Question

2. Another application of angular measurement in astronomy is measuring apparent angular size of celestial objects. Complete the follow ing parts a - f of this question. a. Hold a large coin, such as a quarter or half dollar, at arms length and position your self so that it just covers an object in your field of view. Now move the coin toward your eye, does the apparent angular size of the coin increase or decrease? b. Standing in the same position as in part a hold a smaller coin at arms length. Adjust . the coins distance from your eye until it

Answer 1

Suppose D is the diameter of coin. Suppose initially its distance from the eye is d_1 middot then apparent angular size of coin (see fig(1)) alpha almostequalto D/d_1 now we moved the coin towards our eye. Let it is at a distance d_2 from eye then apparent angular size of coin is beta almostequalto D/d^2 therefore beta/alpha = D/d_2 /D/d_1 = D/d_2 times d_1/D = d_1/d_2 because d_1 > d_2 = > beta/alpha > 1 = > beta > alpha therefore apparent angular size of coin increases. In the above figure apparent angular size are same for both the coins. It is clear that smaller coin are more close to the eye \r\n take a protector and measure the angle alpha and beta that will give the angular size of circle at x and y positions. The two reasons are celestial body is actually near to us size of celestial body is large sun's diameter is nearly 400 times larger than moon while distance is also