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

Light-year (ly)

• A light-year is defined as:

The distance travelled by light in one year

• This can be calculated using:

$\mathrm{distance}=\mathrm{speed}\times \mathrm{time}$

• Where:

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

  • $1\mathrm{year}=60\times 60\times 24\times 365=3.15\times {10}^7\mathrm{s}$

• Hence, the distance travelled by light in one year is:

$1\mathrm{ly}=\left(3\times {10}^8\right)\times \left(3.15\times {10}^7\right)=9.46\times {10}^{15}\mathrm{m}$

• 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, $1\mathrm{degree}=60\times 60=3600\mathrm{arcseconds}$

  • 1 arcsecond = $\frac{1}{3600}$ 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

• Given that $1\mathrm{AU}=1.496\times {10}^{11}\mathrm{m}$, 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 ($1\mathrm{pc}=3.1\times {10}^{16}\mathrm{m}$) and the light-year ($1\mathrm{ly}=9.5\times {10}^{15}\mathrm{m}$) are much greater in size than the astronomical unit ($1\mathrm{AU}=1.496\times {10}^{11}\mathrm{m}$)

• This makes them useful for studying interstellar distances

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