Great Deal! Get Instant \$25 FREE in Account on First Order + 10% Cashback on Every Order Order Now

# 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...

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)

## Solution

Kshitij answered on Nov 27 2021
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