all them numbers hurt my head.
Me too. Too many zeroes. If you understand scientific notation, perhaps this will help:
Distance to Polaris = 2.5x1015 miles
Distance traveled by Polaris in one year (assuming 1 million mph) = 8.7x109 miles
Also, atan is also commonly referred to as arctan or tan-1.
Good luck!
While we are on Polaris, it has not always been the Pole star - not even during well recorded history.
History of Polaris.
Polaris hasn’t always been the North Star and won’t remain the North Star forever. For example, a famous star called Thuban, in the constellation Draco the Dragon, was the North Star when the Egyptians built the pyramids.
But our present Polaris is a good North Star because it’s the sky’s 50th brightest star. So it’s noticeable in the sky. It served well as the North Star, for example, when the Europeans first sailed across the Atlantic over five centuries ago.
And Polaris will continue its reign as the North Star for many centuries to come. It will align most closely with the north celestial pole – the point in the sky directly above Earth’s north rotational axis – on March 24, 2100. The computational wizard Jean Meeus figures Polaris will be 27’09” (0.4525°) from the north celestial pole at that time (a little less than the angular diameter of the moon when at its farthest from Earth).
From: http://earthsky.org/brightest-stars/polaris-the-present-day-north-star (http://earthsky.org/brightest-stars/polaris-the-present-day-north-star)
AndPast and future pole stars.
Indeed, Thuban at times made a better pole star than our modern Polaris. Various sources claim that Thuban almost exactly pinpointed the position of the north celestial pole in the year 2787 B.C.
Meanwhile, our modern Polaris – which many centuries ago was an ordinary star known by the name Phoenice – won’t match Thuban’s precision when it most closely aligns with the north celestial pole on March 24, 2100. Polaris will be 27’09” (0.4525°) from the north celestial pole at that time (a little less than the angular diameter of the moon when at its farthest from Earth), according to the computational wizard Jean Meeus.
The Northern Hemisphere also has had long stretches without a pole star. After the reign of Thuban but before that of Polaris, Kochab in the Little Dipper served as a rather poor pole star in 1100 BC. Kochab was only half again as close to the north celestial pole as it is today.
From Thuban past North Star (http://earthsky.org/brightest-stars/thuban-past-north-star)