The angle of $1^{\prime}$ (minute of arc) in radian is nearly equal to

Explain accuracy and precision in measurement.

The nearest star to our solar system is $4.29$ light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

During a total solar eclipse,the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.

$A$ $LASER$ 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?

$(a)$ How many astronomical units $(AU)$ make $1$ parsec?
$(b)$ Consider a sun-like star at a distance of $2$ parsecs. When it is seen through a telescope with $100$ magnification,what should be the angular size of the star? The Sun appears to be $(\frac{1}{2})^{\circ}$ from the Earth. Due to atmospheric fluctuations,the eye cannot resolve objects smaller than $1$ arc minute.
$(c)$ Mars has approximately half of the Earth's diameter. When it is closest to the Earth,it is at about $\frac{1}{2} AU$ from the Earth. Calculate what size it will appear when seen through the same telescope.