Geodesy methods over time GISC3325 - Lecture 4 Astronomic Latitude/Longitude • Given knowledge of the positions of an astronomic body e.g. Sun or Polaris and our time we can determine our location in terms of astronomic latitude and longitude. US Meridian Triangulation This map shows the first project undertaken by the founding Superintendent of the Survey of the Coast Ferdinand Hassler. Triangulation • Method of indirect measurement. • Angles measured at all nodes. • Scaled provided by one or more precisely measured base lines. • First attributed to Gemma Frisius in the 16th century in the Netherlands. Early surveying instruments Left is a Quadrant for angle measurements, below is how baseline lengths were measured. A non-spherical Earth • Willebrod Snell van Royen (Snellius) did the first triangulation project for the purpose of determining the radius of the earth from measurement of a meridian arc. • Snellius was also credited with the law of refraction and incidence in optics. • He also devised the solution of the resection problem. At point P observations are made to known points A, B and C. We solve for P. Jean Picard’s Meridian Arc • Measured meridian arc through Paris between Malvoisine and Amiens using triangulation network. • First to use a telescope with cross hairs as part of the quadrant. • Value obtained used by Newton to verify his law of gravitation. Ellipsoid Earth Model • On an expedition J.D. Cassini discovered that a one-second pendulum regulated at Paris needed to be shortened to regain a one-second oscillation. • Pendulum measurements are effected by gravity! Newton • Newton used measurements of Picard and Halley and the laws of gravitation to postulate a rotational ellipsoid as the equilibrium figure for a homogeneous, fluid, rotating Earth. • Also determined that gravity acceleration increases from equator to pole. Conflicting Measurements • Various expeditions were undertaken to solve the issue of the shape of the earth. • Is it prolate or oblate? • Measurements of meridian arcs were made. • Newtonian faction Oblate; French faction Prolate Importance of the Issue • From a practical point of view a non- spherical earth has implications for navigation – ultimately it was found that polar flattening would lead to a navigational error of approximately 20 miles in a trans- Atlantic crossing although at the time of the Mission it was believed it could have been as much as 300 miles. from an on-line review of the book by Ian Hopkinson at the following web site: http://www.ianhopkinson.org.uk/tags/maps/ dated 12 May 2012. This post is a review and summary of Larrie D. Ferreiro’s book “Measure of the Earth” Arc measurement campaigns • French Academy of Sciences sponsored two campaigns to measure meridian arcs. • Mission left 1735 with first members returning 1744. • Modern-day Ecuador (average latitude of 1 deg 31 min S) • Lapland (average latitude of 66 deg 20 min N) Meridian arc • The scheme for the determination of the length of a degree is to measure the length of a meridian (a line of longitude) close to the equator by triangulation, making a ground measurement baseline to convert the angular measurements of the triangulation survey into distances and a second baseline to confirm your workings; the latitudes of the ends of the triangulation survey are determined astronomically by measuring the positions of stars. Evolution of Instrumentation Baseline measurement Laser-based EDMI Equipment used in a 1977 survey at the McDonald Observatory near Ft. Davis, TX NGS “Big Red” EDMI used for the survey. Modern Geodesy uses Multiple Techniques Evolution of GPS Receivers 1982 vintage equipment 2010 vintage.