🔍 Key Concepts

• Mercator sailing distance formula using difference of longitude (DLo) and meridional parts (MP) of the latitudes • Converting north/south latitudes correctly to use in D. Lat and meridional parts (remember crossing the equator) • Using the difference of longitude in minutes of arc along the mean latitude vs. Mercator approach with meridional parts

💭 Think About

• First, are the two positions in the same or opposite hemispheres for both latitude and longitude, and what does that imply for signs when you compute D. Lat and DLo? • How do you find the meridional parts for each latitude, and what do you do with the difference in meridional parts in a Mercator sailing problem? • Once you have DLo (in minutes) and the difference in meridional parts, how do you combine them to get the distance, and is the result consistent with the approximate great-circle distance between U.S. East Coast and Cape Town region?

✅ Before You Answer

• Be sure you convert south latitude as negative and north latitude as positive when thinking about differences and meridional parts. • Confirm your difference of longitude from 79°50'W to 18°29'E is taken the shorter way around the globe and converted correctly to minutes. • After computing distance, check whether your answer is in nautical miles and whether the magnitude is reasonable for a passage from the U.S. Southeast coast to South Africa.