Planetary Shapes• Non-rotating, self-gravating, strength-less objects

would be spherical• Rotating bodies, because of the centrifugal force of

rotation, will be oblate spheres with larger equatorial radii than polar. – Anyone standing at sea level on either pole may be 21.36

km closer to the earth's center than standing at sea level on the equator.

• Flatting f = a-c/a• Why was Newton wrong in his estimate of flatting?

The Geoid• Water (or any strength-less fluid) assumes a level

surface (all other things being equal)• Without currents or imposed gradients (like convection)

the surface would follow a constant gravitational potential, or an equipotential or equilibrium surface.– On a rotating planet the equilibrium surface is the oblate

spheroid.– Note that the headwaters of the Mississippi are closer to the

center of the Earth than the mouth of the river is…..!

• On REAL planets there are always distortions• A GEOID is an arbitrarily chosen equilibrium surface

used as a reference.

Near-Earth Asteroid (66391) 1999 KW4

Near-Earth Asteroid (66391) 1999 KW4

• The Asteroid’s rapid spin produces a pronounced equatorial bulge with near-zero gravity

Iapetus

Tidal Deformation• Any satellite that spins at a rate different that its

orbital period will be subject to tidal forces.– There is an elongation of the equipotential surface in a

frame of reference rotation with the satellite that varies with time.

– The equator is alternatively lifted and dropped as the satellite rotates.

• Body tides: are the small (<1 metre) motion of the Earth's surface at periods of about 12 hours and longer. Semi-diurnal amplitude can reach about 55 centimetres (22 in) at the equator

Planetary Spin• Almost all rotating bodies spin about the axis with

their maximum moment of inertia.– Principal moments of inertia C ≥ B ≥ A– Principal axes c ≤ b ≤ a

• The C axis has the lowest kinetic energy possible for any fixed angular momentum. – Rotation about the C axis is the minimum energy

configuration.– Bodies spinning around other axes typically dissipate

kinetic energy into heat until they settle on C axis rotation– Note about Mars and Vesta

Hypsometric Curve• Plot of the percentage of a planet’s surface

that falls within an elevation bin.

Coordinates on the Earth• Latitude:

position north or south of equator

• Longitude: position east or west of prime meridian (runs through Greenwich, England)

Is there anything special about the Greenwich Meridian?

For those who can’t read Latin (or Czech), this is Dr. Britt at the Prague Meridian

This meridian passed through the center of the original (small) dome atop the main building of the Old Naval Observatory, now on the grounds of the United States Navy Bureau of Medicine and Surgery, southwest of the corner of E and 23rd

Can you point out the Paris Meridian?

Greenwich at the same scale. North is up. Can you point out the Meridian?

The Greenwich Meridian