(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An airliner flies from London Heathrow (latitude 51[tex]^{o}[/tex]30' N, longitude 0[tex]^{o}[/tex] 10' W) to Tokyo Narita (latitude 35[tex]^{o}[/tex] 40' N, longitude 139[tex]^{o}[/tex] 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[tex]^{o}[/tex] respectively.

For part c I have found the latitude to be 70.95[tex]^{o}[/tex] 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Astronomy - Latitude and Longitude problem

**Physics Forums | Science Articles, Homework Help, Discussion**