EOSC Lecture 21 Gravity and Isostacy

Gravity

an attractive force between two objects

• strength of the force (F) of gravity depends on:

  • gravitational constant (G) ignore

  • masses involved = m1, m2 and how big they are

  • distance between masses = r. how far apart they are

  • F = G(m1m2/r2)

• how far away from the mass you are is very important

• when you move away from mass, very quickly gravity will drop off

• everything has attraction, just really small

• always acts radially towards the center of an object

Mass

how much matter there is

Weight

how something is affected by the force of gravity

Uniform sphere

same gravitational force at the same distance “r” from the center of mass

• anywhere on the circle is the same force of gravity

• in a uniform body, the force of gravity is lower over large depressions as there is less mass

Non-uniform body

divide it into n pieces; calculate gravity from each piece; add them up

Measuring gravity

• Gal 1cm/s2 = 0.01 m/s2 acceleration due to gravity

• gravimeter

  • essentially a spring and a mass

  • more gravity, mass stretches the spring more

  • measures very small changes

• ground based (since 1930’s)

• airborne (expensive; ~1990’s)

• from space twin satellites (G.R.A.C.E. 2002-2007) Gravity Recovery And Climate Experiment

Small scale gravity anomalies

• topographic variations result in surface density variations, which give gravity anomalies

• e.g. slightly higher gravity over dense metallic ore deposit, slightly less gravity over cave

• applications: oil/gas/mineral exploration, geologic engineering, etc.

Predict how gravity will vary

• consider both density variations and distance variations

• over Earth, variations very small

  • acceleration due to gravity = 9.81m/s2

  • we wouldn’t notice

  • 120 total Gal anomaly

Isostacy

the state of gravitational equilibrium between Earth’s crust and mantle such that the crust “floats” at an elevation that depends on its thickness and density

• iso = same or equal

• stasy = static - stationary or not in motion (in balance)

• larger mass displaces mantle equal to their mass, so percent “floating” above (crust) is higher, i.e. crust is thicker

• masses are equalized when things float

• it takes a very long time for continents to come to equilibrium (float)

• vancouver still rising after glaciation which ended ~50,000 years ago

• when they reach equilibrium, it erases the gravity anomaly

• ocean plate vs. continental plate, the low density of the continental crust supports elevation

• within a continental plate, low density “root” compensates for elevation - thickest part of Earth is the Himalayas

• accounts for why there are no large gravity anomalies on Earth, and why topography does not really relate to gravity anomalies on Earth

• describes how deep metamorphic roots of mountains are exposed at the surface, roots of the mountains rise as the overlying rocks is eroded and removed (isostatic uplift), very slow process

• Himalayas not yet in isostatic equilibrium, still riding due to collision of plates and thickened continental crust producing a positive gravity anomaly

Isostatic rebound

negative anomaly due to the removal of the ice sheet that covered the area over 10,000 years ago, crust is still bouncing back adjusting with isostasy

• strand lines, old beaches that show how they have uplifted since the last ice age in Nunavut