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Microsoft Word - Hwk 8 Elliptical Coordinates (3).rtf SUR 440 Geodesy and GPS Surveying Transformation of Elliptical Coordinates Use the Geodetic Reference System of 1980 (GRS 80). 1. Given the...

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Microsoft Word - Hwk 8 Elliptical Coordinates (3).rtf
SUR 440 Geodesy and GPS
Surveying
Transformation of Elliptical
Coordinates
Use the Geodetic Reference System of 1980 (GRS 80).
1. Given the geodetic coordinates of Station Avenel:
φ = 400 47' XXXXXXXXXX" N
λ = XXXXXXXXXX' XXXXXXXXXX" W
he = XXXXXXXXXXmeters
Compute the geocentric coordinates ( X, Y, Z).
2. Given the geocentric coordinates of Station AP STA
82:

X = -2,104,345.449
meters
Y = -4,352,866.903
meters
Z = 4,148, XXXXXXXXXXmeters
Compute the geodetic coordinates ( φ, λ, he).
3. Compute the mark-to-mark (chord) distance between the two
stations.
4. Compute the geodetic distance ( on the ellipsoid surface)
etween the two points. Use of the geodetic tool kit on the NGS
Website is acceptable.

Alterative CoordT (4).pdf

EllipT Matlab Program
EllipT Matlab Program
%Convert Geocentric Coordinates of a Control Station near Banks,
Alabama to Geodetic Coordinates.
format long
X= XXXXXXXXXX;
Y= XXXXXXXXXX;
Z= XXXXXXXXXX;
a=6378137;
e2= XXXXXXXXXX;
pi= XXXXXXXXXX;

%Find initial Approximation for Latitude
Lat0=atan(Z/sqrt(X^2+Y^2)*(1/(1-e2)))

%Iterate solution for Latitude
N0=a/sqrt(1-e2*sin(Lat0)^2)
Lat1=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N0*sin(Lat0)/Z)))
N1=a/sqrt(1-e2*sin(Lat1)^2)
Lat2=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N1*sin(Lat1)/Z)))
N2=a/sqrt(1-e2*sin(Lat2)^2)
Lat3=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N2*sin(Lat2)/Z)))
N3=a/sqrt(1-e2*sin(Lat3)^2)
Lat4=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N3*sin(Lat3)/Z)))
N4=a/sqrt(1-e2*sin(Lat4)^2)
Lat5=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N4*sin(Lat4)/Z)))

%Update N
N5=a/sqrt(1-e2*sin(Lat5)^2)

%Compute h
h=sqrt(X^2+Y^2)/cos(Lat5)-N5

%Report Lat in Decimal Degrees
Lat5DD=Lat5*180/pi
EllipT
Output_EllipT
Find Initial Approximation for Latitude
Lat0 =

XXXXXXXXXX

Iterate Latitude
N0 =

6.383925708075581e+006


Lat1 =

XXXXXXXXXX


N1 =

6.383925707263495e+006


Lat2 =

XXXXXXXXXX


N2 =

6.383925707259524e+006


Lat3 =
XXXXXXXXXX


N3 =

6.383925707259504e+006


Lat4 =

XXXXXXXXXX


N4 =

6.383925707259504e+006


Lat5 =

XXXXXXXXXX

Use Latitude to Update N

N =

6.383925707259504e+006

Use Iterated Latitude and Updated N to find h
h =

XXXXXXXXXX
Report Latitude in Decimal Degrees
Lat5DD =

XXXXXXXXXX



Geocentric to Geodetic (Closed Form Solution given by Vincenty 1980)
Geocentric to Geodetic (Closed Form Solution given by
Vincenty 1980)
Answered Same DayNov 25, 2021

Solution

Kshitij answered on Nov 27 2021
55 Votes
Question 1: Geocentric coordinates (X, Y, Z)
As per the given data in the question for geodetic coordinates of Station Avenel are as follows:
φ = 40ᶿ 47' 45.52443" N
λ = 115ᶿ 50' 54.61950" W
he = 1537.54 meters
Now for the calculation Geocentric coordinates (X, Y, Z):
Where N is equal to
And the values of e can be calculated by the following element:
Now putting the above given values of φ, λ and he in the above formula will get:
X, m = -2108719.51250085
Y, m = -4352688.04765656
Z, m = 4146301.95361686
Question 2: Geodetic coordinates (φ, λ, he).
As per the given data in the question for geocentric coordinates of Station AP STA 82 are as follows:
X = -2,104,345.449
Y = -4,352,866.903
he = 4,148,293.126 meters
Now for the calculation...
SOLUTION.PDF

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