The moon is observed from two diametrically opposite points $A$ and $B$ on Earth. The angle $\theta$ subtended at the moon by the two directions of observation is $1^{\circ} 54^{\prime}$. Given the diameter of the Earth to be about $1.276 \times 10^{7} \; m$,compute the distance of the moon from the Earth.

How is time regulated in a wristwatch and a cesium clock?

The distance of the Sun from the Earth is $1.496 \times 10^{11} \ m$ and the diameter of the Sun is $1.393 \times 10^9 \ m$. Find the angular diameter of the Sun in radians.

$A$ celestial object is observed from two points $A$ and $B$ on the Earth,which are diametrically opposite. The angle between the two observation directions is $2.9 \times 10^{-4} \text{ rad}$. Taking the diameter of the Earth to be $1.28 \times 10^4 \text{ km}$,find the distance between the Earth and the object.

Which of the following time measuring devices is most precise?
$(A)$ $A$ wall clock
$(B)$ $A$ stop watch
$(C)$ $A$ digital watch
$(D)$ An atomic clock
Give reason for your answer.

The principle of 'parallax' is used in the determination of distances of very distant stars. The baseline $AB$ is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is,the baseline is about the diameter of the Earth's orbit $\approx 3 \times 10^{11} \; m$. However,even the nearest stars are so distant that with such a long baseline,they show parallax only of the order of $1''$ (second of arc) or so. $A$ parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of $1''$ (second of arc) from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres?