Units for Astronomical Distances (OCR A Level Physics)

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Katie M

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Katie M

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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:

fraction numerator left parenthesis 1.471 cross times 10 to the power of 11 right parenthesis plus left parenthesis 1.521 cross times 10 to the power of 11 right parenthesis over denominator 2 end fraction = 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

5-12-1-au_ocr-al-physics

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

5-12-1-parsec_ocr-al-physics
  • Given that 1 AU = 1.496 × 1011 m, trigonometry can be used to express 1 parsec in metres:

tan theta space equals space fraction numerator o p p over denominator a d j end fraction space equals space fraction numerator 1 space A U over denominator 1 space p c end fraction

tan open parentheses 1 over 3600 close parentheses space equals space fraction numerator 1 space A U over denominator 1 space p c end fraction

1 pc = fraction numerator 1 space A U over denominator tan open parentheses 1 over 3600 close parentheses end fraction space equals space fraction numerator 1.496 space cross times 10 to the power of 11 over denominator tan open parentheses 1 over 3600 close parentheses end fraction = 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

Worked Example

The closest star to Earth is a triple–star system called Alpha Centauri, which is approximately 4.35 light-years from Earth. 

Calculate the distance between the Earth and Alpha Centauri in:

a) Astronomical units

b) Parsecs

An astronomical unit is 1.496 × 1011 m

Answer:

Part (a)

Step 1: List the known quantities

  • 1 light-year ≈ 9.5 × 1015 m (from data booklet)

  • 1 AU = 1.496 × 1011 m

  • Distance to Alpha Centauri = 4.35 ly

Step 2: Convert 4.35 light–years into metres

  • 4.35 ly = 4.35 × (9.5 × 1015) = 4.13 × 1016 m

Step 3: Convert from metres into AU

  • 4.13 × 1016 m = fraction numerator 4.13 cross times 10 to the power of 16 over denominator 1.496 cross times 10 to the power of 11 end fraction = 2.8 × 105 AU (to 2 s.f)

Part (b)

Step 1: List the known quantities

  • 1 parsec ≈ 3.1 × 1016 m (from data booklet)

  • 4.35 ly = 4.13 × 1016 m (from part a)

Step 2: Convert from metres into parsecs

  • 4.13 × 1016 m = fraction numerator 4.13 space cross times space 10 to the power of 16 over denominator 3.1 space cross times space 10 to the power of 16 end fraction = 1.3 pc (to 2 s.f)

Examiner Tips and Tricks

You do not need to learn all of the conversion factors for astronomical distances, you just need to know how to use them! The following are given in the data booklet:

1 light–year ≈ 9.5 × 1015 m

1 parsec ≈ 3.1 × 1016 m

However, the astronomical unit (AU) is not, so this could be useful to learn by heart!

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.