Unit T - Astrophysics (copy)

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Centripetal force

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Centripetal force

  • Planets move around Sun in almost circular orbits (same for Moon around Earth)

  • If object travelling in circle, it is constantly changing direction (and so constantly accelerating), meaning there is force acting on it

  • Force causing this is centripetal - acts towards centre of circle

  • This force would cause object to fall towards whatever it’s orbiting, but as object is already moving, it just causes it to change direction

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Gravity

  • Object keeps accelerating towards what it’s orbiting, but instantaneous velocity (at right angle to acceleration) keeps it travelling in circle

  • Force that makes this happen is provided by gravitational force (gravity)

  • Gravitational attraction of Sun keeps planets + comets in their orbits around it

  • Satellites kept in orbits around planets by gravitational attraction of planet

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Gravitational field strength

  • Weight of object varies depending on gravitational field strength (g)

  • G depends on mass of body creating field - larger mass = stronger g (Earth bigger than Moon so object weighs more on Earth than Moon)

  • G also varies with distance - closer to star/planet = stronger g

  • Stronger force = larger instantaneous velocity needed to balance it

  • So closer to star/planet = faster you need to go to remain in orbit

  • For object in stable orbit, if speed of object changes, size (radius) of orbit must do so too - faster moving objects move in stable orbit with smaller radius than slower moving ones

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Different types of orbit

  • Orbits of moons + planets usually slightly elliptical

  • Comets orbit Sun, but have very elliptical (elongated) orbits with Sun at one focus (near one end of the orbit)

  • Comets have much longer orbital periods than Earth - they travel from outer edges of solar system

  • Comets travel much faster nearer Sun than it does at more distant parts of orbit - increased pull of gravity makes it speed up the closer it gets to Sun

  • Some artificial Earth satellites have orbital period of exactly one day - called geostationary satellites, useful in communications because always over same part of planet

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Equation: Orbital speed, Orbital radius, Time period

Orbital speed = 2 * π * orbital radius / time period

v = (2πr)/T

[m/s] = 2π [m]/[s]

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6

Star colour depends on…

Surface temp

Colour depends on the visible light it emits

All stars emit visible light, but how much it emits of each freq depends on surface

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Classifying stars by colour

  • Can classify stars based on colour - red, orange, yellow, white, blue
    All stars of similar colour have similar temp

  • Hotter star = more light of higher freq emitted

  • Cool star emits most visible light at lowest freq (i.e. red light) so appears red

  • White > Yellow > Orange > Red in terms of temp

  • White stars emit all freq of visible light roughly equally

  • Blue stars hotter than white stars - emit more high freq light (blue, indigo, violet) than lower freq (red, orange) so appear blue

<ul><li><p>Can <strong>classify </strong>stars based on <strong>colour</strong> - red, orange, yellow, white, blue<br>All stars of <strong>similar colour </strong>have <strong>similar temp</strong></p></li><li><p><strong>Hotter </strong>star = <strong>more </strong>light of <strong>higher freq </strong>emitted</p></li><li><p><strong>Cool </strong>star emits most visible light at <strong>lowest freq</strong> (i.e. <strong>red light</strong>) so appears <strong><span style="color: red">red</span></strong></p></li><li><p><strong>White &gt; Yellow<span style="color: yellow"> </span>&gt; Orange &gt; Red</strong> in terms of temp</p></li><li><p>White stars emit <strong>all freq</strong> of visible light roughly <strong>equally</strong></p></li><li><p><strong>Blue </strong>stars hotter than white stars - emit more <strong>high freq</strong> light (blue, indigo, violet) than lower freq (red, orange) so appear <strong><span style="color: blue">blue</span></strong></p></li></ul>
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Doppler effect for light

  • When wave source is moving relative to observer, waves undergo change in freq + wavelength when they’re observed, compared to when they were emitted - Doppler Effect

  • Happens with all types of waves, inc. light

<ul><li><p>When wave <strong>source</strong> is <strong>moving </strong>relative to <strong>observer</strong>, waves undergo <strong>change in freq</strong> + <strong>wavelength</strong> when they’re <strong>observed</strong>, compared to when they were <strong>emitted</strong> - Doppler Effect</p></li><li><p>Happens with <strong>all </strong>types of <strong>waves</strong>, inc. <strong>light</strong> </p></li></ul>
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Red shift

  • Light source moving away from you → light it emits shifts towards red end (i.e. lower freq) of visible part of EM spectrum - red shift

  • Astronomers see this happening with light from stars:

    • Light from distant stars red-shifted - observe light with longer wavelength (lower freq) than we’d expect stars to emit

    • So star must be moving away from Earth

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10

Red shift in galaxies

  • Diff elements absorb diff freq of light

  • When light is passed through sample of element, a pattern of dark lines is produced - with dark line at each freq in visible part of EM spectrum that element absorbs

  • When we look at light from distant galaxies, we see same patterns but at slightly lower freq (so longer wavelengths) than they should be

  • Patterns have been shifted towards red end of spectrum - red shift

<ul><li><p>Diff elements<strong> absorb</strong> diff <strong>freq </strong>of light</p></li><li><p>When light is passed through sample of element, a <strong>pattern</strong> of <strong>dark lines</strong> is produced - with dark line at each freq in visible part of EM spectrum that element <strong>absorbs</strong></p></li><li><p>When we look at <strong>light from distant galaxies</strong>, we see <strong>same patterns</strong> but at <strong>slightly lower freq</strong> (so <strong>longer wavelengths</strong>) than they should be</p></li><li><p>Patterns have been <strong>shifted</strong> towards red end of spectrum - <strong>red shift</strong> </p></li></ul>
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Equation: Red shift

Change in wavelength / Reference wavelength = Velocity of galaxy / Speed of light

λ-λ₀ / λ₀ = Δλ/λ₀ = v/c

[m]/[m] = [m/s] / [m/s]

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12

Red-shift suggests the universe is…

Expanding

  • Measurements of red-shift suggest that all distant galaxies are moving away from us very quickly - same result in all directions

  • More distant galaxies have greater red-shifts than nearer ones - bigger observed increase in wavelength

  • Means that more distant galaxies moving away faster than nearer ones

  • Conclusion: whole universe is expanding

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13

CMB Radiation

  • Scientists can detect low freq microwave radiation coming from all directions and all parts of universe

  • Known as Cosmic Microwave Background (CMB) radiation

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CMB Radiation is evidence for…

Big Bang

  • As universe expands + cools, background radiation ‘cools’ + drops in frequency

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15

Big Bang Theory

  1. Initially, all matter in universe occupied single point

  2. Tiny space was very dense + hot

  3. Single point ‘exploded’ - Big Bang

  4. Space started expanding, and expansion is still going on

<ol><li><p>Initially, all matter in universe occupied <strong>single point</strong></p></li><li><p>Tiny space was very <strong>dense</strong> + <strong>hot</strong></p></li><li><p>Single point ‘<strong>exploded</strong>’ - Big Bang</p></li><li><p>Space started expanding, and <strong>expansion </strong>is still going on</p></li></ol>
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