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## Homework Statement

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.

## Homework Equations

cos(AOB) = cos(latA)cos(latB)cos(lonB-lonA)+sin(latA)sin(latB)

## 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: R

^{2}cosAOB

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