Question

Estimate the diameter of the supergiant star Betelgeuse, using its angular diameter of about 0.05 arcsecond and distance of about 600 light years.

Express your answer to three significant figures and include the appropriate units.

Answer 1

Diameter of the star,
`d=1.38* 10^(12)\ m`

Explanation:

Given that,

Angular diameter of the star, angle,
`\theta=0.05\ arcsecond=2.42* 10^(-7)\ radian`

Distance,
`D=600\ ly=5.67* 10^(18)\ m`

We need to find the diameter of the supergiant star Betelgeuse. The relationship between the diameter of star and angle subtended is given by :

`\theta=(d)/(D)`, d = diameter

`d=\theta* D`

`d=2.42* 10^(-7)* 5.67* 10^(18)`

`d=1.37214* 10^(12)\ m`

or

`d=1.38* 10^(12)\ m`

Hence, this is the required solution.

Answer 2

0.05 arc-second = 1 degree/72000 = (pi radians)/(180*72000) = 2.424 x 10^(-7) radians

The distance is roughly:

R*(theta) = (600 light-years)*2.424 x 10^(-7) = 0.00014544 light-years = 1.275 light-hours = (3600 seconds)*(3 x 10^8 m/s)*(1.275) = 1.38 x 10^12 meters.