Questions tagged [geodesy]

The measurement and representation of the Earth, its shape and gravitational field, distances on the Earth, and coordinate systems for locating points on it including longitude and latitude.

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11 views

How to calculate distance of a point from a rhumb line (crosstrack deviation)

Is there any known closed-form or non-iterative way to calculate or approximate the distance of a point from a rhumb line? (i.e. how to find crosstrack deviation from a rhumb line)
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Given two points with 3D coordinates, and three angle observations, how to caculate the coordinate of the third point

Given two points, $M_1(X_1,Y_1,Z_1)$ and $M_2(X_2,Y_2,Z_2)$,$P(X_p, Y_p,Z_p)$ is the unknown point. How to get the coordinates of $P$ by three angle observation . The picture below displays the ...
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30 views

Definition of constant-curvature curve embedded on an Ellipsoid of revolution

I am interested in identifying a type of curve so I can do literature review on it. What is the name of a curve embedded on an ellipsoid of revolution in which the curvature of the embedded curve is ...
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2answers
139 views

Normal vector to ellisoid surface

How do I obtain a normal vector to the surface of an ellisoid, at a given latitude and longitude. Getting the same normal vector for a sphere is trivial.
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how to discretize the geodetic of the paraboloid with euler forward?

I have Paraboloid hiperbolic, parametrizade by (u,v,uv) Operating with the geodesic equation, i have obtained enter image description here But I do not know how to place the obtained in euler ...
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212 views

Understanding differences in Geodetic (WGS84) to ECEF equations?

Methods suggested in this, that and there all recommend the following: $$x = R \cos(\theta) \cos(\phi)$$ $$y = R \cos(\theta) \sin(\phi)$$ $$z = R \sin(\theta),$$ where latitude is $\theta$, ...
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86 views

Cartesian Coordinates to Geo Position [closed]

Having $(lat, lon)$ I used the following formulae to convert it to Cartesian \begin{align} x & = R \cos(lat) \cos(lon)\\ y &= R \cos(lat) \sin(lon) \end{align} Now, I need to convert x,y ...
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260 views

Great-circle distance using haversine formula [closed]

I've been trying to calculate the distance between two locations following the haversine formula. I believe the formula is: $\Delta_\mathrm{lon}=\mathrm{lon}_1-\mathrm{lon}_2$ $\Delta_\mathrm{lat}=\...
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1answer
61 views

Howto calculate the latitude of a given y coordinate from a mercator projected map

Say I have a mercator projection map: I would like to calculation the latitude for different points with one formula. I have already resaerched several sites and wikipedia, where the hole math is ...
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332 views

Distance between two cities on Earth

Barcelona (Spain) has the coordinates (approx): $\theta = 2^\circ$, $\phi = 41^\circ$, and New York has the coordinates: $\theta = −74^\circ$, $\phi = 41^\circ$. Notice that both cities lie on the ...
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247 views

Finding a point along the surface of a ellipsoid

I have read the answers for both of these questions -Finding a point along a line a certain distance from another point and Find a point along line on Earth and I am trying to convert the ...
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Someone please help me out with a simple geometry question about the size and volume of the earth?

I was on Yahoo! Answers and I asked: "Flat-earthers: If the earth was really flat or cubical or rectangularly prismatic, how could the moon rotate around it?", and I was told, "The diameter of the ...
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1answer
31 views

How do I calculate the partials of ECEF coordinates with respect to Geodetic coordinates?

This question could possibly be posted in a different forum but I think the crux of the issue is an incorrect mathematical derivation. This Wikipedia website provides equations for converting from ...
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1answer
71 views

Find Latitude x miles north of starting latitude using ellipsoid earth model

Let us say I am given a starting (latitude, longitude)=(lat,lon) coordinate in degrees. The objective is to compute the new latitude, ...
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Getting points given center and radius (working with latitude and longitude)

I'm trying to solve a problem and I'm sure it is quite easy but I'm not a mathematician at all: Here it goes: I'm trying to draw the coverage area of a satellite, which is supposed to be circular. ...
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226 views

Mercator projection - Use existing equation to solve for degrees

Mercator projection: problem with latitude formula The answer to the previous question explains how to determine the correct pixel position at a given degree on a Mercator map. For example plug in a ...
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51 views

Surface integrals in ECEF coordinates?

I was doing some general thinking about mathematics and calculus, and I was wondering if it is possible to find the surface area of any place on Earth using integration in the Earth-Centered, Earth-...
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1answer
190 views

Convert a vector in Lambert Conformal Conical Projection to Cartesian

I have wind vectors with 2 components $(u, v)$ that are in the Lambert Conformal Conical Projection. I want to compare the vectors with observations of the wind $(u_{obs}, v_{obs})$ that are created ...
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67 views

Determining Earth's circumference using shadows

The problem is: Assuming the Sun is far away from Earth and that light rays are arriving parallel to each other, determine Earth’s circumference, assuming that it is spherical. Does anyone know how ...
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2 Questions on Geodesic Curves and the Earth's Surface.

Maths PhD student Tom and his younger brother James decide to spend their holidays in Japan. They take the British Airways direct flight London-Tokyo. a) What type of curve should the airplane fly in ...
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63 views

Obtain arc points in latitude longitude system

I have an arc of circumference defined by three points, center, start point, and end point; and I want to obtain several points of the arc. With the parametric equations proposed here it seems not ...
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1answer
79 views

Proof that two objects on earth form a tangent line with the earth

So I have this problem where there is a building on earth at point $a$ and a robot with a camera on its head starts walking away from the building and I have to calculate what distance from $a$ does ...
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1answer
167 views

Finding max. and min. daylight duration at a given latitude.

Here's my question: Compute the maximum & minimum daylight duration at the latitude of Phila. PA. (39.9500◦N) in hours and minutes. Approximating to the nearest minute. What would be the best ...
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2answers
687 views

Distance between points on Earth

So the problem is this: Assuming the surface of the Earth is a sphere of circumference 40, 000 kilometers, estimate the distance between Philadelphia and Paris. I'm uncertain how to do this problem....
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1answer
208 views

Question about definition of geodesic curve on a surface

A curve $\sigma$ is defined to be an equivalence class of parametric curve under the equivalence relation of change of parameter. For regular curves there is a canonical element of the equivalence ...
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1answer
326 views

Length of loxodrome (rhumb line) between two points on sphere

I have a sphere with two points on its surface: $A=[x_1, y_1, z_1]$ and $B=[x_2, y_2, z_2]$. I want to find a loxodrome (rhumb line, spherical spiral) with a shortest length that connects these two ...
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1answer
163 views

What is the metric of the grs 80 ellipsoid?

So, similarly to how a $2$-sphere has the metric, and if I understand this correctly: $$ g_{ij} = \begin{bmatrix} R^2 & 0 \\ 0 & R^2\sin^2\theta \end{bmatrix} $$ I was wondering, in geodesy, ...
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200 views

About the geodesic coordinates, and their conversion into cartesian ones

This is more a sort of "let me know if I'm right" question, rather than a real question, but I thought that if is there a place where I can find true and solid trustful answers then it's here. ...
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1answer
201 views

When is a loxodromic curve unique between two points?

Consider 2 arbitrary points, A and B, which are located on Earth's surface. We assume the Earth to be a perfect sphere for the purposes of my question. Each point is given by their latitude and ...
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1answer
133 views

Oblate Spheroidal Coordinates, Confocal Ellipsoidal Coordinates and Geodesy

What is the name of the orthogonal coordinate system that is most commonly used in modern geodesy\geomatics engineering to model the reference ellipsoid? I suspect it is either oblate spheroidal ...
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111 views

Relation between differential geometry and differential geodesy

I am not exactly clear on what are the differences between differential geometry and differential geodesy. Are principles in differential geometry used in differential geodesy ? It appears that ...
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385 views

Wind vector transformation from Gaussian grid to displaced pole grid

I have been given the "u" and "v" component with respect to an earth coordinate reference system(Gaussian grid - https://en.wikipedia.org/wiki/Gaussian_grid http://www.nco.ncep.noaa.gov/pmb/docs/on388/...
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203 views

Determining North-South Line Via Watch Method: Theory & Reason

I recently read that if you're in the northern hemisphere and have an analog watch, then you can point the hour hand at the sun and know that a south line lies between (bisection) the hour hand and ...
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140 views

Latitude Drift using Vincenty Direct Formula

I am impostor here, and am by no means mathematically literate, so please bare with me. I have posted a software question on StackOverflow, regarding an unexpected drift in latitude using Vincenty's ...
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82 views

Translation matrix in spherical coordinates system

I'm using WorldWind software to draw segments (polyline) on the globe to materialize an aircraft flightplan. Each point in a flightplan is named waypoint. Waypoints are expressed in geographical ...
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1answer
106 views

Radius of the Earth at N32.704220, W90.000000?

I want to express a point on a map in radian spherical coordinates. By Google maps, this location is north of Canton, MS, USA just a few hundred feet from US 51. In radian spherical coordinates, $(?,-...
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How much extra sea water is needed?

We might call this the “Noah's Ark” calculation, but in the movie Waterworld (1995) they have the icecaps melting and take poetic license making the ~$220$ feet or so of sea water (one estimate I've ...
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1answer
238 views

Find Latitude of point given Longitude and Great Circle orientation

Given the orientation of a great circle as the cartesian components of the normal vector $(a,b,c)$ to its plane, i.e. all points on the circle described in Earth-Centered Earth-Fixed (ECEF) ...
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Cartesian to geodetic conversion of 3D bounding box - How to calculate latitude and longitude from an axis aligned bounding box

I have a geometry with its vertices in cartesian coordinates. These cartesian coordinates are the ECEF(Earth centred earth fixed) coordinates. This geometry is actually present on an ellipsoidal model ...
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328 views

Calculate a point on a geodesic line on an ellipsoid

I have a problem which i don't understand how to achieve. Maybe someone could sheed some light on it. Have a look at this picture: What I try to achieve is to determine the point D on the geodesic ...
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1answer
309 views

Algorithm for Stepping Through Latitude, Longitude and Height with a Heading

I have a function which reads in latitude, longitude, height, heading and step size. My function should calculate the latitude, longitude and height of the position one step size away in the direction ...
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459 views

Seasonal changes in hours of daylight

I will post my own answer to this question unless someone else posts the same answer first, but I am curious to know what other points of view might lead to different ways of answering it. ...
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Different ways for calculating distance between two geodetic points give me different results

I'm trying to calculate the distance between two geodetic points in two different ways. The points are: A:(41.466138, 15.547839) B:(41.467216, 15.547025) The ...
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2answers
221 views

Circle-circle intersection on a spheroid

Does anybody have formulae to solve the following issue. If you have two circles, defined by their two centres, and a radius for each circle. Where (if the circles intersect) are the two points ...
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822 views

Drawing a Great Circle between two given points on Earth

I need to draw a great circle arc between two latitude and longitude points. For sake of example we will use the coordinates for LAX and JFK. JFK is 40.64°N / 73.78°W LAX is 33.94°N / 118.41°W My ...
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Maximum latitude of a great circle

1 - I am trying to figure out the longitude at which a geodetic great circle reaches its apex. (I have a point and the azimuth at that point identifying the circle) I have found a good resource that ...
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1answer
620 views

Distances are different by ~100-200m

I'm measuring distance of 2 points on Google Map and then in my program converting them into ECEF using this formula. Then using Pythagorean theorem to calculate distance between those 2 points. ...
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1answer
127 views

What property does this equation calculate?

It's pretty difficult to Google for the meaning of a formula. This is the equation, it has to do with ellipses and GIS coordinates. $$\nu =\frac{ a} {\sqrt{(1 - (e^2 \cdot \sin(\varphi))^2)}}$$ $a$ ...
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1answer
2k views

Convert LLA (long, lat, alt) to flat earth model

I would like to divide the globe into 1000 $\times$ 1000 meter geodesic squares, and then map any long / lat to the applicable square. The altitude of each block would be the altitude of the earth at ...
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What is the geodesic between a point and a line (geodesic between two points) on an oblate spheroid?

I found a similiar question that also asks for the distance from a point to a line but works on a sphere. Now I'm trying to figure out the length of the geodesic line ...