calculate lat/lon point

Question

If I have the coordinates of a point (lat lon) and the azimuth angle how can I calculate what points are at "the end' of a distance of 10 miles.

Ex. I am watching North , I know I am at a certain point ... At 10 miles apart what coordinates has that geo point ?

Answer 1

This site has a pretty good collection of formulae. For your case,

Let lon1,lat1 be the starting point, θ the azimuth angle (also often referred to as the "bearing") in radians, d the distance traveled (km), and R the earth's radius (approx 6371 km). Then you can find the final coordinates lon2, lat2 :

lat2 = asin(sin(lat1)*cos(d/R) + cos(lat1)*sin(d/R)*cos(θ))

lon2 = lon1 + atan2(sin(θ)*sin(d/R)*cos(lat1), cos(d/R)−sin(lat1)*sin(lat2))

Note: d/R represents an angle in radians corresponding to the arc length d.

θ is measured such that North=0 degrees, East=90 degrees, and so forth.

Answer 2

That doesn't make much sense. Let's take the first formula

lat2 = asin(sin(lat1)cos(d/R) + cos(lat1)sin(d/R)*cos(θ))

sin(lat1)cos(d/R) -> as sin and cos will never be larger than 1, the largest result can be 1 cos(lat1)sin(d/R)*cos(θ) -> same as above.. the biggest possible result is 1

=> the result is that lat2 according to that formula can be 2 at most.

Answer 3

You need to also have a bearing to calculate this distance as well. For very short distances, great circle distance (the distance along the path of the earth) will be very close to cartesian distance, but the site provided by Jim Lewis' answer is a nice interactive site. This site also has a very extensive set of lat/lon formulas http://williams.best.vwh.net/avform.htm.

Answer 4

calculated and the result doesn't make much sense .. lat is something like 0.566 althought the first lat is 60