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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How is the distance between a point and a polygon boundary computed in a spherical or ellipsoidal coordinate system?

I had previously asked this question on https://gis.stackexchange.com/, but it seems like they don't usually handle "pure math" questions, and it was poorly received, so I closed it. PostGIS ...
shadowtalker's user avatar
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How do I calculate new point after traveling a distance along great circle?

I'm brand new to geo processing/mapping, and I'm struggling with spherical trig, trying to understand what's going on without even knowing the terminology of what I'm looking for. After a lot of ...
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Help understand real and projected distance difference in UTM coordinates

I am learning about UTM coordinate system and reading in Wikipedia: In any zone a point that has an easting of 400000 meters is about 100 km west of the central meridian. For most such points, the ...
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Obtain the shortest distance between two points on a sphere

Let person A be at latitude : 40N and longitude 0.4W Let person B be a the latitude: 40N and longitude 74E Find the shortest distance between them. We use Haversine formula: $$a = \sin^2(\Delta\phi/...
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Why is sine-squared used in the haversine formula?

The traditional "haversine" formula for great-circle distance is traditionally expressed as $$ 2R \arcsin\left(\sqrt{ \sin\left(\frac{\Delta\varphi}{2}\right)^2 + \cos\left(\varphi_1\...
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Derivation of solution for the first geodetic problem on a sphere

Some version of the following formula is often quoted for use in solving the "first geodetic problem" (aka "direct" or "forward" geodetic problem) on a spherical Earth: $$...
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calculate angle between two points in horizontal plane

In the following figure, I have a point A at a know altitude AB from the Earth surface. For simplicity, we can assume spherical Earth. The perpendicular projection of point A to Earth surface is B (&...
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How to find the distance between two sets of given latitude and longitude in Km or Mile? [duplicate]

I was trying to find the solution in (x1,y1) and (x2,y2) format. The theory goes like this: Assume I have these data: lat1=56.986969769 , long1=-97.98689698 lat2=54.98789789, long2=-96.987890878 ...
Sohan Arafat's user avatar
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Solution for the Gravitational acceleration for the equation with L'hospital Rule

Let $b(r) = -G \iiint \frac {r-r_0}{||r-r_0||^3} dm$ be the gravitational acceleration, where $r_0$ is the center of mass of a rigid body. Show that $\lim_{r\to\infty} b(r) = 0$. What is the ...
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Vincenty's Formula Symbols

I have been researching about Vincenty's formula for my new programme but through many books I didn't find any explanation about the upper case A, upper case B and u square . Does someone knows what ...
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How to calculate the middlle coordinate/point on earth between two coordinates? [closed]

Good Afternoon. I need help for a component of my math IA. I need to calculate the middle point between two coordinates on earth to make calculations based on this. I (stupidly) attempted to use the ...
Fguteper's user avatar
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Reverse loxodrome length formula to calculate latitude with given distance between two points on a meridian (longitude is constant to zero)

I'm using a tool I've found online (https://planetcalc.com/713/), which allows calculating the distance between two points on loxodrome using a formula that considers the WGS 84 ellipsoid model. In ...
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Finding a geolocation that is approximately $d$ distance from a given geolocation

I have a geolocation represented using latitude and longitude: $({\phi_1,\lambda_1})$ and a given distance in meters $d$. I want to find an equation for all the geolocations $({\phi_2,\lambda_2})$ ...
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Methods of Calculating Great Circle Distances

I wish to calculate the shortest distance between two points on the Earth. What are the methods of doing this? So far, the ones I know are: Haversine formula, which assumes a spherical Earth - great ...
SoySoy4444's user avatar
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177 views

Path difference on a sphere due to geodesic deviation

Between two points of same latitude but different longitudes [spherical coordinates $(\theta,\phi)$] we measure two lengths of arcs $(s_1,s_2)$ along (1) the geodesic or red great circle (a graphic ...
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Projection of a Great Circle on another

Consider a great circle between $[lat_1, lon_1]$ and $[ lat_2, lon_2]$, on a perfectly spherical earth. Consider a second one : between $[lat_1, lon_1 +b]$ and $[ lat_2, lon_2+b]$. For a very small ...
Sean's user avatar
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Coding a coordinate system rotation

I am trying to calculate the azimuth, elevation and range of a point above the Earth's surface. A handy wikipedia picture to clarify the azer coordinates The latter two are simple, but I am having ...
DrLeprikon's user avatar
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How to get coordinates from second point given the coordinates from first point, distance between them and angle

I have a Point P1 with the coordinates P(405747|5725660) in KBS EPSG:25832. Now I want to get the coordinates of a second Point P2. P2 is exactly 10m away from P1 and 30° from North. Sorry for the ...
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Can an ideal ellipsoid of rotation be espressed exactly with a spherical harmonic series of a finite number of terms?

The ellipsoid of rotation has rotational symmetry, therefore the coefficient of every tesseral and every sectorial base function is zero. The ellipsoid has equatorial symmetry, therefore coefficients ...
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Prove that the loxodrome crosses all meridians at a constant angle

How to prove that the loxodrome (the rhumb line) crosses all meridians at a constant angle? $$\tan\left(\frac{\pi}{4} + \frac{\psi}{2}\right) = e^{k\phi}, \quad k = \text{constant}$$ where $\psi$ ...
Oleh Berehovskyi's user avatar
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Make WGS84 box to fit a circle of radius R

Let's assume I have a WGS84 box given by its north-east and south-west latitude and longitude. I want to make sure that a circle of radius R fits inside that box, i.e. if the box is too small, it ...
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If $p \in H^m$ and $v \in T_p H^m$, then the geodesic $\gamma: R \rightarrow H^m$ is given by $\gamma(t) = \cosh(t)p + \sinh(t) v$

Let $p \in H^{m}$ and $ v ∈ T_{p}H^{m} $ be given with $Q(v,v) = 1$. Then the geodesic $γ : R → H^{m}$ with $γ(0) = p $ and $˙γ^{'}(0) = v$ is given by $$γ(t) = \cosh(t)p + \sinh(t)v$$ with the ...
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North-bearing between two points in Cartesian space

I have two points $P$ and $Q$ given in earth-centered-earth-fixed Cartesian space $(XYZ)$ How can I compute the compass-bearing of $P$ towards $Q$ without going into Geodetic space (Lat, Lon)?
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From straight distance to arc length

Assume that I transformed geodetic coordinates (lat/lon) to Cartesian (x/y/z) with respect to a spherical earth model with radius R. Now, I compute the distance between two points P1 and P2 as D. ...
user3612643's user avatar
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3 answers
376 views

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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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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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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Shortest path to a geodesic

This question has already been asked here, but has not been answered fully. I really want to know the answer, so I ask again. If we have two points A and B on the surface of a sphere, a geodesic ...
Mikako's user avatar
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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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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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1 answer
1k 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}=\...
Jonnah Paris's user avatar
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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 ...
mcfly soft's user avatar
6 votes
4 answers
1k 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 ...
mathinthecity's user avatar
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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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2 answers
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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 ...
Jason Shalom Goldman's user avatar
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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 ...
MrMas's user avatar
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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, ...
Dnaiel's user avatar
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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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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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Function calculating the curvature of earth

I am interested in calculating a box, based on a center point and its ∆ values. The box is an excerpt of the earth' surface. Note that I am not working with a projection of the earth (2D), but with ...
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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-...
ProgrammingEnthusiast's user avatar
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473 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 ...
David's user avatar
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1 vote
2 answers
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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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1 vote
2 answers
289 views

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 ...
user432533's user avatar
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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 ...
Daniel Viaño's user avatar
1 vote
1 answer
196 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 ...
user avatar
2 votes
1 answer
532 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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3 votes
2 answers
3k 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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4 votes
1 answer
793 views

Point to great-circle segment distance (WGS84)

Disclaimer: This is a cross-post from stackoverflow -- the community recommended to post it here again I want to calculate the distance from a point given by latitude and longitude to a line-segment ...
user2033412's user avatar
1 vote
1 answer
452 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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