Astronomy - Latitude and Longitude problem

by Pomico
Tags: astronomy, latitude, longitude
 P: 25 1. The problem statement, all variables and given/known data An airliner flies from London Heathrow (latitude 51$$^{o}$$30' N, longitude 0$$^{o}$$ 10' W) to Tokyo Narita (latitude 35$$^{o}$$ 40' N, longitude 139$$^{o}$$ 45' E). Assuming that the Earth is spherical and the aeroplane takes a great circle route, a)what is the total distance flown in nautical miles b)in what direction (bearing E of N) does the pilot set out from Heathrow c)what is the most northerly location (latitude and longitude) that the plane reaches on its great circle route? 2. Relevant equations sinA/sina = sinB/sinb = sinC/sinc cosa=cosb.cosc+sinb.sinc.cosA 3. The attempt at a solution I have completed parts a) and b) and have found the answers to be 5161 nautical miles and 31.6$$^{o}$$ respectively. For part c I have found the latitude to be 70.95$$^{o}$$ but can't think how to find the longitude as the spherical triangle I have drawn doesn't have enough information and I don't know how to go about finding what I need in order to get the answer. I have attached a copy of my spherical triangle but it's rather small, my artistic skills are rather limited using a laptop with no mouse... On my diagram point N is the North Pole, point H is Heathrow and point P is the most northerly point. All of the numerical values given are in degrees. I have another diagram including point T for Tokyo but have omitted this as I don't think it's necessary for the task. If it is please say, and I will upload it. Thanks in advance!