Unit T - Astrophysics (copy)

Centripetal force

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

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

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

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

Equation: Orbital speed, Orbital radius, Time period

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

v = (2πr)/T

[m/s] = 2π [m]/[s]

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

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

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

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

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

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]

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

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

CMB Radiation is evidence for…

Big Bang

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

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