Astronomy - Planets and The Solar System
Kepler’s 1st Law: “Law of Ellipses” - Solar objects orbit around the sun, in an ellipse shape, not a perfect circle.
Kepler’s 2nd Law: “Law of Equal Areas” - A planet moves faster when closer to the sun, and slower when farther away.
Kepler’s 3rd Law: “Law of Harmonies: - The square of a planet’s orbital period (p) is equal to the cube of the length of the semi-major axis of its orbit (a).
p2 = a3
p = A planet’s orbital period.
a = A planet’s orbital semi-major axis
Newton’s 1st Law: “Law of Inertia” - An object at rest stays in rest, an object in motion stays in motion.
Newton’s 2nd Law: “Force and Acceleration” - The acceleration of an object is directly proportional to the force acting upon it, and the object’s mass. Force = Mass x Acceleration. Force is measured in Newtons.
Newton’s 3rd Law: “Action and Reaction” - For every action there is an equal and opposite reaction.
Newton’s Law of Gravitation: Planet’s move in ellipses, not straight lines, which means that a force must be bending their paths - That force is gravity.
There is a universal attraction among all bodies everywhere in space.
More mass = stronger force, farther away = weaker force.
Fgravity= G ((M1M2)/R2)
G= Universal Gravitational Constant
R=Distance
M=Mass
Fgravity= Gravitational Force.
This equation broken down is essentially: Universal Gravitational Constant x Object1’s Mass x Object 2’s Mass divided by the distance between them equals Gravitational Force.
How did Newton adapt Kepler’s 3rd Law and what are the implications?
Kepler described HOW planet’s and solar bodies moved in space, and Newton proved WHY they do. Kepler described: “Planets move in ellipses around the sun”. Newton described: “Gravity is the force that bends them to do this. The sun’s gravity is what our solar system bends around”.
Momentum: How much motion an object has.
Momentum = Mass x Velocity
Angular Momentum: The measure of the rotation of a body as it revolves around a fixed point. Described as a product of its mass, its velocity, and its distance from said fixed point.
Conservation of Momentum: The total momentum of an isolated system remains constant if no external forces act on it.
Both of these dictate how the solar system is formed, and how the planets orbit the Sun, and how this motion persists.
Mass distribution in our solar system: The sun is the largest body in our solar system (99.85% of the mass in our solar system), which means that it has the largest gravitational force. Because of this, every planet revolves around the sun.
Types of Objects In Our Solar System:
The Sun - Our star.
The Planets - Celestial body that orbits a star.
Dwarf Planets
Moons - A natural object that orbits a planet.
Rings - Huge, flat disks made of particles orbiting a planet.
Comets - A small body in the solar system made of frozen gases, rock, and dust that orbits the Sun.
Asteroids - Small, rocky, metallic, or airless body that orbits the sun as a minor planet.
Dust - Fine, microscopic dry particles of matter.
A Planet’s Surface Temperature:
Distance from the sun: Generally, the further from the sun means that cooler the planet. This is not a rule though.
Atmosphere: A planet with a thick, dense atmosphere traps more heat, warming it.
Geological Activity: (ie. Volcanism, earthquakes, crustal deformation).
Geological activity is mostly determined by a planets internal heat and size. All rocky planets start with an active, molten core, which then cools time, the heat being lost to space. This cooling causes hot material in the mantle and crust to move around. Planets also generate heat from radioactive decay of elements inside their cores.
Dating Planets:
Only applicable to planets with surfaces
The age of the surface ≠ the age of the planet as a whole
-Geological activity can erase evidence
Method 1: Counting Impact Craters
-The rate of impact craters has been constant for several billion years.
-More craters = older
-Works with solid planets and moons
Method 2: Radioactive Rocks
-Measure the age of individual rocks
-Requires direct samples
-Uses the property of radioactivity - radioactive decay
Radioactive Decay:
The natural process where an unstable atomic nucleus (parent nuclide) loses energy by emitting radiation to become a more stable form (daughter nuclide).
Atoms that haven’t decayed = “Parent”
Atoms that have decayed = “Daughter”
With very large amount of atoms of one type, there is a “half-life” - the time it takes for half the sample to decay. After every “half-life”, half of the sample decays again. By comparing the ratio between Parent and Daughter nuclides, we know how many “half-lives” have passed, and therefore how old the sample is.
Formation of the Solar System:
Basic Information: Formed ≈ 4.5 billion years ago from a giant, spinning cloud of dust called a solar nebula.
2) The solar nebula collapses under its own gravity.
3) Material fell towards the center, where things began to become more concentrated and hotter.
4) At the same time, the collapsing nebula begins to rotate faster and faster through the conservation of angular momentum.
5) Near the poles of the nebula, where orbits were slow, the material fell directly into the center.
6) Faster moving material collapsed into a flat disk revolving around the central object.
7) As the disk cooled, the gases interacted (chemically) to create compounds.
8) Eventually, these compounds condensed into liquid droplets or solid grains.
9) The first materials to condense into solid grains were metals and rock-forming silicates.
10) As the temperature dropped, these were joined together throughout the solar nebula.
11) In the inner parts of the disk, the temperature never dropped low enough for materials like ice and carbonaceous organic compounds to condense.
Terrestrial Planets:
Desner, Inner planets. Made of rocks. These planets are closer to the sun because heavier things were pulled closer to the sun during the formation of the solar system.
Giant Planets:
These are the outer planets, comprised of lighter elements, and are much larger than the terrestrial planets. They have way more elements than the inner planets, and all have rings.
Order of the Planets:
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune