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Astronomy - Latitude and Longitude problem

by Pomico
Tags: astronomy, latitude, longitude
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Pomico
#1
Oct22-07, 03:39 PM
P: 25
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!
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Pomico
#2
Oct22-07, 03:41 PM
P: 25
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.
Pomico
#3
Oct24-07, 11:56 AM
P: 25
Never mind, solved it now!

jim mcnamara
#4
Oct26-07, 12:06 PM
Sci Advisor
PF Gold
P: 1,381
Astronomy - Latitude and Longitude problem

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