Q.How diameter of the sun is calculated using parallax method ?

Relative Motion Parallax: Seeing Depth Through Motion

Close one eye and hold your thumb up at arm's length. Now move your head from side to side. Notice how your thumb appears to jump back and forth against the distant wall, while the wall itself barely seems to move. That's relative motion parallax in action — and you've been using it your whole life without realising.

The Intuition: Why Things "Slide" Past Each Other

Imagine you're sitting in a moving train, looking out the window. The trees near the track whip past in a blur. The mountains far away barely seem to shift. The moon? It appears to follow you.

This isn't an illusion — it's geometry. When you move, objects at different distances sweep across your field of view at different angular speeds. The closer an object is, the faster its image moves across your retina (or camera sensor). The farther it is, the slower it moves.

The Precise Statement

Relative motion parallax is the apparent shift in the relative position of two objects when the observer changes their viewpoint. The amount of shift is inversely proportional to the distance of the objects from the observer.

Mathematically, for an object at distance $d$ from an observer moving sideways by a distance $b$ (the baseline), the angular displacement $\theta$ (in radians) is approximately:

This is for small angles. The key insight: if you have two objects at distances $d_1$ and $d_2$, the difference in their angular shifts tells you which is closer and by how much.

The sign of this difference tells you direction: the nearer object appears to move opposite to your motion relative to the farther one.

Why It Matters for Exams

You'll encounter relative motion parallax in three contexts:

1. Astronomy: Measuring distances to nearby stars. Earth's orbit provides the baseline $b$ (2 AU). A star's apparent shift against distant background stars gives its distance via $d = b / \theta$ (with $\theta$ in radians).

2. Robotics and computer vision: A moving camera can reconstruct depth by tracking how image features shift between frames. …