What is meant by the average density of a planet? Do all the planets orbit the Sun in the same direction? Are all of the orbits circular?

Understanding the average density of a planet is pivotal in grasping the planet's structure and composition. Picture a planet as a giant ball where we can measure how much material is packed inside it; that's essentially what average density is—the mass of the planet divided by the volume it occupies. The formula is quite simple:
\[ \text{Average density} (\rho) = \frac{\text{Mass} (M)}{\text{Volume} (V)} \]
This tells us how much space a planet's mass takes up. Denser planets may contain more heavy metals and rock, whereas less dense ones could have more ice or gas. Each planet has its own unique density, which can clue us into its geological history and potential for hosting life.

The concept of planetary motion is not just about planets moving; it's about them following specific paths around the Sun. All the planets in our solar system travel in the same direction—counterclockwise—as viewed from above the Sun's North Pole. This uniform motion is a relic of our solar system's formation, where the protoplanetary disk's rotation set this current path in motion. Over billions of years, despite various gravitational disturbances, the planets have largely continued this initial spin, an example of conservation of angular momentum in action.

The way planets journey through space was meticulously detailed by Johannes Kepler in the 17th century. His three laws of planetary motion revolutionized our understanding. Firstly, he stated that planets move in elliptical orbits with the Sun at one focus. Kepler's second law explained that as a planet travels in its orbit, it sweeps out equal areas in equal times, meaning it moves faster when closer to the Sun. Lastly, Kepler's third law established that the square of a planet's orbital period (the time it takes to revolve around the Sun) is proportional to the cube of the aphelion distance; the farther a planet is from the Sun, the longer it takes to orbit it.

These laws provide us with a way to predict planetary positions and delve into the gravitational dynamics of the solar system.

Planetary orbits are not perfect circles but rather ellipses, shaped like stretched circles. An ellipse has two foci, and interestingly, the Sun occupies one of these points in a planet's orbit. The measure of how 'stretched' an orbit is referred to as its eccentricity. An orbit with an eccentricity of 0 is a perfect circle, while an orbit with an eccentricity closer to 1 is more elongated.

Planets don't remain at a fixed distance from the Sun; their distance varies as they travel through their orbits—closest at the perihelion and farthest at the aphelion. Understanding these orbits helps astronomers predict where planets will be at any given time and informs us about the dynamic nature of our solar system.

Think of angular momentum as the 'spin' of the solar system, a conservation law which ensures that the total spin of an isolated system remains constant unless acted upon by an external force. In the context of our solar system, this principle means that the planets continue orbiting in the same direction as the original cloud of gas and dust that they formed from—the protoplanetary disk. Even the process of planets forming from this disk, growing via accumulating dust and gas, didn't lose that initial push of angular momentum. If you've ever seen a figure skater pull their arms in to spin faster, you've witnessed angular momentum conservation firsthand: just as the skater speeds up, the planets maintained their direction and speed (unless significantly acted upon by other forces) throughout the eons.