Write the ratio of the maximum and minimum time observed in the universe.

$A$ huge circular arc of length $4.4 \; ly$ subtends an angle of $4''$ (arcseconds) at the centre of the circle. How long would it take for a body to complete $4$ revolutions if its speed is $8 \; AU/s$?
Given: $1 \; ly = 9.46 \times 10^{15} \; m$,$1 \; AU = 1.5 \times 10^{11} \; m$.

Explain the concepts of accuracy and precision in measurement with an example.

$(a)$ 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.

$(a)$ The earth-moon distance is about $60$ earth radii. What will be the angular diameter of the earth (approximately in degrees) as seen from the moon?
$(b)$ The moon is seen to have an angular diameter of $(1/2)^{\circ}$ from the earth. What is its relative size compared to the earth?
$(c)$ From parallax measurement,the sun is found to be at a distance of about $400$ times the earth-moon distance. Estimate the ratio of sun-earth diameters.

Define astronomical unit,light year,and parsec.