Calculating Distance with Latitude and Vectors

[courtrigrad]

If you are given latitudes and longitudes of two cities and you want to find the magnitude of the displacement vector, how would you find the distance? Would you have to use the scalar product?

Thanks

 

[BobG]

The most straight forward way is vector subtraction.

The magnitude of both vectors is the radius of the Earth. The latitude and longitude give you the other two polar coordinates needed to define each location's position vector. Convert the polar coordinates to rectangular coordinates (ijk coordinates) by projecting the magnitude onto the x, y, and z axis, and do the vector subtraction.

 

[courtrigrad]

So if the question is: A man flies from Washington to Manilla. Find the magnitude of the displacement vector if the latitudes and longitudes are: 36 N, 70 E, 121 N, 56 W. You would have to convert the latitudes and longitudes into x-y coordinates? How would you do that?

Thanks

 

[OlderDan]

So if the question is: A man flies from Washington to Manilla. Find the magnitude of the displacement vector if the latitudes and longitudes are: 36 N, 70 E, 121 N, 56 W. You would have to convert the latitudes and longitudes into x-y coordinates? How would you do that?

Thanks

It's not just x-y coordinates; it's x-y-z coordinates that you need. The cities are on the surface of the earth, so they are one Earth's radius from its center. Lattitude and longitude give you the rest of the information you need to express the postions of the cities in terms of x-y-z

http://astronomy.swin.edu.au/~pbourke/projection/coords/

Then use the distance formula in cartesian coordinates to find the magnitude of the displacement.