GG 450 Lecture 2 GRAVITY BASICS 1/17/08 GRAVITY
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Gravity, the force that effects our lives more than any other we think of as a constant, but changes in gravity are significant and relatively easy to measure with modern instruments. Since gravity changes with mass and distance away from mass, it is simple to make models of gravity anomalies, but in reality, most gravity anomalies can be fit by a host of models (non-unique). Even so, gravity measurements are often important supplements to other geophysical measurements.
What IS gravity?? Mass attracts mass, but how? Where’s the “spring”?
Gravity and electro-magnetic forces generate FORCE FIELDS. All mass feels the effects of all other mass in the universe, but, since the effect decreases as 1/r2, where r is the distance between the masses, we can often ignore all but the closest and largest masses.
Many forces are POINT FORCES, acting at a point, like poking someone with a finger, force fields act uniformly over space. THIS is why gravitational force can't be felt.
You don't feel gravity pulling you down, you feel the earth pushing you up.
Geophysical studies using these fields are called the POTENTIAL FIELD METHODS, because we can find a SCALAR value at all points in space which tells us the potential effect on any body caused by all masses considered.
The effect on any body can then be determined by differentiation. Just as a body will not feel a magnetic force if it has no susceptibility, a body will feel no gravitational force if it has no mass. More about potential later.
where F is the gravitational force of attraction between the two masses, G is the universal gravity constant (6.6732x10-11 nt•m2/kg2, often called “Big G”), and r is the distance between the two masses. How big is this force?What is the gravitational force between two car-sized masses about 2 meters apart?
F=6.67x10-11 103 103/(22)= 1.67x10-5 nt = 1.67dynes
This is a VERY small force. A dyne is the force of a mosquito slamming into a wall at 1 cm/s. Yet, this is the force that holds the universe together.
gravity is as though all the mass
of the shell were concentrated
at the middle.
But INSIDE the shell, the gravity
caused by the shell is zero
Inside a spherical shell, the gravitational attraction of the nearest sections are exactly compensated for by the attraction of a larger area on the opposite side of the sphere.
What is the gravitational acceleration at the center of the earth?
If the earth is a sphere, we can calculate its mass if we know its radius and the acceleration of gravity.
r ~ 6.378x106 m, or 6.378x108 cm
Always track UNITS, to be sure your logic is correct.
We have thermometers to measure temperature, barometers to measure pressure, fathometers to measure depth, seismometers to measure motion.
We have meters, centimeters, millimeters, and so…
How do you pronounce
How well must we be able to measure T to resolve a change in g of 1 mGal? About 1 microsecond. This is not easy, given the other problems with pendulums, like friction.
This is an “absolute” gravity instrument that measures the time of fall of a mass. Precise to ~3 microgals.
This is called a Lacoste suspension.The mass deflects downwards when gravity increases. The adjusting screw changes the length of the spring until the mass is in its centered position. Such instruments are very portable but only measure gravity RELATIVE to some known value.
The length of the spring when the boom is horizontal is proportional to g.
The adjustment screw changes the length of the spring until the capacitor output is centered. The adjustment dial is then read and converted to a gravity reading in mgals.
A zero-length spring in a Lacoste suspension can be adjusted so that the force need to change the location of the mass does not depend on the length of the spring. This means that there is no "restoring force" and the displacement of the mass relative to its zero displacement position depends only on spring length. It will also have an infinite oscillation period around its zero position.
This system is very sensitive to changes in g.
Your data will have a dial reading like “2045.74”. On the calibration sheet, look for a value of about 2050. You will likely find a number like “0.725” mGals/division. Multiply your dial reading by this number to get RELATIVE mGals.
We can correct our readings to true gravitational acceleration by taking a measurement at a place where the absolute gravity is known. We have such a location outside of the HIG building.
After changing the reading you get at HIG to mGals, subtract it from the absolute gravity at HIG (given on the sheet for the HIG gravity station). This will give you the constant to add to all your readings to correct them to real values of observed gravity.
Gravimeters are extremely sensitive and can drift as the spring(s) age and temperature changes. Thus they are housed in a vacuum, and some (like ours) are kept at a constant temperature. Some meters work only in a limited range of elevation and latitudes, and must be pre-set at the factory for the expected range. Geodetic meters (like ours) have a range which allows them to be used all over the world, sacrificing some precision.
Instrument drift is caused by instrument problems. When an instrument measures such small changes, problems are not unusual.
How do you remove drift?
Is the difference between the two base station readings different by a significant amount? If not - no drift.
Calculate the difference between the two base station readings.
Calculate the amount of time between the two base station readings.
Calculate a drift rate (dial reading per minute)
Add or subtract the appropriate drift correction from each gravity reading.
as we get farther from the mass, gravity decreases.
You place a gravity meter (red) at each of the points above, what effect does the anomalous mass have on gravity?
Because the force of gravity is proportional to the square of the distance between two bodies, and since the gravimeter is only sensitive to the vertical component of gravity, it can be shown that 2-dimensional bodies like each element in the cross section above will have the SAME EFFECT on the gravity measured at the central point (A).
For example the effect of equal density bodies of the two brown regions will contribute equally to the gravity measured at A.
NET EFFECT OF ALL THREE: g~ 5,200 mGals less at the equator than at the poles.
Your ship is moving in the directions shown. What will the Eötvös effect be in each case?
waves on ocean: "gravity" is far from constant as the ship moves up and down. How can gravimeters possibly work at sea??
% g= vertical acceleration caused by density difference rho,
% sphere radius R, centered z below the gravity meter
z=50; % meters
R=[1:5:45]; % meters, plot from 1 to 45 meter radius stepping 5 m
rho=3000; % kg/m^3
% 1 Gal=1 cm/sec^2; 1 m/s^2= 100Gals=100000 mGals
xlabel('sphere radius, m');
title('buried sphere at 50 m depth, rho=3000');