Maps portrayed by which projection are used for navigation by trans-polar routes and for radio and seismic work due to great-circle directions?

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Multiple Choice

Maps portrayed by which projection are used for navigation by trans-polar routes and for radio and seismic work due to great-circle directions?

Explanation:
Great-circle navigation relies on the shortest path between two points on the globe. A gnomonic map makes that path a straight line because every great circle projects to a straight line on a gnomonic projection. This property is especially useful for trans-polar routes, where the shortest paths often pass near or over the poles; centering the projection in the polar region makes those routes appear as simple straight lines that can be drawn directly to plan a course. The same idea helps in radio and seismic work, where the relevant paths or ray directions follow great-circle routes on the sphere, so representing them as straight lines on the map simplifies plotting and analysis. Other projections don’t map all great circles to straight lines, so they’re less convenient for plotting shortest paths: Mercator distorts the great-circle routes into curves; Polyconic and Lambert projections don’t preserve this straight-line relationship for great circles as consistently. This is why the gnomonic projection is the best fit.

Great-circle navigation relies on the shortest path between two points on the globe. A gnomonic map makes that path a straight line because every great circle projects to a straight line on a gnomonic projection. This property is especially useful for trans-polar routes, where the shortest paths often pass near or over the poles; centering the projection in the polar region makes those routes appear as simple straight lines that can be drawn directly to plan a course. The same idea helps in radio and seismic work, where the relevant paths or ray directions follow great-circle routes on the sphere, so representing them as straight lines on the map simplifies plotting and analysis. Other projections don’t map all great circles to straight lines, so they’re less convenient for plotting shortest paths: Mercator distorts the great-circle routes into curves; Polyconic and Lambert projections don’t preserve this straight-line relationship for great circles as consistently. This is why the gnomonic projection is the best fit.

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