Gravity, Isostasy & Heat flow

Chapter 4 pp. 119-126

m

M

Gravity: force which is caused by mass.

g =GMm

r2

r

g is much bigger for smaller r

g is bigger for bigger M and m

G is a universal constantIt never changes. We can ignore it.

uniform sphere

g

gg

Uniform sphere: same gravity at the same distance from center of mass

but no planets or moons are uniform spheres...

Figure 4.16

Non-uniform body: divide it into pieces, calculate gravity from each piece, and add them up

Gravity low expected over large depressions...

... and gravity high expected over large areas of high elevation

Fig. 4.19

Fig. 4.20

mars.jpl.nasa.gov

Mars: big gravity anomalies that correlate with large-scale topography, as we’d expect...

Philippine Plate

Pacific PlateEurasian Plate

Australian-Indian Plate

Arabian Plate

Average Surface Elevation Oceanic: - 4.5 km Continental: + 0.5 km

Earth topography

Earth gravity: small anomalies that do not correlate with topography!

Why?

short video clip - the Grace mission

Fig. 4.11 (kinda sorta)

Isostasy.

Density of ice = 0.9 g/cmDensity of water = 1.0 g/cmDensity of air = 0.0 g/cm

“Just the tip of the iceberg”

Ice heavier than air -- sinks Ice lighter than water -- floats

Reaches a balance determined by the densities

3

3

3

Isostasy (a.k.a. “Isostatic Compensation”

Isostatic CompensationBimodal Topography & Crustal Thickness

Average Crustal Thickness Oceanic: 5 km Continental: 35 km

Average Surface Elevation Oceanic: - 4.5 km Continental: + 0.5 km

Surface elevations: coloursCrustal thickness: contour lines

Mooney et al., 1998

Average Crustal Density Oceanic: 3.0 g/cm Continental: 2.7 g/cm

3

3

low density

Fig. 4.18

low density “root”

Fig. 4.12 Erosion and uplift

How isostasy is maintained (though imperfectly) - 1

Fig. 4.13 Crustal rebound

How isostasy is maintained (though imperfectly) - 2

Fig. 4.15

How isostasy is maintained (though imperfectly) - 3

adding bouyant plutons / thickening the continent

Fig. 4.17

Small-scale gravity anomalies

Local (small area) anomalies• local variations in rock density (mass = density times volume)• can be used to find metal ores• never isostatically compensated because they are small: crust is strong enough to prevent sinking or rising

Regional (large area) anomalies• none would exist if isostasy were perfect• tectonic forces cause anomalies surface pulled down at subduction zone trenches (-) rapidly building mountains lack buoyant roots (+)

Gravity anomalies are still present...

Heat flow

The inside of the Earth is HOT

High temperatures make asthenosphere gooey, allowing plate motion

Heat is needed for convection of the • core (which makes the magnetic field) • mantle (which starts plate tectonics)

Biggest sources of heat: • stored heat from when the Earth formed • heat from decay of radioactive elements

Fig. 4.29

True, except at mid-ocean ridges.

Fig. 4.28

A couple of causes of high heat flow

Football field = about 3 light bulbs’ worth of energy flux

Geothermal gradient• Temperature increases with depth• Geothermal gradient is (change in T) /

(change in depth)– Deep mines are very hot (need AC)– On average 25 degrees per km– Heat can be used for geothermal energy– Temp at drill bit can be > 200 degrees

• Steep gradients do not persist– temperatures in convecting layers increase

just slightly with depth (pressure): 0.4 degrees/km in mantle

Fig. 4.27

convection

conduction

convection

The Earth is gradually coolingHeat loss exceeds heat production from radioactivity, exothermic reactions, etc.Heat loss rate is 44 x 10^12 Watts, but...

Rate of temperature drop: 0.000000046° per year

(F. Stacey, 1980)