solar day.

1) The Sun is directly over a point on the Earth.

2) The Earth has rotated 360degrees, but as it's also orbiting the Sun, the Sun is no longer directly overhead

3) The Earth has had time to rotate a bit more so the Sun is now directly overhead, making the solar day longer than the sidereal day.

Higher Tier

A sidereal day is 4 minutes shorter than a solar day.

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## The Position of the Stars

The Earth orbits around the Sun. So, an observer looking at the night sky from the Earth can see different stars at different times of the year. The stars that can be seen will depend on the Earths position in relation to the Suns position.

Plotting Astronomical Objects

The position of an astronomical object can be measured in terms of angles as seen from the Earth. The angles of declination and ascension describe the positions of the stars relative to a fixed point on the equator.

A star with:

-positive declination will be visible from the northern hemisphere

-negative declination will be visible from the southern hemisphere

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## The Planets

From Earth, the planets look similiar to stars. But, the planets change their positions in complicated patterns when compared to the background of fixed stars.

We can see how planets change their positions by using observations of Venus as an example.

Venus is closer to the Sun than the Earth, so it orbits the Sun more quickly than the Earth does.

If Venus is observed over a long enough period of time (e.g. one month), it can be seen to move compared to the background stars.

1) When Venus is on the same side of the Sun as the Earth, it looks like its travelling in one direction against the background stars.

2) When Venus is on the other side of the Sun to Earth, it looks like its travelling in the opposite direction.

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## The Earth and The Moon

Whilst the Earth is rotating on its axis, the Moon is orbiting the Earth in the same direction.

Due to this orbiting movement, the Moon appears to travel east-west across the sky in a little over 24 hours.

For example, imagine you saw the moon directly above you at a certain time one night. If you looked up again after one complete rotation of the Earth, the Moon wouldnt yet be directly above you. This is because the Earth's rotation would not yet have caught up with the Moons new orbital position.

The Moon appears to travel east-west across the sky in 24 hours and 49 minutes.

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## The Lunar Cycle

The lunar cycle describes the Moon's appearance during its 28-day orbit of the Earth. The Moon's shape during this orbit is due to the part of the Moon that is visible from Earth.

We are able to see the Moon because the Sun's light is reflected from it. The side of the Moon facing away from the Sun appears  dark, and the side facing towards the Sun appears light.

During the Moons orbit around the Earth we can see different faces of the Moon:

- dark face (new Moon)
- light face (full Moon)
- all the points inbetween the new Moon and the full Moon

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## Eclipses

Solar Eclipses

A solar eclipse occurs when the Moon passes between the Earth and the Sun. This can happen during a new Moon and it results in the Moon casting a shadow on the Earth.

A  total solar eclipse occurs when the Moon is directly in front of the Sun and completely obscures the Earth's view of the Sun

Lunar Eclipse

A lunar eclipse occurs when the Earth is between the Sun and the  Moon. This results in the Earth casting a shadow on the Moon.

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## Frequency of Eclipses

Eclipses don't occur every month because the Moon doesn't orbit the Earth in the same plane as the Earth orbits the Sun. (The Moons orbit is inclined 5degrees to that of the Earths)

So, an eclipse can only occur when the Moon passes through the ecliptic (the apparent path the Sun traces along the sky). This is more likely to occur when the Moon is to the side of the Earth rather than between the Earth and the Sun.

There are between 2 and 5 solar eclipses every year, but a total eclipse will only occur roughly every 18 months.

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## Convex Lenses

A convex (or converging) lens bends rays of light inwards as they pass through the lens. If the rays of light entering the lens are parallel, the rays will be brought to a focus at the focal point.

The greater the curvature of a lens, the more powerful it will be. So, if two lenses are made of the same material, a highly curved lens will be more powerful than a flatter lens.

Power (dioptre) =              1
focal length (metre)

If a convex lens has a focal length of 10 cm, calculate its power.

Power =       =  10 dioptres
0.1

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## Ray Diagrams

Ray diagrams are drawn to show how the image of an object would be formed.

1) Draw a ray line that runs from the top of the object parallel to the principal axis. At the middle of the lens, bend the ray inwards so it passes through the focal point.

2) Draw a second ray that runs from the top of the object straight through the centre of the lens as it crosses the prncipal axis.

3) Draw a third ray that runs from the top of the object through the focal point on the same side as the object. When the ray hits the centre of the of the lens, bend it to travel parallel to the principal axis.

4) If the object crosses the principal axis, draw another ray that runs from the bottom of the object, parallel to the principal axis. At the middle of the lens, bend this ray inwards so it passes through the focal point.

5) The image is formed where the rays meet.

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## Telescopes

Objects in space are so far away that rays of light from them seem to be parallel. So, we draw the rays of light entering the telescope as parallel rays.

A simple refracting telescope is made from two converging lenses of different powers. The eyepiece lens is a higher power lens than the objective lens.

An astronomical telescope usually uses a concave mirror for the objective lens instead of a convex lens. This allows them to be larger, which means they can collect more light.

Concave mirrors reflect rays of parallel light and bring them to focus.

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## Angular Magnification

The image of a distant magnified object will appear closer than the object. So, the angle made by ray lines entering the eye is greater.

The increase in angle is called the angular magnification and makes the image appear bigger / closer.

You can calculate the angular magnification of a telescope using:

Magnification = focal length of objective lens
focal length of eyepiece lens

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## Parallax

Parallax can be thought of as the apparent motion of an object against a background.

But it's actually the motion of the observer that causes the parallax motion of an object.

A simple way to observe parallax is if you hold your hand out in front of you with your thumb sticking up and alternately close one eye then the other.

Although your thumb appears to move, in reality you are just looking at it from a different angle.

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## Measuring Distance Using Parallax

Parallax can make a star appear to move in relation to the other stars in the course of the year.

If an observer at position 1 looks at a near star compared to the distant background, it appears to be at position B. But, if the observer then looks at the same star six months later, (position 2) the star appears to be at postition A.

It looks as though the star has moved, but it's actually the movement of the Earth's orbit around the Sun that causes the observer to see this 'change in position'.

The parallax angle of a star is half the angle moved against a background of distant stars in 6 months.

An object that is further away from the Earth will have a smaller parallax angle than a closer object

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## Using Parallax

Astronomers use parallax to measure interstellar distances using the unit parsec (pc). The typical interstellar distance between stars is a few parsecs.

A parsec is the distance to a star with a parallax angle of one second of an arc. It is of a similiar siza to a light year.

Astronomers can use the megaparsec (Mpc) to measure intergalactic distances even though these objects are so far away that the parallax angle is too small too measure.

For example, the nearest major galaxy, Andromeda, is 770,000 parsecs (0.77Mpc) away.

Distance (parsecs) =                     1
parallax angle (Arcseconds)

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## Measuring Distance Using Brightness

Astronomers can also measure the distance to stars by observing how bright the stars are. In theory, this method sounds very simple, i.e a close star will appar brighter than a more distant star. But, stars don't necessarily have the same intrinsic brightness ( the amount of energy a star gives out).

A stars intrinsic brightness depends on its:
- size
- temperature

A large hot star will emit more light than a small or cool star. It may appear brighter even though it is  further away.
So, the observed brightness of a star depends on its:
- intrinsic brightness
- distance from Earth

A star with  low intrinsic brightness may appear dull even if it's close to the Earth. And a star with a very high intrinsic brightness may appear bright even if it's far away from the Earth

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## Cepheid Variable Stars

A Cepheid variable star doesn't have a constant intrinsic brightness. It pulses and its brightness depends on the frequency of the pulses.

This changing frequency can be used to work out the distance to Cepheid variable stars.

By measuring the frequency of the pulses, astronomers can estimate the star's intrinsic brightness. The distance to the star can then be worked out if we know:

- how bright the star really is
- how bright the star appears

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## The Curtis-Shapley Debate

In 1920, a great debate about the scale of the Universe took place between two prominent astronomers - Heber Curtis and Harlow Shapley.

Telescopes had revealed that the Milky Way contained lots of stars. This observation led to the realisation that the Sun was a star in the Milky Way galaxy.

Telescopes had also revealed many  fuzzy objects in the night sky. These objects were originally called nebulae and they played a major role in the debate.

Curtis believed that the Universe consisted of many galaxies like our own, and the fuzzy objects were distant galaxies.

Shapley believed that the Universe contained only one big galaxy and the nebulae were nearby gas clouds within the Milky Way.

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## Edwin Hubble

In the mid - 1920's, Edwin Hubble observed Cepheid variables in one nebula and found that the nebula was  much further away than any star in the Milky Way.

This observation provided the evidence that the observed nebula was a seperate galaxy. This supported Curtis' idea that the Universe containse many different galaxies.

Observations of many Cepheid variables have shown that most nebulae are distant galaxies.

This has allowed astronomers to measure the distance to these galaxies, and so determine the scale of the Universe.

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## The Hubble Constant

By observing Cepheid variable stars in distant galaxies, Edwin Hubble discovered the the Universe was expanding, in fact the further away a star was, the faster it was moving away.

Cepheid variable stars in distant galaxies have been used to accurately calculate the Hubble constant because we know how far away they are.

So, we can use red shift to find out how fast they are moving away (their speed of recession).

Astronomers can now use the Hubble constant and red shift data to calculate the distance to other galaxies.

Speed of recession    =    Hubble Constant     X     Distance
(km/s)                               (s¯¹)                        (km)

(km s¯¹ Mpm¯¹)              (Mpc)

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## Example 1

A galaxy is a distance of 3 x 10²⁰km from Earth. If the Hubble Constant is
2.33 x 10
¯¹⁸ s¯¹ , calculate the speed of recession.

Speed of recession = (2.33 x 10¯¹⁸ s¯¹ ) X (3 x 10²⁰km)

= 700km/s

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## Pressure and Volume

Fluid pressure is caused by particles in a fluid moving about. When a particle collides with an object it exerts a force. This force is felt as pressure.

The amount of pressure depends on:
- the number or collisions per second
- the momentum of the particles

As the volume of a fluid is reduced, the particles have less room to move about. So, they collide with each other more often, increasing the pressure.

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## Pressure and Temperature

If a fluid is heated up, the particles move around faster. This increases their momentum and the force they exert when they collide with each other.

This could have two effects:
1) Increase the volume
2) Increase the pressure (if the volume is kept fixed)

This effect will also work in reverse, i.e. compressing a gas will cause it to increase in temperature.

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## Absolute Zero

As the temperature of a gas is reduced, the particles in the gas move slower and the pressure falls.

The particles eventually stop moving altogether. At this point the particles have no more energy to lose and the temperature can't get any lower. This occurs at -273C, otherwise known as absolute zero.

Absolute temperature is a measure of temperature starting at absolute zero and is measured in Kelvins (K).

To convert from:
- Kelvin into degrees Celsius, subtract 273
- degrees Celsius into Kelvin, add 273

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## The Structure of a Star

A star has three main parts:
- The core is the hottest part of the star where fusion takes place
- The convective zone is where energy is transported to the surface by convection currents.
- The photosphere is where energy is radiated into space

Like all hot objects, stars emit a continuous range of electromagnetic radiation. They emit radiation of a:
- high intensity
- high peak frequency

An object that is red hot emits most of its energy in the red frequency range. The frequency of light given off from a star provides evidence of how hot it is.

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## Using a Star's Spectrum

The removal of electrons from an atom is called ionisation. The movement of electrons within the stom causes it to emit radiation of specific frequencies called line spectra. Different elements have characteristic line spectra.

Due to its high temperature, the spectrum from a star is continuous, apart from spectral lines of the elements it contains (these lines are missing because they are absorbed).

By comparing a star's spectrum to emission spectra from elements, we can see which chemical elements the star contains.

The Sun's spectrum is complex, indicating that it contains more than one element. But, by comparing the spectra we can see that the Sun contains hydrogen as well as some other elements (e.g. helium).

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## The Beginning of a Star's Life

Stars begin as clouds of gas (mainly hydrogen). As gravity brings these clouds together, they become denser.

The force of gravity pulls the gas inwards, causing the pressure and temperature to increase. As more gas is drawn in, the force of gravity increases.

This compresses the gas so that it becomes hotter and denser, and forms a protostar.

Eventually, the temperature and pressure become so high that the hydrogen nuclei fuse into helium nuclei. Energy is released in this fusion process. The star is now a stable main sequence star.

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## The End of a Star's Life

Towards the end of a star's life, its 'fuel' begins to run out (there isn't enough hydrogen left in the core for fusion to continue). The star then goes through several changes (depending on its size).

When the core hydrogenhas been used up, the star becomes cooler. Small stars like our Sun become red giants, while larger stars become red supergiants.

Red giants and red supergiants continue to release energy by fusing helium into larger nuclei such as carbon, nitrogen and oxygen.

Once the helium has been used up, red giants no longer have enough mass to compress the core and continue fusion. They shrink into hot white dwarfs that gradually cool.

Red supergiants have a much greater mass and higher core pressures than red giants, so fusion continues to produce larger nuclei, such as iron.

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## Continued...

Once the core is mostly iron, the red supergiant explodes in a supernova, leaving behind a dense neutron star or a black hole.

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## Alpha Particle Scattering Experiment

At the beginning of the 20th Century, discoveries about the nature of the atom and nuclear processes began to answer the mystery of the source of the Sun's energy.

In 1911, there was a ground-breaking experiment - the Rutherford-Geiger-Marsden alpha particle scattering experiment.

In this experiment, a think gold foil was bombarded with alpha particles. The effect on the alpha particles was recorded and these observations provided the evidence for our current understanding of atoms.

Three observations were recorded:
- Most alpha particles were seen to pass straight through the gold foil
- Some particles were deflected slightly
- A few particles bounced back towards the source

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## Continued...

Particles passing through the foil indicated that gold atoms are composed of large amounts of space. The defection and bouncing back of particles indicated that these alpha particles passed close to something positively charged within the atom and were repelled by it.

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## Conclusions of Experiment

The observations of this experiment brought Rutherford and Marsden to conclude the following:
- Gold atoms, and therefore all atoms, consist largely of empty space with a small, dense core. They called this core the nucleus
- The nucleus is positively charged
- The electrons are arranged around the nucleus with a great deal of space between them

We now know that the nucleus contains positive protons and neutral neutrons held togetehr by the short ranged strong nuclear force.

Protons normally repel each other, but this nuclear force is much stronger than the repulsive electrical force. So when protons are close enough, the nuclear force takes over and the protons fuse into a larger nucleus.

This fusion process releases large amounts of energy and is the source of the Suns power.

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## Telescopes

As astronomers try to gather more evidence about the Universe, they need to examine objects that are a very long way from Earth.

These distant objects will often emit very faint or weak radiation. So, in order to pick up this radiation, larger complex and more expensive telescopes need to be built.

Astronomers use different types of ground-based or space-based telescopes, including radio, optical and infra-red.

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Radio Telescopes use a small metal reflector to reflect radio waves onto a reciever. Radio waves aren't blocked by clouds or affected by weather, so radio telescopes are able to detect objects that are too cool to emit much visible or infrared light.

A large radio telescope is needed in order to produce good-quality images, but even then the images produced will not be as clear as ones produced by an optical telescope.

Infrared Telescopes work much like optical telescopes. They have a better resolution than radio telescopes and can observe cooler objects that dont give off visible light.

But, because infrared light is easily absorbed by the Earth's atmosphere. these telescopes need to be:
- built at high altitude
- based in space

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## Diffraction

Radiation is diffraction by the aperture of a telescope. To produce a sharp image, the aperture must be much larger than the wavelength of the radiation.

Large radio telescopes can detect weak radio waves. But, radio waves have a long wavelength affected by diffraction, so the image produced isn't very sharp.

Light has a very short wavelength. Optical telescopes have a much larger aperture than the light's wavelength, so they can produce a sharp image.

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## Ground-Based Optical Telescopes

There are several locations of major astronomical observatories, for example, the:
- Royal Observatory in Greenwich (the largest refracting optical telescope in the UK)
- Mauna Kea Observatories, Hawaii (the largest optical reflecting telescopes in the world).

Astronomical factors will often influence the choice of a site. For example, Hawaii has proven an ideal location because of its:
- high altitude (less atmosphere above it to absorb light from distant objects)
- isolated location (less pollution to interfere with the recieved signal)
- equatorial location (gives best view of solar eclipses)

There are often factors that should be considered when planning, building, operating or closing down an observatory
- cost
- environmental and social impact near the observatory
- working conditions for employees

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## Space-Based Telescopes

Space-based telescopes, e.g. the Hubble Telescope, can obtain images of the Universe that can't be obtained in any other way.

- They avoid the absortion and refraction effects of the Earth's atmosphere.
- They can use parts of the electromagnetic spectrum that the atmosphere absorbs.

- They are very expensive to set up, maintain and repair
- There are uncertainties associated with space programmes, e.g. launch delays

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## Funding Developments in Science

Most of the big new telescopes are developed through international co-operation.

There are several advantages to this kind of joint venture:
- The cost of building the telescopes is shared
- Expertise can be shared
- Astronomers can book time on telescopes in different countries, allowing them to see stars on the other sides of the Earth.

These telescopes can be accessed:
- directly at the site
- through remote computer control (so astronomers don't have to travel to each telescope and can use it at convenient times)
- through the Internet (schools in the UK can access the Royal Observatory in this way)

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