Astronomy 1101: Planets to Cosmos

The Family of the Sun and the Dance of the Planets

Key Ideas:

The Solar System contains:

The planets all lie in nearly the same plane and orbit in the same general direction.

Every object in the Solar System feels gravitational pulls from all of the other objects in the Solar System.

The Three-Body Problem

Gravitational Interactions

Resonances

The Golden Age of Planetary Exploration

The Solar System has been explored using robotic spacecraft & astronauts:

Much of what we know about the Solar System has been learned in the last 35 years of planetary exploration.

The next few years will see a number of new missions to visit Mars, Saturn, Comets and Asteroids.

The Family of the Sun

The Sun is a middle-aged, average sized star surrounded by a system of orbiting objects:

The Terrestrial Planets:

The Jovian Planets:

Dwarf Planets:

Small Solar System Bodies:

(Graphic by R. Pogge)
Solar System Mass vs. Semi-Major Axis Plot
Contents of the Solar System by Mass
Plot of the Mass (in Earth Masses) vs. orbital Semi-Major Axis (in AU) for all of the major constituents of the Solar System other than the Sun. Click on the image to view full size.

The Eight Planets, in order from the Sun:

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, & Neptune

First 6 were known from antiquity, and are all visible to the naked eye as viewed from the Earth.

The last two were discovered using telescopes:

Uranus
Discovered by William Herschel (UK) in 1781.

Neptune
Predicted mathematically using orbital deviations of Uranus and Newtonian Gravity by Urbain LeVerrier (France) and John Couch Adams (UK)
Found at predicted location by Johann Galle (Germany) in 1846.

Basic Properties of the Planets

Locations:

All orbit in the same direction & plane:

These facts provide us with important clues to the formation of the Solar System.

The Sun

The Sun is a middle-aged, average-sized star.

The Sun shines because it is hot:

Kept hot by nuclear fusion in its core

Terrestrial Planets

Mercury, Venus, Earth & Mars

"Earth-Like" Rocky Planets:

Rocky Planets:

The Jovian Planets

Jupiter, Saturn, Uranus & Neptune

Gas Giants (Jupiter & Saturn):

Ice Giants (Uranus & Neptune):

Dwarf Planets

New class of objects defined by the IAU in 2006. They have the following properties:
  1. They must orbit the Sun, and not be satellites of another, larger body

  2. They are shaped by self-gravity: which means that they have sufficiently large masses that their self-gravity overcomes internal rigid-body forces and shapes them into spheroids in "hydrostatic equilibrium". Usually means it is larger than about 800km in diameter, but it depends on the material it is made of (rock, ice, or a mix).

  3. Their gravity is insufficient to have cleared the neighborhood around their orbit.
The third property is what distinguishes dwarf planets from the other, larger 8 planets in our Solar System. It is a statement about gravitational dominance in their immediate vicinity - dwarf planets are too small to have altered their immediate surroundings, unlike planets.

There are currently four (4) recognized Dwarf Planets as of July 2008:

There are currently another 40 or so candidate Dwarf Planets, most in the outer solar system, that are subjects of ongoing study to determine if they satisfy the "shaped by gravity" criterion to become offical dwarf planets.
Note:
In June 2008, the IAU formally defined the term plutoid to designate the subclass of trans-Neptunian dwarf planets. At this writing (July 2008) there are 3 "plutoids" so-defied: Pluto, Eris, and Makemake.

The Giant Moons

A Moon is any natural satellite orbiting around another, larger object (planets or dwarf planets).

The largest of these are the "Giant Moons":

Many smaller moons, both rocky & icy, are found throughout the solar system orbiting all planets except for Mercury & Venus. Only these two planets have no moons.

Trans-Neptunian Objects

Dwarf Planets Pluto and Eris are the largest of a class of icy bodies found orbiting beyond Neptune.

Examples:

The Leftovers: Small Solar System Bodies

The remaining inhabitants of the Solar System are a huge number of small objects:

Asteroids:

Meteoroids:

Comets:

All of these are the leftover material from the original formation of the Solar System.

Beyond Kepler

Newton's formulation of Kepler's Laws of Planetary Motion is only strictly true for idealized systems with only 2 massive bodies.

But, the Solar System is a many-body system:

How do we address this many-body problem?

The Three-Body Problem

Let's start relatively simple:

What is the orbit of a small body in the combined gravitaional field of two larger objects orbiting each other?

Some examples:

A formal solution of the problem was proposed by French mathematician and physicist Joseph-Louis Lagrange (1736-1813) These are known as the Lagrange Points, labelled L1 through L5.

Earth-Moon Lagrange Points

Earth-Moon Lagrange Points

L4 and L5 are stable:
Can have objects trapped in stable "tadpole" orbits.

L1 through L3 are unstable:
Objects at these points are easily nudged out of their orbits and drift away (no long-term orbits without special circumstances, like firing engines for "station-keeping maneuvers").
In reality, because the Earth/Moon system has a mutual elliptical orbit, the locations and the properties of the Lagrange points differ in detail from the simple circular-orbit approximation used by Lagrange to make the problem soluble by solving Newton's equations of motion algebraically. In general, the real problem is solved numerically using computers.

Jupiter Trojan Asteroids

An example of objects trapped in stable orbits at the L4 and L5 Lagrange points are the Trojan Asteroids of Jupiter. These are two families of asteroids that that follow and lead Jupiter around the Sun as part of the Sun-Jupiter system.

Jupiter Trojan Asteroids.

Gravitational Interactions

To a first approximation, the orbits of most objects around the Sun are simple 2-body Keplerian orbits: Since the Gravitational Force gets weaker as the inverse square of the distance between objects:

Long-Range Perturbations

Long-range interactions between two massive bodies orbiting the Sun.

The extra object-to-object gravitational forces accelerate the bodies relative to their Keplerian orbits

Any systematic deviation of a body's orbit from a simple Keplerian path is usually a sign that the body is being perturbed by the gravity of another, nearby object.

The Discrepant Orbit of Uranus

William Herschel accidentally discovered the planet Uranus in 1781 while sweeping the sky with his telescope in his backyard in Bath, England.

Uranus is the 7th planet, orbiting beyond Saturn.

Subsequent measurements of the orbit of Uranus started showing systematic discrepancies between the predicted and actual positions of Uranus in the sky. By the 1840s, these discrepancies had become as large as 1 arcminute!

The problem was, if you added up the perturbations from the known planets, it wasn't enough to explain the discrepancy seen.

The Discovery of Neptune

Two theorists, Urban LeVerrier in France and John Couch Adams in England, predicted that the deviations were due to the gravitational influence of another, unknown massive planet beyond Uranus.

Using the deviant motions of Uranus, they independently calculated where this unknown 8th planet should be.

On Sept 23 1846, Galle found Neptune only 52 arcminutes from where Leverrier predicted it would be!

This was possible because between Uranus' discovery in 1781 and the 1840s, Neptune passed through opposition with Uranus, when the perturbation of Uranus by Neptune's gravity is strongest. If their configuration had been conjunction, there would not have had a measurable perturbation. Neptune would have eventually been discovered by accident like Uranus, in fact Galileo saw it while observing Jupiter but thought it was a fixed star! [NOTE: Galileo's notebooks showed that he observed Neptune twice during observations of Jupiter on 1612 Dec 28 and 1613 Jan 27. At this time, Neptune and Jupiter were in conjunction in the sky. Because this conjunction also occurred near when Neptune was in opposition, its motion was very small and undetectable to Galileo's small telescope, and he thought it was a fixed star.]

Close Encounters

Close encounters between objects have much stronger effects: Examples:

Short Period Comets
An incoming comet on a large elliptical or near-parabolic orbit with a very long period is driven into a smaller elliptical orbit with a shorter period after a close gravitational encounter with Jupiter.

The dashed path is the orbit the comet would follow if it had no Jupiter encounter.
The solid line show the new, smaller ellitpical comet orbit after a close gravitational encounter with Jupiter,

Gravitational Slingshot
A spacecraft catches up with Jupiter from behind, and is accelerated by Jupiter's strong gravity. This, combined with Jupiter's orbital motion, give the spacecraft a boost in speed, slinging it into the outer solar system.

This method of "gravity assist" is used to send spacecraft into the outer Solar System by robbing Jupiter of a tiny bit of its orbital energy. This is much more energy efficient than having to carry a very heavy payload of fuel to rocket the spacecraft to those speeds.

This was done by all outer Solar System explorers (Voyager 1 & 2, Pioneer 10 & 11, Cassini, and New Horizons).

Above is the Cassini gravity assist trajector to Saturn. Boosts from Venus, Earth, and Jupiter were used to get Cassini to Saturn with minimal expenditure of fuel (and so less spacecraft weight).

The reverse process, where the encounter occurs with the spacecraft getting in front of the planet, can be used to take energy from the spacecraft, dropping it deeper into the inner Solar System. This is done for spacecraft bound for Mercury like MESSENGER.

Orbital Resonances

Small perturbations at opposition usuall happen at different places along the object's orbit. But, if the periods of the object and its perturber are whole-number ratios, you can get regular, periodic pertubations at the same place in the orbit. We say that such synchronized pairs of orbits are Orbital Resonances.

The analogy is to consider a child on a swing being pushed another person:

If the pushes of the child come at random times, sometimes pushing with their swing and boosting them, other times pushing against their swing and slowing them down, they average out and the swing doesn't change much.

However, if the pushes are all timed just right so that you push the child with their swing each time, the in-phase pushes build up and the child's swing gets amplified.

Such a well-timed push is called exciting a resonance.
Orbital resonances are a way to amplify small long-range gravitational perturbations.

Naming Resonances

Resonances are named for the number of orbits completed by each body in the pair. Examples:
Pluto is in a 2:3 Resonance with Neptune
Pluto completes 2 orbits for every 3 orbits of Neptune.
Pluto is the smaller object being driven by Neptune.

Asteroid Hilda is in a 3:2 Resonance with Jupiter
Hilda completes 3 orbits for every 2 orbits of Jupiter.
Hilda is the smaller object being driven by Jupiter.

Resonances in the Solar System

Some examples of important orbital resonances in the Solar System:
Main Asteroid Belt Resonances with Jupiter
Kirkwood Gaps - unstable resonances cleared of asteroids
Asteroid Families - stables resonances populated with asteroids orbiting with the same periods.
Trojan Asteroids - 1:1 resonance with Jupiter

Kuiper Belt Resonances with Neptune
Pluto and the Plutinos in 2:3 resonance orbits
Twotinos - objects in 1:2 resonance orbits

Jupiter and Saturn Systems
Jupiter: 1:2:4 Laplace Resonance of the moons Io, Europa, and Ganymede
Saturn: many resonant moons and resonant gaps in the rings.
We will meet each of these as we begin our exploration of the Solar System in upcoming lectures.

Dynamical Evolution (again)

The Solar System is not a "static" clockwork that moves exactly the same forever Close Encounters and Resonances amplify these changes: All of these effects have helped "shape" the Solar System over its long history.

As we explore the Solar System in more detail later in the course, we will keep on the lookout for signs of this "dynamical evolution", and use it to help read the dynamical history of the Solar System.

Updated: 2014, Todd A. Thompson
Copyright © Richard W. Pogge, All Rights Reserved.