# Minimimum separation of to resolve 2 stars

1. Nov 13, 2005

### siifuthun

A telescope has an objective mirror of 6m. An astronomer uses it to
determine if a certain object is a binary star, i.e. two stars in orbit
around a common point. If the object is 25 light years away (a light
year is the distance light travels in one year) what is the minimum
separation of the two stars if they can just be resolved?

The only notes I have about resolution were taken in class about satellite cameras. In that case, would:

d_min = h(lambda)/(a)

still apply? d_min is minimum separation between the 2 objects, h would be the distance from the stars to the telescope, but what value would lambda be? The wavelength of light? And would 'a' be the area of the mirror? Does the fact that it's an objective mirror change anything? Or would this apply only to a lens?

2. Nov 14, 2005

### SpaceTiger

Staff Emeritus
The resolution of a diffraction-limited telescope is

$$\theta=\frac{1.22\lambda}{D}$$

where $\lambda$ is the wavelength of light and D is the diameter of the telescope. In addition, the angular separation of two objects at a distance, d is

$$\Delta \theta=\frac{r}{d}$$

where r is their physical separation.

Using these two formulae, you should be able to solve the problem. For the wavelength, I would just take it to be in the center of the optical portion of the electromagnetic spectrum, since this is where the typical star emits most of its light.