Parallax (Edexcel International A Level Physics)

Revision Note

Katie M


Katie M



Determining Distance using Parallax

  • The principle of parallax is based on how the position of an object appears to change as the position of the observer changes
    • For example, when observing the scale on a metre ruler, looking at eye level gets a different reading to viewing from above or below the scale
  • Stellar parallax can be used to measure the distance to nearby stars
  • Stellar Parallax is defined as:

The apparent shifting in position of a nearby star against a background of distant stars when viewed from different positions of the Earth, during the Earth’s orbit about the Sun

  • It involves observing how the position of a nearby stars changes over a period of time against a fixed background of distant stars
    • From the observer's position the distant stars do not appear to move
    • However, the closer object does appear to move
    • This difference creates the effect of stellar parallax

Using Stellar Parallax

  • A nearby star is viewed from the Earth in January and again in July
    • The observations are made six months apart to maximise the distance the Earth has moved from its starting position
  • The Earth has completed half a full orbit and is at a different position in its orbit around the Sun
    • The nearby star will appear in different positions against a backdrop of distant stars which will appear to not have moved
    • This apparent movement of the nearby star is called the stellar parallax

Calculating Stellar Parallax

  • Applying trigonometry to the parallax equation:
    • 1 AU = radius of Earths orbit around the sun
    • = parallax angle from earth to the nearby star
    • = distance to the nearby star
    • So, tan(p)fraction numerator A U over denominator d end fraction
  • For small angles, expressed in radians, tan(p)p, therefore: pfraction numerator A U over denominator d end fraction
  • If the distance to the nearby star is to be measured in parsec, then it can be shown that the relationship between the distance to a star from Earth and the angle of stellar parallax is given by

p space equals space 1 over d

  • Where:
    • p = parallax (")
    • d = the distance to the nearby star (pc)
  • This equation is accurate for distances of up to 100 pc
    • For distances larger than 100 pc the angles involved are so small they are hard to measure accurately

Worked example

The nearest star to Earth, Proxima Centauri, has a parallax of 0.768 seconds of arc.

Calculate the distance of Proxima Centauri from Earth

  1.  in parsec
  2.  in light–years

Part (a)

Step 1: List the known quantities

    • Parallax, p = 0.768"

Step 2: State the parallax equation

p space equals space 1 over d

Step 3: Rearrange and calculate the distance d

d space equals space 1 over p space equals space fraction numerator 1 over denominator 0.768 end fraction space equals space 1.30 space p c

Part (b)

Step 1: State the conversion between parsecs and metres

    • From the data booklet:

1 parsec ≈ 3.1 × 1016 m

Step 2: Convert 1.30 pc to m

1.30 pc = 1.30 × (3.1 × 1016) = 4.03 × 1016 m

Step 3: State the conversion between light–years and metres

    • From the data booklet

1 light–year ≈ 9.5 × 1015 m

Step 4: Convert 4.03 × 1016 m into light–years

fraction numerator 4.03 cross times 10 to the power of 16 over denominator 9.5 cross times 10 to the power of 15 end fraction = 4.2 ly (to 2 s.f)

Exam Tip

It is important to recognise the simplified units for arc seconds and arc minutes:

arcseconds = "

arcminutes = '

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Katie M

Author: Katie M

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.

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