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Find the distance between Helsinki and Seattle.....

  1. Apr 11, 2016 #1
    1. The problem statement, all variables and given/known data
    This is an astronomy problem. I know how to find cos(AOB) but I am not sure what to do after this.
    Find the distance between Helsinki and Seattle along the shortest route. Where is the northernmost point of the route, and what is its distance from the North Pole? The longitude of Helsinki is 25degrees East and latitude 60degrees; the longitude of Seattle is 122degrees West and latitude 48degrees. Assume that the radius of the Earth is 6370 km.
    The answers are supposed to be: 7,640 km(approximate distance), northernmost point = 79degrees North, 45degree West, in North Greenland 1,250 km from the North Pole.

    2. Relevant equations
    cos(AOB) = cos(latA)cos(latB)cos(lonB-lonA)+sin(latA)sin(latB)

    3. The attempt at a solution
    cos(AOB) = cos(60)cos(48)cos(122-25)+sin(60)sin(48) = (0.5)*(0.66913060635)*(-0.1218693434)+(0.86602540378)*(0.74314482547) = 0.6028090437
    I know to get the great circle distance between A and B I need
    R, the radius of the earth which is 6370 km. Is the distance between A and B: R*AOB?
    The scalar product is: R2cosAOB
     
    Last edited: Apr 11, 2016
  2. jcsd
  3. Apr 11, 2016 #2

    gneill

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    A web search should turn up a suitable reference on great-circle routes. For example, this page.
     
  4. Apr 11, 2016 #3
    That still doesn't really help me. The astronomy book that I have does a poor job at explaining the steps. I'm trying to study on my own
     
  5. Apr 11, 2016 #4

    gneill

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    I'm not sure what you're missing. That page shows how to calculate the great-circle distance (and even has an example similar to your problem), and shows how to find the northernmost point along the route.
     
  6. Apr 12, 2016 #5

    SteamKing

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    This is a problem in terrestrial navigation. I'm not sure why you are using an astronomy book for an explanation.
     
  7. Apr 12, 2016 #6

    haruspex

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    The same calculations arise: two coordinates specified as latitude and longitude, and wanting to know the angle between them.
     
  8. Apr 12, 2016 #7
    I am reading the page on the link you gave me, I will get back to you when I have figured it out.
     
  9. Apr 12, 2016 #8
    The astronomy book gives me this problem as the first problem in the book.
     
  10. Apr 12, 2016 #9
    I am understanding the problem better than I at first did
     
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