The diameter of the supergiant star betelgeuse is [tex]1.38 x 10^{12} meters[/tex]
Betelgeuse is the brightest star in Orion. It marks the western shoulder of the constellation. Betelgeuse is one of the largest known stars and is at least the size of the orbits of Mars or Jupiter around the sun. That's a diameter is about 700 times the size of the Sun, or 600 million miles.
The angular diameter distance is a distance measure used in astronomy.
Estimate the diameter of the supergiant star betelgeuse, using its angular diameter of about 0.05 arcsecond and distance of about 600 light-years:
[tex]0.05 arcsecond = \frac{1 degree}{72000}[/tex]
A minute of arc (arcminute) is a unit of angular measurement equal to of one degree. A second of arc or arcsecond (arcsec) is 1/60 of an arcminute,
[tex]0.05 arcsecond = \frac{\pi radians}{180*72000}[/tex]
[tex]0.05 arcsecond = 2.424 * 10^{-7} radians[/tex]
The distance is roughly
[tex]R*(\theta) = (600 lightyears)*2.424 * 10^{-7}[/tex]
[tex]R*(\theta) = 0.00014544 lightyears[/tex]
[tex]R*(\theta) = 1.275 lighthours [/tex]
[tex]R*(\theta) = (3600 seconds)*(3 *10^{8} m/s)*(1.275) [/tex]
[tex]R*(\theta) = 1.38 x 10^{12} meters) [/tex]
Grade: 9
Subject: mathematics
Chapter: angular diameter
Keywords:
the supergiant star betelgeuse, angular diameter, arcsecond, distance, astronomers
