JBaxidn
Answered

IDNLearn.com connects you with experts who provide accurate and reliable answers. Join our knowledgeable community to find the answers you need for any topic or issue.

how do you find the actual diameter of a star going from arcseconds to kilometers?

ex The supergiant star Betelgeuse (in the constellation Orion) has a measured angular diameter of 0.044 arcsecond. Its distance has been measured to be 427 light-years. What is the actual diameter of Betelgeuse?


Sagot :

What you have is a skinny, skinny sector of a circle ... like a slice of pie.
The radius of the pie is 427 light-years, and the angle in the center, at
the tip of the slice, is 0.044 second.  That's about  0.000012 degree. 

The question is:  What's the length of the crust out at the fat end of the slice ?

This is a case where it's very handy to measure your angles in radians
instead of degrees. That way, whatever fraction of a radian is at the tip,
the same fraction of the radius is the length of the arc (the crust).

To change degrees to radians, multiply by  (pi)/180 .

0.044 second = 0.000012 degree = about  2.133 x 10^-7 radian .

So the diameter of the star is about  (2.133 x 10^-7) of 427 light years.

I'll leave that part for you to finish up.