Weighing Earth

Announcements & Reminders

1. ES 123 Essay: Due Friday November 24, 3:00 p.m. (B&GS 10)

2. Lab final: Tuesday December 5, 10:30 - 11:20 a.m. room NS-145

3. Course final: Saturday December 9, 2:00 - 4:00 p.m. NS-1 FORMAT: Multiple choice (45 questions)

Proposed Change to Course Marking Scheme

Either the original marking scheme, or:

ES 023: final exam = 75%

ES 123: final exam = 65%

... whichever is higher.

Essay Marking Scheme

Style, Format, Grammar, Research, Clarity

Too Much Thinking, Too Few Facts

Four basic elements - earth, water, air, and fire.

Objects move toward their own elemental sphere - e.g., rocks fall to earth.

“Proof”, he claimed, that heavier objects fall faster than lighter ones.

A brief history of gravity

Aristotle(384 BC-322 BC).

http://library.thinkquest.org/27585/history/

New Ideas, Old Observations Nicolaus Copernicus proposed that Earth orbits the Sun (with the rest of the planets). Legend says that Galileo disproved Aristotle by dropping two weights from the leaning tower of Pisa. Johannes Kepler (1571 AD-1630 AD) discovered three laws of planetary motion.

Nicolaus Copernicus(1473 AD-1543 AD).

http://library.thinkquest.org/27585/history/

Galileo Galilei (1561 AD-1642 AD)

A brief history of gravity

A Man, an Apple, and a New Theory Legend says that Newton was struck on the head by a falling apple, prompting his ideas on gravity. Based on Kepler’s laws, Newton formulated the Universal Law of Gravitation Published in 1687 in Philosophiae Naturalis Principia Mathematica, or simply Principia.

Sir Isaac Newton(1643 AD-1727 AD)

http://library.thinkquest.org/27585/history/

A brief history of gravity

Newton’s Universal Lawof Gravitation

F = GMmr2

F = Force of gravity (in Newtons, of course)

G = Universal Gravitational Constant = 6.67x10-11 N-m2/kg2

M,m = masses of two objects (kg)

r = distance between the two objects (m)

Gravitational Acceleration

g = GMr2

Using this formula, we can weigh Earth! (g = 9.80 m/s2, r = 6.38x106 m)

M = r2g/G

= 5.98x1024 kg

… OK, but not so easy for other planets ...

Gravity: Version 2

Einstein’s General Theory of Relativity (GTR) again changed our view about gravity. GTR predicts black holes, slowing down of time & bending of light by a gravitational field. The predicted bending of light by the sun was observed in 1919.

Albert Einstein

(1879 AD-1955 AD)

A brief history of gravity

http://library.thinkquest.org/27585/history/

T2 = A r3

M

T = orbital period, in secondsr = average radius of orbitA = 5.92x1011 s2-kg/m3

Kepler’s Third Law

Sample calculation 1: Mass of the Sun

T = 365x24x3600 = 3.15x107 sr = 1.50x1011 m

M = Ar3/T2 = 2.01x1030 kg

T2 = A r3

M

T = orbital period, in secondsr = average radius of orbitA = 5.92x1011 s2-kg/m3

Kepler’s Third Law

Sample calculation 2: Geostationary orbit

T = 24x3600 = 86400 sME = 5.98x1024 kg

r = [MET2/A]1/3 = 4.22x107 m = 42,400 km

Height of orbit = 42400 - RE = 35700 km

Measuring g: Exploration Geophysics

Absolute g can be measured accurately in the laboratory using pendulums

In the field, relative g can be measured using a gravimeter

Spatial variations in g can be used to map subsurface geology

Worden gravimeter

Measuring g: Exploration Geophysics

Gravity data reduction removes the effects of Earth rotation and ellipsoidal shape, using the International Gravity Formula

Instrument drift

Elevation, using the Bouguer and Free Air corrections

Local topography, using the Terrain correction

Worden gravimeter

Measuring g: Exploration Geophysics

NA Mid-continent rift: Gravity anomaly

Units of gravitational acceleration:

1 Gal = 1 cm/s2

Typical unit for gravity maps:

mGal = 10-5 m/s2