This is an introduction to the Solar System, its formation, and composition, with special emphasis on the "terrestrial" or "inner" planets. I take a kind of historical approach, noting the patterns and regularities observed, for example, by Tycho Brahe, described by Johannes Kepler, and explained by Sir Isaac Newton. Laplace and even the philosopher Immanuel Kant figure into shaping our modern-day notions of the origin and composition of the solar system.
"Early attempts to explain the origin of this system include the nebular hypothesis of the German philosopher Immanuel Kant and the French astronomer and mathematician Pierre Simon de Laplace, according to which a cloud of gas broke into rings that condensed to form planets." - Encarta, http://encarta.msn.com/encyclopedia_761557663/Solar_System.html
Homework Set 1
Taking the point of view of a first-time visitor, one of the first things you would notice about the Solar System is that the spacing between the planets' orbits consistently increases as you move away from the Sun (with one exception). Furthermore, it's not a linear increase, so we need essentially two figures, at different scales, to represent the solar system (pictures courtesy of "The Nine Planets"):
Titius-Bode's law: Distance, r, of the nth planet from the Sun (in A.U.s) is given by:
rn = 0.4 + 0.3 x 2n
|Mercury||-infinity, -1||0.4, 0.55||0.39|
The Dead White Guys:
eccentricity, e, = (a2 - b2)/a2 where a, b semi-major, semi-minor axes
Assuming stable, circular orbit, Kepler's 3rd Law derives from:
centripetal force = gravitational force
Expressing angular velocity in terms of period,
About Amateur Radio Satellites (OSCARs)
Planet, radius R, distance r from Sun, receives:
As a result of Ercv, planet heats up and re-radiates energy; reaches steady state (heat received equals heat radiated, Erad).
Black-body Radiator: idealized surface for which relationship between T and radiated energy may be derived from thermodynamic (statistical mechanics) first principles:
The total surface of a planet is
so total radiated
Setting received and radiated energies equal:
Example: Earth - r = 149.6 x 106 km = 1.496 x 1011 m so T = 278o K = 5o C (very close)
|Actual Temperatures (oK)||Calculated|
Homework Set 2
Once the mass and radius of a planet are determined, bulk density can be estimated:
|Planet||r (kg/m3)||ru (kg/m3)|
PV = nRT (ideal gas law)
Larger planets have higher interior pressures and vice versa, so comparisons between planets, and with materials observed at surface of Earth, must be referenced to a standard state (like STP).
By "guessing" at EOS for planetary materials (or as gotten from seismic data), can estimate uncompressed densities, ru. Will discuss this process later.
Note decrease in density away from Sun - result of more volatile elements relative to refractory elements as T drops away from Sun
Moon is exception: binary accretion, fission, capture - little iron
Jupiter has 4 major (Galilean) satellites:
|Galilean Moon||r||103 km from Jupiter|
Saturn's Major Moons:
|Moon||r||103 km from Saturn|
Oblateness: Because of rotation, planets tend to be larger at equator (even if solid, but elastic).
For a body in hydrostatic equilibrium, oblateness is approximately equal to
non-dimensional centripetal acceleration,
For a spherically symmetric body, as we'll show later,
As an example, consider Earth:
Homework Set 3
|Ideal Body (in order of increasing central concentration)||I, moment of inertia|
|planet, mass m, in orbit of radius r||1.0 mr2|
|ring, radius R, mass m, spinning about sym. axis||1.0 mR2|
|hollow sphere, radius R||2/3 mR2|
|homogeneous sphere, radius R||2/5 mR2|
|sphere, core radius 1/2R, core density = 2 x mantle density||0.367 mR2|
|mass concentrated on axis||0.0 mR2|
Angular momentum of a system remains constant unless external torque acts on the system.
Moment of Inertia of 2-Part Planet
Moment of inertia for planet spinning on its own axis, given above. For body orbiting primary, consider body a point mass, so I = mr2
Albedo is the fraction of light that is reflected by a body or surface. It is commonly used in astronomy to describe the reflective properties of planets, satellites, and asteroids.
Albedo is usually differentiated into two general types: normal albedo and bond albedo. Normal albedo, also called normal reflectance, is a measure of a surface's relative brightness when illuminated and observed vertically. The normal albedo of snow, for example, is nearly 1.0, whereas that of charcoal is about 0.04. Investigators frequently rely on observations of normal albedo to determine the surface compositions of satellites and asteroids. The albedo, diameter, and distance of such objects together determine their brightness. If the asteroids Ceres and Vesta, for example, could be observed at the same distance, Vesta would be the brighter of the two by roughly 10 percent. Though Vesta's diameter measures less than half that of Ceres, Vesta appears brighter because its albedo is about 0.35, whereas that of Ceres is only 0.09.
Bond albedo, defined as the
fraction of the total incident solar radiation reflected
by a planet back to space, is a measure of the
planet's energy balance. (It is so named for the American astronomer
George P. Bond, who in 1861
published a comparison of the brightness of the Sun, the Moon, and Jupiter.) The
value of bond albedo is dependent on the spectrum of the
incident radiation because such albedo is defined over the entire range
of wavelengths. Earth-orbiting satellites have been used to measure the
Earth's bond albedo. The most recent values
obtained are approximately 0.33. The
Moon, which has a very tenuous atmosphere and no
clouds, has an albedo of 0.12. By contrast, that of
Venus, which is covered by dense clouds, is
Copyright 2004, Judson L. Ahern