Solar System

We place the Sun at the centre of the heliocentric system of eight planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune (Pluto!?)

The Terrestrial Planets (Mercury → Mars) and the Jovian Planets (Jupiter → Neptune) together have a mass of 0.0014 the mass of the Sun, and they shine by reflected light.

The planets obey the laws of Kepler and Newton, and move in elliptical orbits around the Sun. All planets orbit counter-clockwise (the orbits are said to be Direct). The orbital plane lies very close to the Ecliptic Plane (the plane of the Earth’s orbit); the variation is no more than ± 8°. Orbital eccentricities are all less than 0.1 (except Mercury).

A planet’s Sidereal Rotation Period refers to its rotation with respect to the stars. The atmosphere of the Jovian planets rotate slightly faster at the equators than at the poles and the rotation periods are sometimes based on their magnetic field as this is generated in the core of the planet.

We define a planet’s Oblateness ϵ by,

ϵ = (rϵrp)/rϵ ; where rϵ is the equatorial radius and rp the polar radius.

The equators of the planets are inclined to their orbital plane by varying amounts. The rotation axes of Mercury, our Moon, and Jupiter, are nearly aligned with their revolution axes: Whereas Earth, Mars, Saturn, and Neptune are tilted at about 25°. The equatorial inclination is less than 90° for all these bodies, so they all rotate west to east (Direct Rotation). Venus and Uranus rotate east to west (Retrograde). The rotation axis of Uranus lies in its orbital plane.

Mercury and Venus have slow rotation rates which may be explained by Spin-Orbit Coupling and Resonance. The synodic rotation period of Venus (its rotation period with respect to Earth) is 146 days, which is one quarter of its synodic orbital period. The sidereal orbital period of Mercury is two-thirds of its sidereal orbital period. Venus is in a 4:1 synodic resonance with Earth, and Mercury in a 3:2 sidereal lock with the Sun.

The masses of the terrestrial planets are all less than the mass of the Earth (often abbreviated as M). The Jovian planets are within the range 15 M to 318 M. The masses are determined by :

  1. Kepler’s third law, using satellite orbits.
  2. The planet’s gravitational perturbation of the orbit of other bodies.

Planetary radii are deduced from;

  1. Apparent optical size of planetary disc
  2. Timing the Occulations of stars
  3. Timing reflected radar pulses

Dividing a planet’s mass by its total volume gives its mean density as,

<ρ> = M/(4πR3/3)

For terrestrial planets the densities are in the range 3,400 to 5,500 kg/m3 which reflects the fact that they are composed of heavy non-volatile elements. The very low densities of the Jovian planets imply a composition similar to the Sun (H and He dominating).

Due to the changing density, pressure and temperature; the interior of planets are differentiated rather than being homogeneous.

The Jovian planets and Venus have thick obscuring atmospheres but the other planets reveal surface markings. A planet’s colour relates to its surface and atmospheric composition. The Albedo of an object is the fraction of incident sunlight reflected by it. For planets with no atmosphere the Albedo is low as basaltic rock is a poor reflector. N.B. Albedos are a function of wavelength.

When a Blackbody heats to some temperature, its spectrum of emitted light has a characteristic shape called a Planck Curve with one maximum.

A blackbody’s emission peaks at the wavelength, λmax ≈ 0.002898 m/T (Wien’s Law).

A planet that radiates more energy per second than it receives from the Sun must have an internal heat source. Planets known (from IR observations) to produce excess heat are Jupiter, Saturn, Neptune, and of course, the Earth.

Stefan’s Law of blackbody radiation relates the energy flux
F (energy radiated per unit area per unit time, W/m2) to the temperature,

F = σT4 W/m2

Where the constant σ ≈ 5.67 x 10-18 Wm-2K-4

Our Sun radiates like a blackbody at the rate (T = 5,800K),

R2 F ≈ 3.8 x 1026W

which is the Sun’s luminosity L.

Mercury and the Moon have essentially no atmosphere. Venus and Mars posses a CO2 atmosphere, and the Earth’s atmosphere is N2 and O2. The principle constituents of the Jovian atmospheres are H2 and He. Incoming solar UV and x-rays usually ionize the atmospheric atoms or dissociate molecules to form the layered ionosphere.

To a first approximation, an atmosphere behaves like a perfect gas (the particles interact through elastic collisions). Such a gas obeys the equation, P = nkT, where P is the pressure (the rate of change of the particles momenta from collisions) in units of force per unit area (N/m2), n is the number density (#/m2), T is the absolute temperature (K), and k is Boltzmann’s constant ≈ 1.38 x 10-23 J/K.

From the continuous collisions the particles achieve an equilibrium distribution of velocities,

F(v) dv ∝ exp( -½mv2/kT)vdv

Known as the Maxwellian Distribution: The peak of this distribution defines a most probable speed

Vp = (2kT/m) 1/2

The average kinetic energy per particle is,

<KE> = (m/2)<v2> = 3kT/2

And the root mean squared is vrms = (3T/m) 1/2

To retain an atmosphere, a planet must have ve ≥ 10 vrms and a given type of molecule is retained when TGMm/150kR.

The Jovian planets have retained all gases, and the terrestrial planets have lost their H2 and He, but retained N and CO2.

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~ by jamesdow2013 on March 31, 2013.

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