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Mechanics & Stress Analysis*
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  • A-Level Physics


Instead of using metres and kilometres, distances are measured in far larger units:

  • Astronomical units, AU: the mean distance between the Earth and the Sun. ~150 million km

  • Light-Years, ly: the distance and electromagnetic wave travels in one year. ~ 9.5x1015 m

  • Parsecs, pc: the length of the adjacent side of a right-angled triangle with angle 1 arcsecond and opposite side length 1 parsec. ~ 3.1x1016 m

Parsec diagram, AU diagram, Astronomical unit diagram, cosmology diagram., EngineeringNotes, Engineering Notes

The angle is measured in arcseconds because of stellar parallax – objects further away appear to be moving more slowly than object closer to earth, and nearby stars appear to move differently depending on where in the earth’s orbit we are. Parallax in arcseconds, p, can be calculated for a known distance, d, measured in parsecs:

p = 1/d parallax (in arcseconds) = 1 / distance (in parsecs)
d = 1/p distance (in parsecs) = 1 / parallax (in arcseconds)

1 second of arc = (1/3600)°

The Cosmological Principal

The Cosmological Principal states that, on a large scale, the universe is:

  • homogeneous (every part is the same as another)

  • isotropic (looks the same in every direction)

  • and the laws of physics apply everywhere.

We apply this principle when investigating the universe, allowing us to use standard mechanics to solve problems on a cosmological scale.

Doppler Shift & Hubble's Law

The Doppler Shift is the way in which frequency and wavelength change with the motion of the wave's source, relative to you. This happens because the waves bunch together in front of the source and stretch out behind it. The extent of bunching and stretching depends on the sources velocity. 

  • Red shift occurs when a light source moves away from us, as the wavelengths become longer and the frequencies become lower, so the light shifts towards the red end of the spectrum.

  • Blue shift occurs when a light source moves towards us, as the opposite happens and the light shifts towards the blue end of the spectrum.

  • The same principal applies to sound waves: as the source moves towards you, the frequency increases and wavelength decreases; as it moves away the frequency decreases and wavelength increases. For example, a high speed train approaching, passing, and disappearing from a level crossing.

The amount of shift can be calculated with the Doppler Equation:

Δλ/λ ≈ Δf/f ≈ v/c

Δλ and Δf represent the difference between observed and emitted wavelength and frequency. v is the velocity of the source, and c the speed of light, 3 E8 m/s.