The distance of the Sun from Earth is $1.5 \times 10^{11} \,m$ and its angular diameter is $2000 \,s$ when observed from the Earth. The diameter of the Sun will be ...........

The difference between the length of a mean solar day and a sidereal day is approximately .......... minutes.

Calculate the angle of $(a)$ $1^{\circ}$ (degree),$(b)$ $1^{\prime}$ (minute of arc),and $(c)$ $1^{\prime \prime}$ (second of arc) in radians. Use $360^{\circ} = 2\pi \text{ rad}$,$1^{\circ} = 60^{\prime}$,and $1^{\prime} = 60^{\prime \prime}$.

What is called a basis? What is parallax? Define angular diameter.

Calculate the solid angle subtended by the periphery of an area of $1 \, cm^2$ at a point situated symmetrically at a distance of $5 \, cm$ from the area. (in $, sr$)

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?