Astronomy 217

 
 

Prof. Andrew W. Steiner

 
 
Oct. 20, 2021
 
 

TA James Ternullo

Last Time

  • Models of the Solar Interior

Today

  • Objects in the Solar System

Solar System with the Naked Eye

  • To the naked eye, the solar system consists of our Moon (Luna), the planets Mercury, Venus, Mars, Jupiter & Saturn, and the occasional passing comet or meteor.
  • This was also how the ancients knew the solar system. Mercury, first described ~1000 BC, was thought to be two separate objects until reconciled by the Greeks around 400 BC.

Solar System Discovery

  • From Copernicus, we discovered that Earth is also a planet.
  • From Kepler and Newton came the ability to predict motions in the Solar System.
  • Galileo’s telescope revealed moons of Jupiter in 1610.
  • Uranus was discovered to be a planet in 1781 by William Herschel.
  • Neptune was discovered in 1846 by Johann Galle, based on a prediction by Urbain Le Verrier and John C. Adams, though it had been seen by Galileo in 1612 and several others later, but not recognized as a planet.

Small Bodies

  • Telescopic observations of have revealed a multitude of smaller bodies.
  • Ceres, the largest resident of the asteroid belt, was discovered in 1801 and considered a planet until a multitude of other asteroids were discovered in the 1850s.
  • Pluto, the largest(?) resident of the Kuiper Belt, was discovered in 1930. Its discovery was based on a search for the cause of perturbations of Neptune’s orbit (later found to be an error), revealing an orbit that crosses Neptune’s.

Modern Solar System

  • Our modern picture of the solar system consists of one star, eight planets, 166 moons, and a larger number of smaller objects, including eight asteroids, and more than 100 Kuiper belt objects, with diameters greater than 300 km.
  • In 2006, the International Astronomical Union introduced a new category, dwarf planet, to cover intermediate size objects like Pluto and Ceres.
  • Membership requires sufficient mass that self-gravity makes the object spherical, but insufficient size to clear other objects from its orbit.
  • To date 5 dwarf planets have been named and estimates suggest 100s more are present beyond Neptune.

Planet Parameters

  • The characteristics of the planets, or any newly observed object in the solar system, must been determined by observation.
  • The Orbital period can be observed directly, as can Rotation period.
  • Distance from Sun can then be calculated using Kepler’s laws.
  • Radius can be calculated from measurements of the angular size.
  • Masses can be determined by Kepler’s law for bodies with satellites or by perturbations of other orbits.
  • Density can be calculated knowing radius and mass

Planetary Statistics

  • Clearly there are two types of planets

Two Types of Planets

  • This image of the eight planets and the Sun provides a visual sense of the strong differences between the four terrestrial and four jovian planets.

Terrestrial vs. Jovian Planets

  • Terrestrial planets: Mercury, Venus, Earth, Mars
  • Terrestrial planets are small and rocky and lie close to the Sun. They rotate slowly and have weak magnetic fields. Except for Earth’s Moon (which is atypically large), they have few small moons and no rings.
  • Jovian planets: Jupiter, Saturn, Uranus, Neptune
  • Jovian planets are large and gaseous and lie far from the Sun. They rotate quickly and have strong magnetic fields. They typically have many moons, some large, and rings.

Terrestrial Exceptions

  • This general division between terrestrial and jovian planets does not indicate that members of these classes are undifferentiated. For example, among the terrestrial planets,
  • While all have atmospheres, these are very different, as are the surface conditions. Only Earth has oxygen in its atmosphere and liquid water on its surface.
  • While Earth and Mars spin at about the same rate, Mercury spins much slower. Venus is slow and retrograde.
  • Only Earth and Mars have moons.
  • Only Earth and Mercury have magnetic fields.

Solar Heatings

  • Because of the increasing orbital size, the Sun provides significantly less energy to the outer planets.
  • The flux suffers geometric dilution $$ F(r) = \frac{L_{\odot}}{4 \pi r^2} = \frac{4 \pi R_{\odot}^2 \sigma_{\mathrm{SB}} T_{\odot}^4}{4 \pi r^2} $$
  • A planet of radius \( R \) in an orbit of radius \( r \) will absorb $$ W_p = \frac{L_{\odot}}{4 \pi r^2} ( \pi R^2) (1- A) $$
  • \( A \) is the albedo, the fraction of light reflected by the planet
  • The albedo varies greatly depending on the planets composition, cloud cover, etc.

Planetary Temperature

  • Eventually, if the planet has no internal heat source, and it has a uniform temperature, this temperature will be determined by equilibrium with \( W_p \): $$ W_p = \frac{L_{\odot}}{4 \pi r^2} ( \pi R^2) (1-A) = L_p = 4 \pi R^2 \sigma_{\mathrm{SB}} T_p^4 $$
  • The resulting planetary temperature is $$ T_p = \left[ \frac{L_{\odot} (1-A)}{16 \pi \sigma_{\mathrm{SB}} r^2 }\right]^{1/4} $$
  • Replacing $$ L_{\odot} = 4 \pi R_{\odot}^2 \sigma_{\mathrm{SB}} T_{\odot}^4 $$ we get $$ T_p = \left( \frac{R_{\odot}}{r} \right)^{1/2} \left[ \frac{(1-A)}{4} \right]^{1/4} T_{\odot} $$
  • For our solar system, this equilibrium blackbody temperature is $$ T_p \approx 279~\mathrm{K}~(1-A)^{1/4} \left( \frac{r}{1~\mathrm{AU}}\right)^{-1/2} $$

Actual Temperatures

  • The equilibrium temperature for the Earth: $$ T_p \approx 279~\mathrm{K}~(1-A)^{1/4} \left( \frac{r}{1~\mathrm{AU}}\right)^{-1/2} $$ is \( T_p = 279~\mathrm{K} \times 0.88 \times 1 = 245~\mathrm{K} = -28^{\circ} C \)
  • Clearly the Earth is much warmer than this, \( T_p = 290~\mathrm{K} \)
  • The cause is the Earth's atmosphere
  • For some other planets, internal source of energy, like gravitational contraction or radioactivity boost the planet’s surface temperature.
  • If neither rotation or an atmosphere spread the solar radiation, a planet’s sunward side can reach a higher temperature $$ T_p \approx 395~\mathrm{K}~(1-A)^{1/4} \left( \frac{r}{1~\mathrm{AU}}\right)^{-1/2} $$

Greenhouse

  • Gases like carbon dioxide, water vapor & methane have high opacities in the infrared, but lower opacities in the optical.
  • Thus the solar photons, with an characteristic temperature of 5800 K, can pass through the atmosphere, but thermal photons from the Earth, with a characteristic temperature of 290K, can not as easily escape.
  • The combination of reflected solar light and thermal emission results in a double peaked spectrum for most planets.

Asteroids

  • The term asteroid is ill-defined, generally meaning objects larger than meteoroids (< 10 m) and smaller than planets.
  • In recent years, distinction is increasingly made between rocky or metallic asteroids, comets and Kuiper Belt objects, which are both rich in ices.
  • Though the remnants of planetesimals from the Early Solar system, they have been extensively changed by internal heating, surface impacts and solar radiation.

Asteroid Belt

  • Demarcating the boundary between the terrestrial and Jovian planets, lies the asteroid belt.
  • Total mass of \( \approx 0.0004~\mathrm{M}_{\oplus} \) is composed of countless particles ranging from dust to 1000 km in size, \( \approx 10^6 \) with diameter > 1 km.
  • 4 asteroids, Ceres, 4 Vesta, 2 Pallas, and 10 Hygiea contain > half of the mass.
  • The distribution of orbits is affected by interactions with Jupiter, with orbital resonances being underpopulated.

Groups and Families

  • Many of the asteroids in the asteroid belt are members of families with as many as 100 members, having orbital elements (semimajor axis, eccentricity, orbital inclination).
  • Outside of the asteroid belt lie groups of asteroids, like the Trojans that dwell in the Jupiter’s L1 and L2 Lagrange Points.
  • Near Earth asteroids are divided into 3 groups. Aten (a < 1 AU), Apollo (a > 1 AU, q < 1.017 AU) & Amor (1.017 AU < q < 1.3 AU).

Comets

  • Unlike asteroids, comets are composed largely of ices.
  • Comets originate in the outer solar system, following highly elliptical orbits with semi-major axes of 5-50 AU, for short period comets, to ~100,000 AU for long period comets.
  • As they come close to the Sun, they develop coma (a temporary atmosphere) and sometimes 2 tails.
  • The dust tail tracks the comet’s orbit while the ion tail follows the solar wind directly away from the Sun.

Kuiper Belt

  • Beyond the orbit of Neptune (30 AU), out to perhaps 55 AU, lies another band of small solar system bodies, forming the Kuiper Belt.
  • Discovered in 1992 contains perhaps 100 times the mass of the asteroid belt, spread over 10 times larger range in radius.
  • Likely the source of Centaurs and Short-Period Comets.

Pluto

  • Discovered in 1930, Pluto was once classified as the ninth major planets. However the discovery of the Kuiper Belt, revealed it to be the first of a new class of large Kuiper Belt objects.
  • Though it has it’s own moons, including Charon with a mass 12% that of Pluto, Pluto’s mass is a fraction of that of Earth’s Moon (< 1/5) or the large moons of the Jovian planets.
  • Pluto maintains an atmosphere of \( \mathrm{N}_2 \), \( \mathrm{CH}_4 \), and \( \mathrm{CO} \) over a surface of the ices of these gases.