The polar circumference of Earth is 40,000km. What distance corresponds to a change of one degree of latitude? A change of one one arcminute of latitude? Hint, an arcminute is 1/60th of a degree.
hint: 1 degree is 1/360 of the circumference.
To find the distance corresponding to a change of one degree of latitude, we need to know the fraction of the polar circumference that one degree represents.
Given that the polar circumference of Earth is 40,000 km, we can calculate the distance of one degree of latitude using the following steps:
1. Determine the fraction of the polar circumference represented by one degree of latitude.
Fraction = 1 degree / 360 degrees = 1/360
2. Calculate the distance corresponding to this fraction of the polar circumference.
Distance = Fraction x Polar Circumference
= (1/360) x 40,000 km
= 111.111 km (rounded to the nearest three decimal places)
Therefore, a change of one degree of latitude corresponds to a distance of approximately 111.111 km.
To calculate the distance corresponding to one arcminute of latitude, which is 1/60th of a degree, we follow a similar process:
1. Determine the fraction of the polar circumference represented by one arcminute of latitude.
Fraction = 1 arcminute / 360 degrees = 1/60
2. Calculate the distance corresponding to this fraction of the polar circumference.
Distance = Fraction x Polar Circumference
= (1/60) x 40,000 km
= 666.667 meters (rounded to the nearest three decimal places)
Therefore, a change of one arcminute of latitude corresponds to a distance of approximately 666.667 meters.