Calculating a Distance on the Surface of the Earth

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. wrote:

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

Victor Fraenckel wrote:



I would be interested. Can you just post it somewhere?



--
Bruce E. Stemplewski
GarXface OCX and C++ Class Library for the Garmin GPS
www.stempsoft.com

I'm no scientist nor that good at math, but the original poster seemed
to ask a question which didn't quite fit with the drawing he put up on a
website or the first answer I read.

He proposed a 200km line tangential to the earth's surface at the
starting point. He then proposed dropping a line "straight down" to the
earth from that point, and measuring the distance between the starting
point and the ending point on the earth's surface.

The line he dropped to the earth's surface was shown by angle and symbol
as a right angle to the original tangential line. Straight down to the
earth's surface to me would be a radial line, one from the end of the
200km line toward the center of the earth.

I suppose the line dropped at a right angle was intended. I'm curious to
know the reasoning behind the question.

--
Bob Ball
If you want to think positive thoughts, surround yourself with positive people.
If you want to email me, eliminate the negative.

There's a third possibility too: the "vertical" dropped line is
perpendicular to the earth's surface (or to the surface of a pool of
liquid) at the point it reaches the surface. This is the usual
definition of a "vertical" line to a surveyor.

If the earth was spherical, or is assumed to be a sphere, then a
vertical line perpendicular to the surface also goes through the centre
of the earth. But with an ellipsoidal earth, a vertical line misses the
centre, and a radial line isn't perpendicular to the surface (except at
the poles and on the equator).

        Dave