Q.When the planet Jupiter is at a distance of 824.7 million kilometer from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of the Jupiter.

The parallax method is the standard technique for measuring distances that are too large to reach with a metre scale — distances of planets, stars, and other astronomical objects — and, run in reverse, for measuring the sizes of such objects once their distance is already known.

Parallax itself is the apparent shift in an object's position that occurs purely because the observer's own position has changed — you can see this yourself by looking at your own hand alternately with your left eye and then your right eye closed; the hand appears to shift against the background, even though it hasn't moved at all. For astronomical distances, this idea is scaled up: instead of two eyes, two widely separated observation points (on the Earth's surface, or — for even more distant stars — two points on opposite sides of the Earth's orbit around the Sun, a baseline of 2 astronomical units) are used to sight the same object simultaneously. If $b$ is the known baseline between the two observation points and $\theta$ is the measured parallax angle (the angle between the two lines of sight, as seen from the object), then the object's distance is $D = b/\theta$ (with $\theta$ in radians) — because for a very distant object, $b \ll D$, and the angle is small enough that the arc and the straight baseline are essentially the same length. …