Gravity - Part 1 Flashcards
What is Newton’s Law of gravitation?
Gravity is the attraction on one body due to the mass of another body
What is the equation for Newton’s Law of gravity?
F=G((M1M2)/r^2
Where:
F = force (N)
G = Gravitational constant (6.67*10^-11 Nm^2/kg^2)
M1, M2 = mass of two objects
r= distance between centres of two objects
What is Newton’s Second Law of Motion? Use in context of m1
F=m1*a
Where:
F - force, m1 = mass and a = acceleration of the object (m/s^2)
For Earth’s gravitational field, what are a, m2 and r equal to?
a = gravitational acceleration on the Earth's surface (g) m2 = mass of Earth (M) R = distance from observation point to Earth's centre of mass
What effect does being away from surface have on gravitational acceleration?
Less gravitational acceleration away from surface
What is the value of Earth’s gravitational acceleration? How does it vary at poles?
- 78 m/s^2 normally
9. 83 m/s^2 at poles
What 3 factors cause gravitational acceleration increase at poles? (1+2 decrease acceleration at equator, 3 increases acceleration at equator)
What is the nets loss in acceleration at equator?
- Less inward acceleration because of outward acceleration caused by the spinning of the Earth
- There is less acceleration at equator as Earth’s bulges at equator increasing radius to the centre of the mass
- The added mass of the bulge creates more acceleration
net loss of 0.5m/s^2
What is the variance in mGal from equator to pole?
5000mGal
What does the free air correction account for?
Local change in gravity due to elevation
Why must a free air correction be added to the observed values?
Higher elevations have lower gravitational acceleration than elevations at sea level
What is the equation for free air correction (FAC)?
FAC = h*0.308
Where:
h = elevation of the station above sea level (m)
What is the free air gravity anomaly corrected for?
Observed gravity corrected for the latitude and elevation of the station
What is the equation for the free air gravity anomaly (gfa)?
gfa = g - gt + FAC
Where:
g - gravitational acceleration observed at station
gt = theoretical gravity
In the free air anomaly equation (gfa), how does the equation correct for latitude?
By subtracting theoretical gravity from observed gravity, thus accounting for bulge and spin of Earth
What effect does adding the free air correction (FAC) to free air anomaly equation (gfa)?
Puts back gravity lost to elevation so corrects for increased radius to Earth’s radius
What does it mean when the free air anomaly shows high/low readings?
Near mass excess when high
Near mass deficiency when low
How does topography appear in free air anomaly curves?
Sharp topographical features mimicked by the free air anomaly
What does the Bougeur correction account for?
How?
Gravitational attraction of mass above sea level (accounts for excess in mass)
This is done by approximating the excess mass as an infinite slab with thickness (h) is equal to elevation of station
What is the attraction of the Bougeur infinite slab? (equation)
BC = 2∏pGh Where: BC - Bougeur correction p - density of slab G - universal gravitational constant h - thickness of slab (elevation of station)
What is the simplified Bougeur correction equation?
BC = 0.0419ph
How does p (density), vary on land and at sea?
On land - 2.67 g/cm^3
At sea - 1.03 g/cm^3
What is the equation for the Bougeur gravity anomaly (gB) on land?
gB = gfa - BC
What does the Bougeur gravity anomaly on land equate every 9m increased mass below the observation point?
1 mGal greater than the observed gravity
What is the equation for the Bougeur correction on land?
BC = 0.0419 * 2.67 * h BC = 0.122 * h
What are the three general properties of gravity anomalies?
- Above sea level, Bougeur anomaly is always less than free air
- Short-wavelength changes in free air due to abrupt topographic changes have been removed by BC so smoother than FAA
- Mass excess results in positive changes in gravity anomaly, mass deficiencies are negative
What is the Bougeur correction for water?
BC = -0.0419 (pw - pl) * hw
=> BC = - 0.0687 * hw
What is the equation for the Bougeur anomaly at sea?
BAs = FAA + 0.0687 * hw
The infinite slab gives a simple Bougeur anomaly, Why?
Terrain corrections have not been made, in rugged areas nearby mountains this can have a big effect
What is the equation for the total Bougeur anomaly?
TBA = BA + TC Where: TBA - Total Bougeur anomaly BA - Bougeur anomaly TC - terrain correction
