$A$ $LASER$ is a source of very intense,monochromatic,and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. $A$ laser light beamed at the Moon takes $2.56 \; s$ to return after reflection at the Moon's surface. How much is the radius of the lunar orbit around the Earth?

If the angular diameter of the Sun is about $30'$ and its distance from the Earth is $1.5 \times 10^{11} \, m$,then the solar diameter is:

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?

The angle subtended by a plate of diameter $2 \, cm$ at a distance of $1000 \, cm$ from the eye is ..... (in $^\circ$)

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01 \, cm^3$ of oleic acid per $cm^3$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4 \, cm^2$ by considering $100$ spherical drops of radius $\left(\frac{3}{40 \pi}\right)^{1/3} \times 10^{-3} \, cm$. Then the thickness of the oleic acid layer will be $x \times 10^{-14} \, m$. Where $x$ is ...... .

Why is the parallax method not used to measure the distance of stars that are $100$ light-years away?