Lecture 7 gravity and related issues
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Lecture 7 – Gravity and Related Issues. GISC-3325 11 February 2008. Scheduling Issues. Next class and lab will be on OPUS and GPS processing using OPUS. Next week I will be out. Monday or Wednesday (18 and 20 Feb) will be first exam. Chapters 1-4 and all lectures and labs

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Lecture 7 gravity and related issues

Lecture 7 – Gravity and Related Issues

GISC-3325

11 February 2008


Scheduling issues
Scheduling Issues

  • Next class and lab will be on OPUS and GPS processing using OPUS.

  • Next week I will be out. Monday or Wednesday (18 and 20 Feb) will be first exam.

    • Chapters 1-4 and all lectures and labs

  • Lab 3 – BM recovery: due 25 February 2008.


Lecture 7 gravity and related issues

Lab 2: Problem

How do I get this to work?



Which model to use
Which model to use? Difference is 1 mgal.

  • NAVD88 - Modeled Gravity uses a model developed for the NAVD88 adjustment rather than current gravity values.


Lecture 7 gravity and related issues

Review of Height Systems Difference is 1 mgal.

  • Helmert Orthometric

  • NAVD 88

  • local gravity field ( )

  • single datum point

  • follows MSL


Earth s gravity field from space
Earth’s Gravity Field from Space Difference is 1 mgal.

  • Satellite data was used for global models

    • Only useful at wavelengths of 700 km or longer

  • Lower wavelength data from terrestrial or marine gravity of varying vintage, quality and geographic coverage

Terrestrial and marine gravity data in NGS data base.



Gravity
Gravity Difference is 1 mgal.

  • Static gravity field

    • Based on long-term average within Earth system

  • Temporally changing component

    • Motion of water and air

    • Time scale ranges from hours to decades.

  • Mean and time variable gravity field affect the motion of all Earth space vehicles.


G ravity r ecovery a nd c limate e xperiment
G Difference is 1 mgal.ravity Recovery And Climate Experiment

www.csr.utexas.edu/grace/gravity/



Grace 111 days of data
GRACE 111 days of data Difference is 1 mgal.


Grace 363 days of data
GRACE 363 days of data Difference is 1 mgal.


Lecture 7 gravity and related issues

Orbit inclination: 89.048 degrees Difference is 1 mgal.

Eccentricity: 0.000775

Semi-major axis: 6,849,706.754m

Distance between satellites: 222,732.810 m


Grace
GRACE Difference is 1 mgal.


How does grace work
How does GRACE work? Difference is 1 mgal.

  • Motion of two satellites differ because they are at different positions in space.

  • When the lead SV approaches a higher gravity mass it accelerates as it moves beyond it decelerates.

  • Distance changes between SVs is measured precisely.


Lecture 7 gravity and related issues

GRS 80 defined not only by geometric but also physical parameters (gravity).

From www.dgfi.badw.de/geoidis/REFS/grs80.html


Gravitational acceleration
Gravitational Acceleration parameters (gravity).

  • The magnitude of acceleration (b) due to the Earth’s mass on the surface using a spherical geometric reference surface (R) is:

    • b = GM/R2


Centrifugal acceleration
Centrifugal Acceleration parameters (gravity).

  • Direction is always perpendicular outward from the spin axis.

  • It is a function of angular velocity of the Earth squared and the distance from the point of interest on the surface of the sphere to the axis of rotation.

  • ω = 7292115e-11rad sec-1

  • We can compute this value as ratio of degrees over time.


Magnitude of centrifugal acceleration
Magnitude of centrifugal acceleration parameters (gravity).

  • Varies from equator to poles.

  • Compute magnitude by velocity squared times the distance from the point of interest to the spin axis.


Gravitational attraction
Gravitational Attraction parameters (gravity).

  • Is the vector sum of gravitational and centrifugal acceleration.

  • The actual acceleration of gravity varies from place to place, depending on latitude, altitude, and local geology.

  • By agreement among physicists, the standard acceleration of gravity gn is defined to be exactly 9.80665 meters per second per second (m s-2), or about 32.174 05 feet per second per second.


More mind numbing detail
More mind-numbing detail… parameters (gravity).

  • At latitude p, a conventional value of the acceleration of gravity at sea level is given by the International Gravity Formula,

    • g = 978.0495 [1 + 0.0052892 sin2(p) - 0.0000073 sin2 (2p)] cm per second per second (cm s-2).

  • The mean Earth gravity is about 981 000 mGal (the well-known 9.81 m/s2), varies from 978,100 mGal to 983,200 mGal from Equator to pole due to the Earth's flattening and rotation.


Gravitational potential
Gravitational Potential parameters (gravity).

  • Magnitude of the potential is the work that must be done by gravity to move a unit mass from infinity to the point of interest.

  • Is dependent on position within the gravitation field.


Equipotential surfaces
Equipotential Surfaces parameters (gravity).

  • Surface having constant gravity potential NOT constant gravity.

    • Also known as level surfaces or geopotential surfaces.

  • Surfaces are perpendicular at all points of the plumb line (gravity vector).

  • A still lake surface is an equipotential surface.

    • It is not horizontal but curved.



Lecture 7 gravity and related issues

Image from Featherstone, W, “Height Systems and Vertical Datums” Spatial Science, Vol 51 No. 1, June 2006


Properties of equipotential surfaces
Properties of equipotential surfaces Datums” Spatial Science, Vol 51 No. 1, June 2006

  • They are closed continuous surfaces that never cross one another.

  • They are formed by long radius arcs. Generally without abrupt steps.

  • They are convex everywhere.


Geopotential number
Geopotential Number Datums” Spatial Science, Vol 51 No. 1, June 2006

  • C (geopotential number) – is a value derived from the difference in gravity potential between an equipotential surface of interest and the geoid.

  • Represents the work required to move a 1kg mass from the geoid to the geopotential surface at the point of interest.

  • C is numerically similar to the elevation of the point in meters.


Leveling issues
Leveling Issues Datums” Spatial Science, Vol 51 No. 1, June 2006

  • Height

    • The distance measured along a perpendicular between a point and a reference surface.

  • Raw leveled heights

    • Non-unique. Depending on the path taken a different height will be determined for the same point. They have NO physical relevance.


Geopotential numbers
Geopotential Numbers Datums” Spatial Science, Vol 51 No. 1, June 2006

  • Geopotential numbers

    • Unique, path-independent

    • Geopotential number (C) at a point of interest (p) is the difference between the potential on the geoid and potential at the point.

      • C = W0-Wp


Lecture 7 gravity and related issues

Leveled Height vs. Orthometric Height Datums” Spatial Science, Vol 51 No. 1, June 2006

 h = local leveled differences

H = relative orthometric heights

Equipotential Surfaces

B

Topography

 hAB

=  hBC

A

C

HA

HC

HAChAB + hBC

Reference Surface (Geoid)

Observed difference in orthometric height, H, depends on the leveling route.


Orthometric height
Orthometric Height Datums” Spatial Science, Vol 51 No. 1, June 2006

  • Vertical distance from the geoid to the point of interest. (along curved plumb line).

  • Orthometric height (H) may be determined from H = geopotential number / mean gravity along plumb line

    • We use assumptions about mass density to estimate mean gravity.


Dynamic heights
Dynamic Heights Datums” Spatial Science, Vol 51 No. 1, June 2006

  • Takes the geopotential number at a point and divides it by a constant gravity value.

  • The constant value used in the US is the normal gravity value at 45 degrees N latitude

    • 980.6199 gals


Cc area dynamic heights
CC area Dynamic Heights Datums” Spatial Science, Vol 51 No. 1, June 2006

NAVD 88 and dynamic heights differ by only 1 mm at this station.


Dynamic heights1
Dynamic Heights Datums” Spatial Science, Vol 51 No. 1, June 2006

NAVD 88 = 2026.545 m

DYN Hght= 2023.109

Difference = 3.436 m



Dynamic height problems
Dynamic Height Problems predicted one.

  • Dynamic height corrections applied to spirit-leveled height differences can be very large (several meters) if the chosen gravity value is not representative for the region of operation.


Lecture 7 gravity and related issues

ITRF96/GRS-80 ellipsoid surface predicted one.

NAD 83 datum

G99BM

G99SSS

GEOID99

MSL

SST

global geopotential surface

Average of 52 cm

NAVD 88 datum

NOTE: heights are not to scale