$A$ far-off planet is estimated to be at a distance $D$ from the Earth. If its diametrically opposite extremes subtend an angle $\theta$ at an observatory situated on the Earth,the approximate diameter of the planet is .............

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

What is parallax? Explain the parallax method to measure the distance between the Earth and a planet.

It is claimed that two cesium clocks,if allowed to run for $100$ years,free from any disturbance,may differ by only about $0.02\; s$. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of $1\; s$?

The mean distance of the sun from the earth is $1.5 \times 10^8 \text{ km}$ (nearly). The time taken by the light to reach the earth from the sun is.....$\text{min}$

$(a)$ 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.