IBPhysicsHLRevision NotesNuclear & Quantum PhysicsFusion & StarsDetermination of Stellar Radii

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Determination of Stellar Radii (HL IB Physics)

Revision Note

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Determination of Stellar Radii

  • The radius of a star can be estimated by combining Wien’s displacement law and the Stefan–Boltzmann law
  • The procedure for this is as follows:
    • Using Wien’s displacement law to find the surface temperature of the star
    • Using the inverse square law of flux equation to find the luminosity of the star (if given the radiant flux and stellar distance)
    • Then, using the Stefan-Boltzmann law, the stellar radius can be obtained

Summary of Stellar Equations (1), downloadable AS & A Level Physics revision notesSummary of Stellar Equations (2), downloadable AS & A Level Physics revision notes

Worked example

Betelguese is our nearest red giant star. It has a luminosity of 4.49 × 1031 W and emits radiation with a peak wavelength of 850 nm.

Calculate the ratio of the radius of Betelgeuse rB to the radius of the Sun rs.

Radius of the Sun, rs = 6.95 × 108 m.

Answer:

Step 1: List the known quantities

  • Luminosity of Betelgeuse, L = 4.49 × 1031 W
  • Peak wavelength of Betelgeuse, λmax = 850 nm = 850 × 10−9 m
  • Radius of the Sun, rs = 6.95 × 108 m

Step 2: Write down Wien’s displacement law

λmaxT = 2.9 × 10−3 m K

Step 3: Rearrange Wien’s displacement law to find the surface temperature of Betelguese

Estimating the Radius of Stars Worked Example equation 1

Step 4: Write down the Stefan-Boltzmann law

L = 4πr2σT4

Step 5: Rearrange for r and calculate the stellar radius of Betelguese

Estimating the Radius of Stars Worked Example equation 2

Step 6: Calculate the ratio rB / rs

Estimating the Radius of Stars Worked Example equation 3

  • Therefore, the radius of Betelguese is about 1000 times larger than the Sun’s radius
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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.