Geodesy A look at the Earth

What is Geodesy? - The Merriam Webster Dictionary defines Geodesy as, "a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field." - so more simply, Geodesy is the study of all aspects concerning the shape, size, and movements of the Earth.

History: - Geodesy dates back to the earliest of civilizations ● Back then, people were concerned more with the immediate lands around them, not the Earth as whole as we see it today ● Later, it expanded to the distances from the home to the markets and other places of exchange ● As transportation evolved, so did the need for more exact measurements of locations. Therefore Geodesy evolved.

History continued: - Earliest conceptions about the world held that is was flat ● First ideas of a spherical Earth didn't come about until 6th century BC - What methods of observation led to the Earth being a sphere? vs.

Dawn of the sphere: - The first reasonings for a spherical Earth relied on astronomical observations (weird that looking into space teaches us about Earth) 1.Earth's shadow on a lunar eclipse is curved 2.Polaris (North star) lowers in the sky as one travels south 3.Pythagoris reasoned that mathematically a sphere is a more perfect shape, therefore the gods would have fashioned Earth as such

As science often does... - The first attempts to "measure" the size of Earth began with pure conjecture 1.Plato guessed the circumference to be between 62,800 km and 74,000 km 2.Archimedes approximated a circumference of 55,500 km - Clearly they weren't entirely accurate...

Increasing accuracy: - First "accurate" measurement of the Earth's circumference was done by the Greek Eratosthenes ● "Measured" angle of the Sun at two points during the summer solstice o One point the sun was directly overhead (showed to the bottom of a well) o Other, the sun's angle of elevation measured to be 1 / 50th of a circle

Eratosthenes cont: - By "knowing" the distance between the two points to be now 1/50th of the total sphere, he calculated the circumference to be ~46,620 km (not bad) - Actual circumference is a little over 40,000 km

Others of note: - Posidonius: calculations of 240,000 stadia and later 180,000 stadia ● stadia is an ancient distance measurement - Aryabhata: Indian mathematician who accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles. This approximation remained the most accurate for over a thousand years.

Others of note: - Biruni ( ): Persian who used many trigonometry equations (mostly triangulation) to solve many complex geodesic equations. Attained a radius value of 6,339.9 km, just shy of today's values. ● Used the same techniques to calculate the heights of mountains and depths of valleys

"Modern" additions: - The first modern update comes from the development of the meridian arc measurement meridian arc ● First uses by Jean Picard in 1700 and later by Jacques Cassini ● Showed that the Earth was not a perfect sphere but more of an oblate ellipsoid of revolution

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So, what next... How do we get a more accurate picture of the Earth? What techniques or technologies would help?

Space! - That's right! To get a more accurate picture of the ground below us, we need to look to the sky above us.

Space Age: - The first satellite for geodesic research was launched in 1962 ● "The U.S. Army developed the SECOR (Sequential Collation of Range) system and the first SECOR transponder was orbited on ANNA-1B in The system operated on the principle that an electromagnetic wave propagated through space undergoes a phase shift proportional to the distance traveled. A ground station transmitted a phase modulated signal which was received by the satellite-borne transponder and returned to the ground. The phase shift experienced by the signal during the round trip from ground to satellite and back to ground was measured electronically at the ground station which provided as its output a digitized representation of range." - o So the information they utilized from the radio waves was based on the phase, or timing of the received signals

Modern Geodesy: - Modern Geodesic techniques all stem from those original space efforts: 1.Global Positioning System (GPS) and Global Navigation Satellite System (GNSS) - same thing but GPS is the american version 2.Very Long Baseline Interferometry (VLBI) 3.Satellite Ranging System (SLR) 4.Satellite Altimetry (measuring ocean height and topography)

1.) GPS and GNSS: - A total of 32 (optimally) satellites are maintained in orbit at any time o 31 operational satellites in orbit as of today (July 2013) o Allows for a minimum signal from 4 satellites

GPS Background Each GPS spacecraft ● Carries highly accurate clock ● Transmits its clock and position ● Signals are transmitted on 2 (or 3) frequencies

GPS Satellite Signal Structure Code modulation: ● Identifies SV ● Spread power ● Range X GPS signal

GPS Background GPS Positioning

What is GPS used to do? ● First there is the obvious: ● Used to determine exact positioning of objects and locations on the surface of Earth ● Besides the obvious: ● Determination of the TEC in the ionosphere ● TEC = Total Electron Content ● Based on differing delays of different frequencies as they pass through the atmosphere ● Important in studying the overall effects of the Sun’s activities on Earth

Ionospheric Parameters GPS can be used to measure Ground-Based Receivers ● Total Electron Content (TEC) ● Scintillation Parameters: S 4 and σ Φ Space-Based Receivers ● Electron Density Profiles (EDP) ● Scintillation Parameters: S 4 and σ Φ S4= sqrt (( - 2 )/ 2 ), where I is the intensity of the signal and <> is the ensemble mean. σ Φ = sqrt(( - 2 ), where Φ is the phase of the signal.

2.) VLBI: - VLBI, Very Long Baseline Interferometry, was developed for improved resolution in radio astronomy o Resolution of radio (and optical) images increases as a function of the aperture size o By using multiple radio antennae over long distances (baselines) effectively increases the size of radio aperture

VLBI basics: The same radio is gathered by different antennae and each signal is matched to a highly accurate atomic clock

VLBI basics: Each data set is then synchronized and correlated together to achieve a much stronger measurement of the radio data gathered Nowadays, as technology has improved, larger and larger amounts of data are able to be utilized as digital recording becomes more and more efficient Tapes are no longer used, everything is digital now

Geodetic VLBI: - It was quickly discovered that VLBI could be used to get clearer picture of Earth as well as space ● By using the very accurate timing data between the antennae sites, many of Earth's motions could be more accurately tracked. ● What motions in particular do you think VLBI could effectively track?

VLBI's geodetic contributions: - Variations in the Earth's orientation and length of day o clearer picture of the Earth's axial precession, nutation, and polar wandering o Earth's spin is actually slowing down and the day being lengthened by ~2 ms every century

- Maintenance of the terrestrial reference frame - Measurement of gravitational forces of the Sun and Moon on the Earth - Regional deformation and uplift or subsistence - And one of its greatest contribution... ● The first direct evidence of plate tectonic movement! VLBI's geodetic contributions:

Plate Tectonics: - Because of VLBI's high resolution, plate motion can be measured very precisely o millimeter accuracy! - By tracking time differences of many quasars using a global system of antennae, the change in baseline distance between the antennae can be tracked and measured directly

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3.) SLR: - SLR stands for Satellite Laser Ranging and does exactly what it sounds like ● SLR stations emit ultrashort pulses of light at satellites that are equipped with special reflectors ● This data gives extremely precise ranging measurements that can be used in a variety of ways o If you want to know more: 

4.) Satellite Altimetry: - Measuring the topography (heights) of the oceans using dual-band altimeters on satellites o Topex/Poseidon, Jason-1 and Jason-2 - Very useful in tracking climate change in both the short term as well as long term - Objectives: - Good flash presentations:

Is this important? Global sea level has risen about 3 millimeters (0.1 inch) a year since Topex/Poseidon (on the left) began its precise measurement of sea surface height in 1993 and was followed by Jason-1 in In this graph, the vertical scale represents globally averaged sea level. Seasonal variations in sea level have been removed to show the underlying trend. Image credit: University of Colorado

Most important detail in geodesy: - Time! For any of these techniques to work, a standard time reference needs to be used across the board o You also need extremely accurate clocks. o Accurate clocks = good correlation of data between multiple observation points - Modern UTC: ons/a/ad/Standard_time_zones_of_the_worl d.png