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

## 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: R2cosAOB

Last edited:

gneill
Mentor
A web search should turn up a suitable reference on great-circle routes. For example, this page.

• science_rules
A web search should turn up a suitable reference on great-circle routes. For example, this page.
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

gneill
Mentor
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
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.

• science_rules
SteamKing
Staff Emeritus
Homework Helper
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
This is a problem in terrestrial navigation. I'm not sure why you are using an astronomy book for an explanation.

haruspex
Homework Helper
Gold Member
2020 Award
This is a problem in terrestrial navigation. I'm not sure why you are using an astronomy book for an explanation.
The same calculations arise: two coordinates specified as latitude and longitude, and wanting to know the angle between them.

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.
I am reading the page on the link you gave me, I will get back to you when I have figured it out.

This is a problem in terrestrial navigation. I'm not sure why you are using an astronomy book for an explanation.
The astronomy book gives me this problem as the first problem in the book.

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.
I am understanding the problem better than I at first did