1. The problem statement, all variables and given/known data a. Suppose you do not know your location (on Earth) or the direction of north. Now suppose you track one particular star in the sky. You measure its exact position in the sky and record the exact time of the measurement. How many such measurements are necessary to deduce the length of the sidereal day? Your answer should not involve any formulas or calculations. It should just be a positive integer representing the number of measurements needed together with a brief explanation. b. Suppose you were also able to locate the North Star. Would that allow you to deduce the length of the day with fewer measurements? Note: For part b, instead of knowing the location of the North Star, it is also enough to either know your latitude or know which direction is north. 3. The attempt at a solution Okay... Part a. I am not sure how to do, but I think I know part b. PART A: I am not sure. My guess was: With 3 equidistant points you could trace a smooth arc length in the sky. I could then use the ratio between this arc length and the time taken and the ratio between the circumference of the star's path and the length of the sidereal day to calculate the length of the sidereal day. The only problem is, I don't know if I can calculate the circumference of the star's path given only an arc length. Intuitively I feel there should be a way, but I have searched long and hard and have not come up with one. Point me in the right direction? PART B: The distance between the star being tracked and the north star would be the radius of the star's path. Another position would allow me to calculate the angle between the vectors from the north star to each of the two positions. The ratio between this angle and the arc length would equal the ration between the total circumference and the length of the sidereal day. Thanks in advance.