OCR A Level Physics

Revision Notes

5.12.2 Stellar Parallax

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Stellar Parallax

  • The principle of parallax is based on how the position of an object appears to change depending on where it is observed from
    • When observing the volume of liquid in a measuring cylinder the parallax principle will result in the observer obtaining different values based on where they viewed the bottom of the meniscus from


  • 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 star changes over a period of time against a fixed background of distant stars
    • To an observer the position of distant stars does not change with time
  • If a nearby star is viewed from the Earth in January and again in July, when the Earth is at a different position in its orbit around the Sun, the 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


The Parallax Equation

  • 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 1 space A U over denominator d end fraction
  • For small angles, expressed in radians, tan(p)p, therefore: pfraction numerator 1 space 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

Make sure you know the units for arc seconds (") and arc minutes (')

  • 1 arcminute is denoted by 1'
  • 1 arcsecond is denoted by 1" 

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