Can the Hubble telescope measure the diameter of Betelgeuse?

[Decimal]

Homework Statement

The star Betelgeuse is 427 lightyears from earth. Betelgeuse has a diameter 800 times that of the sun, where the diameter of the sun equals $1.39*10^6 km$. Given that Betelgeuse has an angular resolution given by the Rayleigh Criterion of 58 nRad, is it possible for the Hubble telescope to measure the diameter of Betelgeuse?

Homework Equations

Equation for angular resolution $$ \Delta\theta = \frac {1.22 \lambda} {D}$$

The Attempt at a Solution

I think I am supposed to check whether the angular diameter of Betelgeuse is not less than the angular resolution of the telescope. However I don't really understand the theory behind this. I thought angular resolution had to do with the ability of the telescope to distinguish two objects with a certain angular separation. In this case there is only one object, so what am I trying to distinguish? What would I see through the telescope if the angular diameter is too small?

Thank you!

 

[DrClaude]

I thought angular resolution had to do with the ability of the telescope to distinguish two objects with a certain angular separation. In this case there is only one object, so what am I trying to distinguish?

You want to measure the diameter, hence distinguish between the left side and the right side of the star.

 

[Decimal]

Okay, I understand. So if you were to look at a star that's too small for the angular resolution of the telescope, would it just be blurry and out of focus? Because you can't distinguish the two sides?

 

[BvU]

would it just be blurry and out of focus

It would be in focus, but indistinguishable from the image from a point source.

 

[Decimal]

It would be in focus, but indistinguishable from the image from a point source.

Ah of course, I see now. Thanks a lot!