# Estimating the Radius of Stars(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## Estimating the Radius of Stars

• 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

#### 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

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

Step 4: Write down the Stefan-Boltzmann law

L = 4πr2σT4

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

Step 6: Calculate the ratio rB / rs

### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers