# 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 ...
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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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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: $$... • 329 0 votes 0 answers 54 views ### 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 (&... 0 votes 0 answers 25 views ### 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 ... • 101 0 votes 0 answers 28 views ### 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 ... 0 votes 0 answers 23 views ### 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 ... 0 votes 1 answer 200 views ### 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 ... • 11 1 vote 0 answers 117 views ### 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 ... • 111 0 votes 1 answer 76 views ### 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}) ... • 303 0 votes 1 answer 724 views ### 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 ... • 133 2 votes 2 answers 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 ... • 40.3k 0 votes 1 answer 171 views ### 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 ... • 145 0 votes 0 answers 49 views ### 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 ... 0 votes 1 answer 701 views ### 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 ... • 105 1 vote 0 answers 60 views ### 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 ... • 397 3 votes 1 answer 458 views ### 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}$$where \psi ... 0 votes 0 answers 29 views ### Make WGS84 box to fit a circle of radius R Let's assume I have a WGS84 box given by its north-east and south-west latitude and longitude. I want to make sure that a circle of radius R fits inside that box, i.e. if the box is too small, it ... • 103 1 vote 0 answers 33 views ### If p \in H^m and v \in T_p H^m, then the geodesic \gamma: R \rightarrow H^m is given by \gamma(t) = \cosh(t)p + \sinh(t) v Let p \in H^{m} and  v ∈ T_{p}H^{m}  be given with Q(v,v) = 1. Then the geodesic γ : R → H^{m} with γ(0) = p  and ˙γ^{'}(0) = v is given by$$γ(t) = \cosh(t)p + \sinh(t)v$$with the ... • 121 0 votes 1 answer 495 views ### North-bearing between two points in Cartesian space I have two points P and Q given in earth-centered-earth-fixed Cartesian space (XYZ) How can I compute the compass-bearing of P towards Q without going into Geodetic space (Lat, Lon)? • 103 0 votes 1 answer 648 views ### From straight distance to arc length Assume that I transformed geodetic coordinates (lat/lon) to Cartesian (x/y/z) with respect to a spherical earth model with radius R. Now, I compute the distance between two points P1 and P2 as D. ... • 103 3 votes 3 answers 376 views ### Given two points with 3D coordinates, and three angle observations, how to caculate the coordinate of the third point Given two points, M_1(X_1,Y_1,Z_1) and M_2(X_2,Y_2,Z_2),P(X_p, Y_p,Z_p) is the unknown point. How to get the coordinates of P by three angle observation . The picture below displays the ... 0 votes 0 answers 152 views ### Definition of constant-curvature curve embedded on an Ellipsoid of revolution I am interested in identifying a type of curve so I can do literature review on it. What is the name of a curve embedded on an ellipsoid of revolution in which the curvature of the embedded curve is ... • 215 0 votes 2 answers 2k views ### Normal vector to ellisoid surface How do I obtain a normal vector to the surface of an ellisoid, at a given latitude and longitude. Getting the same normal vector for a sphere is trivial. • 155 2 votes 1 answer 430 views ### Shortest path to a geodesic This question has already been asked here, but has not been answered fully. I really want to know the answer, so I ask again. If we have two points A and B on the surface of a sphere, a geodesic ... • 63 3 votes 2 answers 3k views ### Understanding differences in Geodetic (WGS84) to ECEF equations? Methods suggested in this, that and there all recommend the following:$$x = R \cos(\theta) \cos(\phi)y = R \cos(\theta) \sin(\phi)z = R \sin(\theta), where latitude is $\theta$, ...
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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 ...