Geodesy Questions

Relevant questions from GEM1030 2019
QUESTION 1
Observations made with a T2 theodolite to the Sun and a Reference Object (RO) from a point in
Trinidad are provided in Table Q1. Use information provided in Table Q1 together with extracts
from the Star Almanac for Land Surveyors attached to this examination paper to calculate the
azimuth of the RO.
[25 marks]
Date: 13th February 2019
Temperature: 27º C
Pressure: 1013 hPa
Latitude: 10º 38’ 24” North
Face
L
L
R
R
RO
North
Horizontal
Vertical
circle
Circle
RO
000º 00’ 00”
Sun
115º 47’ 23”
57º 51’ 25”
Sun
296º 22’ 18”
303º 20’ 13”
RO
180º 00’ 13”
Table Q1. Solar observation data.
Object
Sun
Local
Time
08:47:28
08:52:51
QUESTION 3
Figure Q3 shows gravity anomalies and deflection of the vertical across Trinidad from the
EGM2008 model: Absolute gravity was observed in Port of Spain at the location shown as a ‘*’
in Figure Q3 with data provided in Table Q3.
a)
In terms of the geology of Trinidad, explain the variation in gravity anomalies shown in
Figure Q3.
[10 marks]
b)
Use the data in Table Q3 to compute the free air anomaly and the Bouguer anomaly at the
Port of Spain station. Compare results with the gravity anomaly interpreted from Figure Q3.
[9 marks]
c)
Explain why deflection of the vertical shown in Figure Q3 is plotted as vectors.
[6 marks]
Station Designation Port of Spain
Latitude (WGS84) 10° 39’ 8.172 Longitude (WGS84) 61° 31’ 0.480 West
Adopted Gravity Value g = 978169234.45 μgals
Elevation 7.0 Metres above MSL
Table Q3. Absolute gravity observed in Port of Spain, Trinidad.
Figure Q3. Gravity anomalies and deflection of the vertical across Trinidad from EGM2008.
QUESTION 4
The Technical Manual for the Geocentric Datum of Australia offers the following trial data in
relation to computations on the surface of a spheroid.
Flinders Peak
37° 57’ 03.72030″ South 144° 25’ 29.52440″ East
Buninyong
37° 39’ 10.15610″ South 143° 55’ 35.38390″ East
Ellipsoidal Distance
54,972.271 m
Forward Azimuth
306° 52’ 05.37″
Reverse Azimuth
127° 10’ 25.07″
Computed for a spheroid with:
Semi-major axis 6378137.0 m
Inverse flattening 298.257222101
a)
Use appropriate formulae from sheet attached to this examination paper to calculate the
distance between points at Flinders Peak and Buninyong together with the forward and reverse
azimuths. Compare results with those provided in the Technical Manual for the Geocentric
Datum of Australia.
[19 marks]
b)
Identify by name the method recommended for spheroidal computations in Technical Manual
for the Geocentric Datum of Australia, state why this is the preferred method and why trial
data is provided in the manual.
[6 marks]
QUESTION 5
A satellite is in circular orbit at 20,000 km above the Earth. The orbital plane of the satellite is
inclined at 60 degrees to the equator, the longitude of the ascending node is 80 degrees west and
it passes the equator heading northeast at 1000 GMT. Take constants for the Earth as GM =
3986005×108 m3s-2, radius = 6400 km and rate of rotation = 7292115×10-11 rads-1.
a)
Use spherical trigonometry to find the latitude and longitude of the satellite at 1200 GMT.
[10 marks]
b)
Find the geocentric coordinates of the satellite at 1200 GMT.
c)
Determine whether the satellite can be seen above the horizon at 1200 GMT from a point in
Trinidad with:
[5 marks]
Latitude 10.5º North and Longitude 61.3º West, equivalent geocentric coordinates are:
X= 3021965.508, Y= -5519732.929 and Z= 1166307.363.
[10 marks]
Relevant questions from GEM1030 2018
QUESTION 1
An aircraft makes a journey from Trinidad to London travelling at an average altitude of 9000 m
and speed of 300 ms-1. Given locations for the points of departure and arrival as:
Trinidad: φ = 10º 35’ 43” North λ= 61º 20’ 17” West
London: φ = 51º 08’ 52” North λ= 00º 11’ 20” West
Take the radius of the Earth as 6371 km and use spherical trigonometry to calculate:
a)
The flight time to the nearest minute.
[6 marks]
b)
The azimuth of travel at the starting point in Trinidad.
[5 marks]
c)
The location of the aircraft when it has travelled half of the distance of its passage. [14 marks]
QUESTION 3
A survey mark near San Fernando on the south west coast of Trinidad is tied using geodetic quality
GPS observations to give geocentric coordinates relative to WGS84 as follows, with each
component having an accepted accuracy of 3 mm:
X = 2997613.776
Y = – 5514238.672
Z = 1130967.145
The EGM2008 geoidal model gives a separation at the WGS84 location for the mark of -43.285
m.
Mean sea level observed for 30 days at a tide gauge that is tied to the survey mark by two way
levelling with a misclosure of 2 mm gives a height for the mark of 11.522 m.
a)
Calculate the ellipsoidal height of the survey mark in WGS84 with a = 6378137 m and e2 =
0.006694380.
[8 marks]
b)
Use the separation provided by the geoidal model to find the orthometric height of the survey
mark and compare this with the height determined from the tide gauge data.
[4 marks]
c)
Discuss the difference in height values obtained for the survey mark using corrected GPS and
tide gauge data. The discussion should consider sources of error that exist in both methods for
height determination and reference surfaces used.
[13 marks]
QUESTION 4
Two points in Trinidad are observed with GPS to give geocentric coordinates at two points in time
as given in Tables Q4a and Q4b.
Geocentric coordinates
Point name
X (metres)
Y (metres)
Z (metres)
ALBN
2989768.707
-5509832.405
1172450.783
FRTN
2978246.299
-5527208.473
1118828.808
Table 4a. Geocentric coordinates for two locations in 2007.
Geocentric coordinates
Point name
X (metres)
Y (metres)
Z (metres)
ALBN
2989768.783
-5509832.316
1172450.897
FRTN
2978246.267
-5527208.433
1118828.906
Table Q4b. Geocentric coordinates for two locations in 2015.
Equivalent geodetic coordinates for ALBN in 2007 are:
Latitude: 10º 39’ 48.58” North
Longitude: 61º 30’ 52.81” West
Spheroidal height: 19.101 m
Using a topocentric reference frame with the origin at point ALBN in 2007, find the East and
North displacement of point FRTN relative to ALBN between 2007 and 2015.
[25 marks]
Relevant questions from GEM1030 2017
QUESTION 1
a)
The Star Almanac for Land Surveyors tabulates values for declination of the Sun and for the
equation of time. Describe the apparent motion of the Sun relative to the Earth on an annual
basis and hence explain these terms.
[10 marks]
b)
Using information from the Star Almanac for Land Surveyors provided in Tables Q1a and
Q1b at the end of this paper, find the true latitude and longitude on the Sun at the scheduled
start time of this examination. Note that the convention adopted in the Star Almanac is that
GHA for the Sun = UT+E.
[15 marks]
Relevant questions from GEM1030 2016
QUESTION 1
On 29th January 2016 a surveyor in Trinidad at a latitude of 10° 38′ 19.1″ observed zenith angles
to the Sun using two faces as given in Table Q1 together with a temperature of 32°C and pressure
of 1013 hPa.
Instrument
Zenith angle
Local Time
Face
(° ‘ “)
(hh:mm:ss)
Left
71° 01′ 43″
16:42:30
Right
288° 28′ 21″
16:44:44
Table Q1. Observed zenith angles and times.
Use this data to compute a single azimuth for the Sun stating the time to which this value relates.
Appropriate corrections should be applied. Tabulated data necessary to determine corrections and
other required information is provided in Tables Q1a to Q1e attached to this paper. [25 marks]
QUESTION 4
a)
Location of two points, A and B, are given in Table Q4. Compute the distance between A and
B on the surface of the WGS84 spheroid with semi-major axis 6378137 m and eccentricity
squared of 0.00669438.
Point
Latitude
Longitude
A
12° 30′ 19″ North
60° 50′ 07″ West
B
14° 06′ 13″ North
59° 57’ 09” West
Table Q4. Location of Points A and B in WGS84.
.
[12 marks]
b) Kivioja’s algorithm offers a direct solution to the principal problem of geodesy by application
of geodesic formulae, principles of which are shown in Figure Q4.
Figure Q4. Principles of geodesic formulae
Clairauts formula, given by:  cos  sin  = constant is also employed. Write the geodesic
formulae in a format the is suited to Kivioja’s algorithm and explain how these formula are
implemented within that algorithm.
[13 marks]