How can the small angle formula be used to measure the physical size of a star?

[Fisicks]

Basically this formula relates the angular size of an object (how big the object appears to an observer), the actual physical size d of the object, and the distance D from the observer to the object.

So let's say i want to find the physical size of Betelgeuse. As a scientist figuring this out, how would you find theta, or angular size of a star 600 light years away, and what is the angular size actually measuring?

 

[belliott4488]

I'm not sure what you're asking. It's simple enough to draw a right triangle with one leg as the line from the observer to the center of the star, and the other leg as a radius of the star, taken perpendicular to the first line. The angle at the observer's end is half the angular size (since we're looking at the radius and not the diameter), which you get get using the inverse tangent.

If you know the distance to the star and its angular size, which you measure optically, the you can get the radius of the star by using the tangent of the half-angle.

The angles in such cases are very small of course ...

 

[Fisicks]

thank you for clearing that up for me

 

[Integral]

Unfortunatly stars are too far away. Even in the best telescope they are points with no angular size. There are a few stars which are close enough to measure their paralax as the Earth moves in its orbit.