Gravity
Galileo made the first important observations on the force of gravity
Newton - deduced the Law of gravitation
- all material bodies in the universe attract one another with forces that are determined by their masses and separation.
The force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. This can be written as the following equation:
F=(G*M1*M2)/(D*D)
If masses are measured in grams and distance in centimeters then G is about 6.6 x 10-8
Also -
Force
= mass x acceleration or F=MAIf you replace F in the gravity equation with this definition of F you get:
MA =G*M1*M2/D*D
If we measure the acceleration (A) of a mass M1 (ie a pendulum weight, weight on a spring) we can solve for the mass of the earth since, by rewriting the equation above:
A*M1 = G* M1*M2/D*D
where M1 is the mass of the weight and M2 is the mass of the earth.
Cancel M1 on each side. Then:
A (measured acceleration) = G (constant)*M2 (mass of earth)/D*D (distance to center of earth)
This tells us acceleration is constant on the earth (Galileo's observation) and it permits measurement of mass of earth.
So - using the equation:
F=G*M1*M2/D*D
if we measure the force of gravity (F=g=MA) on the surface of the earth, we get an idea of the distance to the center and of the density of the underlying earth mass (density = mass/volume).
With modern instruments we can measure the force of the earth's gravity with an accuracy about one part in 50 million. At the equator the value is 978.049 cm/sec2 at the pole the value is 983.221 cm/sec2.
What factors cause variations in the force of gravity?
- centrifugal force
- the shape of the earth
When we talk of shape can refer to:
1 - the reference ellipsoid = the mathematical model which best approximates the planet's average shape.
2 - the geoid = the sea level earth
3 - real earth with all its irregularities
To obtain actual gravity measurements - we must make corrections to observed values:
Observed value: Gobs
Latitude correction - Corrects for shape of the earth and centrifugal force = Gobs-Go
Free air correction - Corrects for elevation - Gobs-Go+free air correction = free air anomaly
Bouguer correction - Corrects for extra mass in mountains
- Gobs-Go+free air correction-Bouguer correction = Bouguer anomaly
If all done correctly Bouguer anomaly should be zero but:
On land the Bouguer anomaly is usually negative, over ocean usually positive. Why? Because surface elevation differences are balanced by internal inequalities of density. The state of balance achieved is called isostacy. This is the concept that surface topography is balanced by internal density variations.
A change in elevation by erosion or deposition will upset the isostatic balance and require readjustment at depth of the thickness and possibly the density of the underlying block
Evidence suggests isostatic equilibrium is the natural state of the crust and adjustment takes place slowly but continuously.
Isostacy permits both erosion and deposition to proceed for longer periods than would occur in a case of no adjustments. This is due to the fact that the weight of sediments causes the crust to sink thereby keeping the depositional basin deep longer. Also the removal of material will cause a mountainous crustal block to rise, resulting in more material to be eroded.
How does isostatic equilibrium occur?
- by movements of material in the upper mantle flowing out from under crustal blocks that are sinking and flowing in to fill in under areas where crustal blocks are rising.
- Possibly also phase changes in upper mantle that result in a change in volume. If a crustal block rises, pressure goes down and the underlying mantle material may change from a denser to a less dense phase and thus take up more volume for the same mass. The opposite could occur where the pressure goes up due to added mass.