If we observe a star over 6 months and obtain a parallax angle (p) for the star, how can we calculate the distance to the star?

Write the angle in seconds (1/3600 of a degree). It'll be less than 1 second for any star. Now, take the reciprocal of the number of seconds. (1/seconds). That number is the distance to the star, in "parsecs". 1 parsec = about 3.26 light years. The nearest star, Alpha Centauri, has a parallax of 0.75481 second. The reciprocal of that number is 1.3248 . Multiply that by 3.26156 light years per parsec, and you get 4.32103 light years. The awesome thing about it is how in the world they were able to measure 0.75481 of a second of parallax. That's 0.00020967 of one degree ! And they have to measure it between two times that are six months apart ! ! And that's the nearest star, with the greatest parallax ! ! ! Totally incredible.

The answer is orbit around nucleus