I am given the great circle equations of two paths. The first one is
Longitude = 168 degree.
and the second one is:
tan(Lattitude)=.11 cos(Longitude) + .64 sin(Longitude)
However, I am not sure I understand what these represent.
For example, when I then try to depict these two great circles on a map (For the code below, I use as model the example found here):
library(CircStats)
library(geosphere)
library(maps)
great_circle_1 <- function( lattitude ){
return( 168 )
}
great_circle_2 <- function( longitude ){
return( atan( ( 0.11 * cos(longitude * pi / 180) + 0.64 * sin( longitude * pi / 180 )) ) * 180 / pi)
}
map("world", col="#f2f2f2", fill=TRUE, bg="white", lwd=0.05)
lat_c1_1 <- -50
lon_c1_1 <- great_circle_1( lat_c1_1 )
lat_c1_2 <- 90
lon_c1_2 <- great_circle_1( lat_c1_2 )
inter_c1 <- gcIntermediate(c(lon_c1_1, lat_c1_1), c(lon_c1_2, lat_c1_2), n=50, addStartEnd=TRUE)
lines(inter_c1)
lon_c2_1 <- 150
lat_c2_1 <- great_circle_2(lon_c2_1)
lon_c2_2 <- -50
lat_c2_2 <- great_circle_2(lon_c2_2)
inter_c2 <- gcIntermediate(c(lon_c2_1, lat_c2_1), c(lon_c2_2, lat_c2_2), n=50, addStartEnd=TRUE)
lines(inter_c2)
My problem is that contrary to the examples on the website (and what my intuition would dictate), the two grand circles appear as a flat lines (rather than curved ones). I wanted to make sure that this is not due to a comprehension error on my behalf over how to understand the great circle equation as formulated.
I am assuming spherical earth.
I gather that there are different conventions as to the coordinate systems. Since this is a question about conversions, for information, I use the longitude and latitudes as given on google map, for example the original Waterloo has coordinates (50.7167, 4.3833).