Question

A star’s distance (d) and its parallax angle (p) are related to each other as:
$
  {\text{A}}{\text{. d = }}\dfrac{1}{p} \\
  {\text{B}}{\text{. d = }}\dfrac{1}{{{p^2}}} \\
  {\text{C}}{\text{. p = }}\dfrac{1}{{{d^2}}} \\
  {\text{D}}{\text{. none of these}} \\
 $

Answer 1

Hint: The farther a star the lesser change is observed in its background. Now think of the relation.

Complete answer:
Parallax is the technique used to measure great distances. It is a great astronomical distance measuring technique used since ages. While looking at something from two different vantage points the object appears to shift positions compared to the far off background. The angular shift is called the parallax and it is one angle of a triangle and the distance between the two vantage points is one side of the triangle.
It works like the star is noticed from one place on the earth and then it is looked from a very far situated place on earth itself. The background of the star changes definitely and it is this change which gives the measure of the proximity of the star to our planet.

The farther the star is the lesser the parallax shift, and the closer the star is the more is the change in parallax observed.
There is inverse proportionality between the proximity of the star and its parallax angle.
So,$d = \dfrac{1}{p}$.

So, the correct answer is “Option A”.

Note:
Parallax method gives an approximate idea and is good in case of comparison purposes but is not absolute.