Cosmology: (a) distances measured in astronomical unit (AU), light-year

The idea

Cosmological distances are so large that metres are impractical, so astronomers use the astronomical unit (AU) and the light-year (ly). One AU is the average Earth–Sun distance, about 1.50 × 10¹¹ m, convenient for distances within the Solar System. One light-year is the distance light travels in a vacuum in one year, about 9.46 × 10¹⁵ m, convenient for distances to stars and galaxies. To convert, multiply the number of AU or ly by the appropriate metre value. For example, 4.2 ly ≈ 4.2 × 9.46 × 10¹⁵ m ≈ 3.97 × 10¹⁶ m. Choose the unit that keeps numbers manageable and state it clearly.

What earns the marks

• One astronomical unit (AU) is the average distance from the Earth to the Sun, approximately 1.50 × 10¹¹ m.
• One light-year (ly) is the distance electromagnetic radiation travels through a vacuum in one year, approximately 9.46 × 10¹⁵ m.
• The light-year is a distance, not a time, despite containing the word ‘year’.
• Convert AU to metres by multiplying by 1.50 × 10¹¹, and ly to metres by multiplying by 9.46 × 10¹⁵.
• AU is suited to Solar System distances, while ly is suited to interstellar and intergalactic distances.
• A light-year equals the speed of light multiplied by the number of seconds in a year: 3.00 × 10⁸ m s⁻¹ × 3.16 × 10⁷ s ≈ 9.46 × 10¹⁵ m.

Common mistakes and how to put them right

• Treating the light-year as a unit of time.

  Put it right: It is a distance, defined as the distance light travels in one year.

• Confusing AU with the radius of the Sun.

  Put it right: AU is the Earth–Sun distance, not the Sun’s radius.

• Using 365 days exactly without converting to seconds when deriving the light-year.

  Put it right: Convert one year to about 3.16 × 10⁷ s before multiplying by the speed of light.

• Mixing units within a calculation, such as adding AU to metres.

  Put it right: Convert all distances to the same unit before combining them.

Exam tips

• Quote the metre equivalent of AU or ly when converting, and keep units visible throughout.
• Check whether the question expects an answer in AU, ly or metres, and convert only at the end.
• Remember that a light-year is a distance; if a question asks for time, use the light-travel time instead.