Light bends 1° for every 69 miles you travel. A more precise measure is approximately 69.17 miles or 111.32 kilometers.
This means the actual position of an object is different from where it appears. You can test this by observing Polaris and using right angle triangles.
For instance, if you are at 30° North Latitude, then Polaris will appear 30° above the horizon.
To calculate the distance from the North Pole (90° North) to 30° North latitude:
Distance in Kilometers = (90° – 30°) × 111.32 km/degree = 60° × 111.32 km/degree = approximately 6,679.2 km
Distance in Miles = (90° – 30°) × 69.17 mi/degree = 60° × 69.17 mi/degree = approximately 4,150.2 mi
If you intend to travel 69 miles south, you should continue until Polaris appears at 29° from your horizon.
Using the Southern Cross (Crux) and the Pointer Stars to find the South Celestial Pole (SCP):
Identify the Southern Cross constellation, notable for its four main stars arranged in a cross shape.
Extend an imaginary line through the long axis of the Southern Cross. This line will roughly point towards the SCP.
Observe Alpha Centauri and Beta Centauri, known as the “Pointer Stars.” Draw a line perpendicular to the line between these two stars. The intersection of this line with your extended line from the Southern Cross marks the location of the SCP.
Imagine someone is on an island at 10° North latitude and wants to travel 200 miles north.
Since light bends approximately 1° for every 69 miles, traveling 200 miles north will change their latitude by about 2.9° (200 miles ÷ 69 miles/degree).
New latitude = 10° + 2.9° = 12.9° North latitude.
Once the journey is made, Polaris should appear approximately 12.9° above the horizon when viewed from the new latitude of 12.9° North.
Solving Celestial Navigation Problems
Let’s assume you’re on an island somewhere in the ocean. You look in the sky, cannot see Polaris, but can locate the SCP and see that it is 10° from your horizon.
1) How many miles would you need to travel to be directly under Polaris?
2) How many miles would you need to travel to see Polaris? As right now it’s not even visible.
