Lets try two low tech approaches first.
Go to an open field or a place where there is direct sunshine from 10 a.m. till 2 p.m. and can be accessed at night. Daytime Place a yardstick in the ground and mark the end of the shadow every 10 minutes with a red flags. Using a string, form a curve through the points. Using an appropriate measuring device, make the point closest to the yardstick . Using a string connect the base of the yardstick to the point makes from above.