Astronomical Distances (AQA A Level Physics): Revision Note

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) 

  • Slightly further away from the Sun in July (1.521 × 10¹¹ m)

• Calculating the mean of these two values gives:

$1\mathrm{AU}=\frac{(1.471\times {10}^{11})+(1.521\times {10}^{11})}{2}=1.496\times {10}^{11}\mathrm{m}$

• Therefore, 1 astronomical unit (AU) is approximately 1.5 × 10¹¹ m

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

How Far is an Astronomical Unit?

An astronomical unit (AU) is the mean distance between the Earth and the Sun

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 is:

1 ly = (3 × 10⁸) × (3.15 × 10⁷) = 9.46 × 10¹⁵ m

• Therefore, 1 light–year is approximately 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 × 60 = 3600 arcseconds

  • 1 arcsecond = 1/3600 degree

• The parsec is defined as:

The distance at which the radius of the Earth's orbit (1 AU) around the Sun subtends at an angle of 1 arcsecond

How Far is a Parsec?

A parsec is defined using parallax angles

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

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

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

$1\mathrm{pc}=\frac{1\mathrm{AU}}{\tan \left(\frac{1}{3600}\right)}=\frac{1.496\times {10}^{11}}{\tan \left(\frac{1}{3600}\right)}=3.09\times {10}^{16}\mathrm{m}$

• Therefore, 1 parsec is approximately 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 for studying interstellar distances

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