Question

Anybody know the proper answer to this in AU??

Answer 1

It depends if that angle is in degrees or radians; let's assume radians because then there's a trick.

If we draw the line from the star to the sun, we have a right triangle, angle .000302/2, opposite 1 AU and hypotenuse x the distance we seek.

`\sin (.000302)/(2) = (1)/(x)`

The trick is for really small angles the sine is (approximately) equal to the angle in radians:

`x = 2/.000302 = 6622.52 \textrm{ AU}`

Let's see if our approximation made a difference in the last digit:

`x = 1/\sin(.000302/2) = 6622.52\textrm{ AU}`

Nope, no difference to six sig figs.

Answer: 6623