The great circle distance from LAT 25° 50'...

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Question 1 of 2066636eea28f7522a1c51b2e5

The great circle distance from LAT 25° 50' N, LONG 77° 00' W to LAT 35° 56' N, LONG 06° 15' W is 3616 miles, and the initial course is 061.7° T. The position of the vertex is LAT 37° 34.9' N, LONG 25° 59.0' W. Determine the latitude intersecting the great circle track 600 miles west of the vertex, along the great circle track.

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Question 1 of 20

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🔍 Key Concepts

• Great circle and vertex – understand how latitude changes as you move away from the vertex along a great circle, and that the vertex is the point of maximum latitude on the great circle (in this hemisphere/case). • Angular distance and arc length – relate 600 miles to angular distance on the Earth using nautical miles per degree, and think about that distance along a great circle (not along a meridian). • Spherical triangle relationships – especially how to use the vertex latitude and longitude with the great circle course to find nearby points on the same great circle.

💭 Think About

• First, think about whether the latitude at a point west of the vertex should be higher, lower, or equal to the vertex latitude. How does the latitude behave as you move away from a great circle’s vertex? • Convert the 600 miles into an angular distance in degrees of arc. Then think: are you moving 600 miles along the great circle track, or directly north/south on a meridian? How does that affect the latitude change? • Using the idea that the vertex is where the track is momentarily due east–west (course ≈ 090°/270°), consider how the track tilts as you go west of the vertex. Should you expect only a small or a large change in latitude over 600 miles?

✅ Before You Answer

• Confirm that the vertex latitude is the maximum latitude on this great circle between the two given positions; the latitude at any other point along this arc must be less than or equal to the vertex latitude. • Make sure you use 60 NM per degree of great-circle distance when converting 600 miles into degrees of arc along the track, not as a simple change in latitude on a meridian. • Before choosing an answer, compare each option to the vertex latitude 37° 34.9' N and ask: Is the direction of change (up or down in latitude) and the magnitude of change over 600 NM reasonable for a great circle at this latitude?

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