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Homework Help: Astronomy - Latitude and Longitude problem

  1. Oct 22, 2007 #1
    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!
     
  2. jcsd
  3. Oct 22, 2007 #2
    One thing I forgot, on my diagram the distance d is the longitude of P plus the longitude of H.
    I assumed I would go about the second part of the problem by finding d and subtracting the longitude of H as that is essentially what I did for the first part in finding the latitude of P.
     
  4. Oct 24, 2007 #3
    Never mind, solved it now!
     
  5. Oct 26, 2007 #4

    jim mcnamara

    User Avatar

    Staff: Mentor

    Consider posting your solution so that others can search the forums and find what you did.
     
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