1A Estimate the diameter of the supergiant star Betelgeuse u

1A: 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.

Solution

In astronomy, the angular diameter is given by the following formula:

=206265d/D

- Angular Diameter
d - diameter of the object
D - distance between the observer and the object

206265 is simply the number of arcsecs in a radian.

So before we chuck in the values we have to rearrange the equation in a way that we isolate d, which is what we want, so let\'s do just so:

=206265d/D

D=206265d (I moved D to the other side here)

to the other side here).

D=206265dD206265=d, by moving 206265 to the left hand side, we get d isolated. So now we chuck in the values:

Now to turn our d into km, we need to know how many km\'s there is in a light year. A light year is equal to 9.46071012 km.

9.460710129.11015=861744026,37367578 which is 861744026,4 km

The diameter of the Sun is 1 392 000 km. If you meant to compare the two, then the diameter of Betelgeuse is 619 times the diameter of the sun!

861744026,41392000619
0.044428206265=dd=9,1105 light years, because we were using light year