Units for Astronomical Distances (OCR A Level Physics): Revision Note

Units for Astronomical Distances

• Astronomical distances are very large and as a result, are usually measured using:

  • Astronomical Units (AU)

  • Light–years (ly)

  • Parsecs (pc)

Astronomical Unit (AU)

• The astronomical unit (AU) is defined as

  The mean distance from the centre of the Earth to the centre of the Sun

• As the Earth’s orbit around the Sun is elliptical it will be slightly closer to the Sun in January (1.471 × 10¹¹ m) than it is in July (1.521 × 10¹¹ m)

• Calculating the mean of these two values gives:

$\frac{(1.471\times {10}^{11})+(1.521\times {10}^{11})}{2}$ = 1.496 × 10¹¹ m

• Therefore, 1 astronomical unit = 1.496 × 10¹¹ m ≈ 1.5 × 10¹¹ m

• The astronomical unit is useful for studying distances on the scale of the solar system

Light–year (ly)

• A light-year is defined as:

  The distance travelled by light in one year

• This can be calculated using:

Distance = speed × time

• Where:

  • The speed of light is 3 × 10⁸ m s^–1

  • 1 year = 60 × 60 × 24 × 365 = 3.15 × 10⁷ s

• Hence, the distance travelled by light in one year = (3 × 10⁸) × (3.15 × 10⁷) = 9.46 × 10¹⁵ m

  • Therefore, 1 light–year ≈ 9.5 × 10¹⁵ m

Parsec (pc)

• Angles smaller than 1 degree can be measured in arcminutes or arcseconds

  • 1 degree = 60 arcminutes

  • 1 arcminute = 60 arcseconds

  • Therefore, 1 degree = 60 x 60 = 3600 arcseconds

  • 1 arcsecond = 1/3600 degree

• The parsec is defined as

  A unit of distance that gives a parallax angle of 1 second of an arc (of a degree), using the radius of the Earth’s orbit (1 AU) as the baseline of a right–angled triangle

• Given that 1 AU = 1.496 × 10¹¹ m, trigonometry can be used to express 1 parsec in metres:

$\tan \theta =\frac{opp}{adj}=\frac{1AU}{1pc}$

$\tan \left(\frac{1}{3600}\right)=\frac{1AU}{1pc}$

1 pc = $\frac{1AU}{\tan \left(\frac{1}{3600}\right)}=\frac{1.496\times {10}^{11}}{\tan \left(\frac{1}{3600}\right)}$ = 3.09 × 10¹⁶ m

• Therefore, 1 parsec ≈ 3.1 × 10¹⁶ m

• The parsec (1 pc = 3.1 × 10¹⁶ m) and the light-year (1 ly = 9.5 × 10¹⁵ m) are much greater in size than the astronomical unit (1 AU = 1.496 × 10¹¹ m)

• This makes them useful when studying interstellar distances

  • For example, on the scale of distances between the Earth and stars, or neighbouring galaxies