The great circle distance from LAT 35° 08.0'...

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Question 1 of 2066636eea28f7522a1c51b2e9

The great circle distance from LAT 35° 08.0' S, LONG 19° 26.0' E to LAT 33° 16.0' S, LONG 115° 36.0' E is 4559 miles and the initial course is 121° T. Determine the latitude of the vertex.

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Question 1 of 20

66636eea28f7522a1c51b2e9

The great circle distance from LAT 35° 08.0' S, LONG 19° 26.0' E to LAT 33° 16.0' S, LONG 115° 36.0' E is 4559 miles and the initial course is 121° T. Determine the latitude of the vertex.

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🔍 Key Concepts

• Great circle vertex occurs where the track crosses the highest (or lowest) latitude on the great circle • Relationship between initial course, starting latitude, and the vertex: use meridian angle / course formulas for great-circle sailing • Use the fact that along a great circle, difference of longitude from the vertex is related to the change in latitude and the initial course

💭 Think About

• How can you use the initial course at the departure point to find the meridional angle (the longitude difference) from the departure to the vertex? • What trigonometric relationship connects the initial course, the departure latitude, and the vertex latitude when the great-circle track is symmetric about the vertex? • Once you have the vertex latitude from your formula, how can you check if it makes sense compared with both endpoint latitudes (should it be farther from the equator or closer)?

✅ Before You Answer

• Write down the correct spherical trigonometry relation for a great-circle track: make sure your formula uses the initial course at departure, not the final course • Confirm that your computed vertex latitude is between the equator and the pole and is more southerly than both endpoints (because this track is in the Southern Hemisphere and bends toward the pole) • After computing, do a quick sense-check: does the vertex latitude, combined with the longitudes of departure and arrival, give a plausible great circle distance close to 4559 NM when cross-checked with standard great-circle formulas?

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Question 1 of 2066636eea28f7522a1c51b2e9

The great circle distance from LAT 35° 08.0' S, LONG 19° 26.0' E to LAT 33° 16.0' S, LONG 115° 36.0' E is 4559 miles and the initial course is 121° T. Determine the latitude of the vertex.

Back

Question 1 of 20

66636eea28f7522a1c51b2e9

The great circle distance from LAT 35° 08.0' S, LONG 19° 26.0' E to LAT 33° 16.0' S, LONG 115° 36.0' E is 4559 miles and the initial course is 121° T. Determine the latitude of the vertex.

No comments yet

Be the first to share your thoughts!

If the question has a related picture, it will appear here.

🔍 Key Concepts

💭 Think About

✅ Before You Answer

👋 Hi! I'm Genie, your AI study assistant. How can I help you with this question?

Quick actions

— No credit card needed