air_cowboy
13th Jul 2007, 15:44
which of the following differences in latitude will give the biggest difference in the initial great circle track and the mean great circle trackbetween 2 points separated by 10 degrees change of longitude?
a) 60N and 60S
b) 60N and 55N
c) 30S and 30N
d) 30S and 25S
and y???
thanks.....
Alex Whittingham
13th Jul 2007, 16:00
The standard formula for convergency is change of longitude x sine mean latitude so, if the change of longitude is the same, the pair with the greatest mean latitude between each end and half way, which is where the question is effectively asking about, will give the greatest track change.
Answer (a) has a halfway point at the equator. The mean latitude between 60ºN and the equator is 30ºN.
Answer (b) has a halfway point at 57º30'N. The mean latitude between 60ºN and 57º30'N of is 58º45'N.
Answer (c) has a halfway point at the equator. The mean latitude between 30ºN and the Equator is 15ºN
Answer (d) has a halfway point at 27º30'S. The Mean latitude between 30ºS and 27º30'S is 28º45'S.
I'd choose (b). There is another argument that defines 'mean track' as the initial track direction and the final track direction added together and divided by two. That affects the logic of the answers with end points in different hemispheres but doesn't, I think, affect the choice of answer. Foxy question, where is it from?