Re: Calculating a Distance on the Surface of the Earth

On Jan 27, 6:47 pm, Victor Fraenckel <vict...@xxxxxxxxxxxxxx> wrote:
O.B. wrote:
I've managed to summarize the problem I'm trying to solve in the PDF
below. Basically, I have a point on the earth's surface at a given
latitude and longitude. If I moved 200km away from this point to the
East, I'd actually be above the surface of the earth due to the
curvature of the earth. If at the point, I were to drop straight down
to the surface of the earth, I'd like to know the distance between
this new point on the earth and the original point. I'd like to
repeat this calculation with heading 200km to the North. Help?

http://www.dafunks.com/misc/EllipseProblem.pdf

O.B.

I am not sure I understand what you want to calculate. I can provide you
with a PDF of a paper by T. Vincenty in which he published algorithms
that will allow you to:

1.
Given: The latitude/longitude of a point on the earth's surface and the
distance and direction to a second point, compute the latitude and
longitude of the second point.

2.
Given: The latitude and longitude of two points on the earth's surface,
compute the distance between the points and the azimuths of each point
from the other.

If this is helpful I would be glad to send you the paper.

Vic

I'm definitely interested in the paper, but I'm not sure how it will
help me.

Basically, I am trying to plot a couple of 2D circles on the earth,
each given a center point in latitude and longitude degrees and a
radius in meters (200 km in the example). Think of the circle as a
rigid flat 2D surface that is laid on top of the earth at sea-level
centered at the given latitude and longitude. Since the earth is not
flat, the circumference of the circle does not touch the earth. By
dropping the edge of the circle straight down (as noted in the PDF),
the circle then becomes an ellipse since the earth is an ellipsoid.

At this point, one can visually see that the distance between the
center of the circle and the new edge (on the earth surface) is
greater than 200km. My question is how to calculate exactly what this
new distance is? That is, the distance between the center and the far
east edge as well as the distance between the center the far north
edge.

I'm using Gnuplot to make the 2D plot. I need to know the distance
between the center point and the far east point (range1) as well as
the distance between the center point and the far north point (range2)
in degrees to perform the plot. So assuming x and y are the center
points in latitude and longitude degrees, I'd issue the following
commands to plot the ellipse:

set parametric
set trange[0:2*pi]
plot x + range1 * cos(t), y + range2 * sin(t) title 'RoI_1'

All I really need to know is the algorithm to calculate the two
distances in meters; I already have algorithms in place to covert the
distances to degrees.
.

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