Astronomy: Planets, Gravity, and the Universe

• These notes cover topics from astronomy lectures, including planetary characteristics, the scale of the universe, gravity, orbits, the solar system's structure, meteorites, Earth's structure, atmospheres, and climate.

Our Place in the Universe

• Terrestrial planets have rocky surfaces and may have liquid oceans.
• Planets are held together by gravity but too small to start nuclear fusion.
• Giant planets consist mainly of gases like hydrogen, helium, and water, also referred to as “gas giants” or “ice giants”.
• Moons orbit planets.
• Asteroids are rocky or icy objects orbiting a star and are remnants from planet formation.
• Comets, described as "dirty snowballs," also orbit stars and are leftovers from planet formation.
• Mars features long valleys, canyons, and massive volcanoes.

The Scale of the Universe

• The universe contains many galaxies, including the Milky Way.
• 1 nanogram equals 10⁻⁹ grams.
• A Mars climate orbiter mission failed due to a conversion error between English and metric units.
• The Earth-Sun distance is 1 AU, equivalent to 1.5 x 10¹¹ meters.
• The Sun's diameter measures 14 x 10¹⁰ cm.
• Distance is calculated as speed multiplied by time.

Gravity and Orbits

• Velocity is speed in a particular direction; speed is a scalar quantity.
• Distance equals velocity multiplied by time, assuming constant velocity.
• Acceleration measures the rate of change of velocity, with units such as km/s per s.
• Acceleration occurs when speed, direction, or both change.
• Planets move in ellipses, a type of conic section.
• In circle terminology, the center is the middle of the circle.
• Ellipses have a major axis (long side) and a minor axis (short side).
• Semimajor and semiminor axes are halves of their respective axes.
• The center is in the middle of the ellipse.
• Two foci lie on the major axis, and the sum of the distances from the foci to any point on the ellipse is constant.
• Eccentricity measures an ellipse's roundness, ranging from 0 (a circle) to nearly 1.
• Kepler developed laws of planetary motion, imagining planets on heavenly spheres and working as Brahe’s assistant.
• Kepler's first law: Each planet orbits the Sun in an ellipse, with the Sun at one focus; perihelion is the closest point to the sun, and aphelion is the farthest.
• Kepler's second law: A line joining a planet and the sun sweeps out equal areas during equal intervals of time; planets move more slowly near apoastron.
• Kepler's third law: The square of a planet's orbital period is proportional to the cube of the semimajor axis of its orbit.
• P² is proportional to a³, where p is in years, and a is in AU.
• Kepler’s laws describe how planets move; Newton explained why.

Newton’s Laws of Motion

• Newton's first law: Objects maintain their state of motion unless acted upon by an external force (law of inertia).
• Newton's second law relates the change of motion to the force acting on the body. Force = mass x acceleration
• Newton's third law: For every action, there is an equal and opposite reaction. F₁ = -F₂

Universal Law of Gravitation

• Every mass attracts every other mass.
• Attraction is directly proportional to the product of the masses.
• Attraction is inversely proportional to the square of the distance between the centers. $$F = G \frac{M₁M₂}{d²}$$
• G is the constant of proportionality, equaling 6.67 x 10⁻¹¹ N m²/kg².

Force, Velocity, Acceleration, and Newton's Laws

• Newton's Laws are a theory or hypothesis and model to be tested.
• Force over mass is needed for acceleration; force equals mass times acceleration.
• The force on mass M due to Earth's gravity results in weight.
• The unit of force is the Newton (N), equivalent to kg x m/s².
• Acceleration is the change in velocity over time.
• Gravitational and electromagnetic forces vary inversely with the square of the distance.
• Closer objects experience stronger forces, while farther objects experience weaker ones.
• Velocity diminishes outwards, increasing the circumference of orbits and period of planets farther from the sun.
• Gravity is proportional to the masses of objects.
• Kepler determined that the periods P of planets orbiting the sun depend on distance from the sun, where p² is proportional to a³.
• Newton proposed that P² = (4π²/GM) a³ = (2π)²a(a²/GM) from his formula for gravitational force.
• Newtonian physics states all planets and ordinary objects move by the same laws.
• Gravity is balanced against orbital velocity, conserving angular momentum.
• Orbiting objects are constantly falling toward the primary mass but always falling "over the horizon."
• Ellipses are significant because all paths of objects bound by another mass are ellipses, allowing predictions of their paths.
• Earth satellites follow elliptic orbits, as stated by Kepler's first law.
• Orbits are around the center of mass (Earth's center).
• The orbit’s period relies on the distance from Earth's center. Orbital velocity decreases with distance from Earth.
• Geosynchronous satellites have a period of 1 day, allowing them to track one spot on Earth continuously and matching Earth's rotation period.
• Satellites serve many purposes, like GPS and satellite data systems.
• Rigid-body motion applies to objects like balls, wheels, and the “solid Earth”.
• All points on a rigid body rotate with the same period.
• Angular velocity is constant (degrees per second), while linear velocity increases linearly with distance.
• For rigid bodies, velocity equals distance divided by time and also 2πα/Ρ.
• Commensurability occurs when two orbits are at specific distances to give simple multiples of periods.
• A testable scientific model makes falsifiable predictions and can be revised if needed.
• Quantitative models are preferred for their testability.
• Theory is a concept that survives repeated testing.

Conservation of Mass and Energy

• Energy remains constant, although it can change forms.
• Forms of energy include kinetic (motion), potential (position), thermal (heat), light (electromagnetic), chemical (in bonds), ionization (binding electrons), and nuclear (stored in atomic nuclei).
• Kinetic energy formula: K = 1/2mv².
• A joule (J) is equivalent to a Newton-meter (N m).
• Gravitational potential energy depends on height and mass: U = mgh, where U is potential energy, m is mass, and g is gravitational acceleration.
• Momentum (p) equals mass multiplied by velocity.
• Momentum is conserved when mass is in motion.
• Angular momentum is also conserved if no external force is applied: Angular momentum equals distance x mass x velocity (L = rmv).
• Conserved quantities include mass, energy, momentum, and angular momentum.
• Mass is a form of energy.

Structure of the Solar System

• The Sun contains most of the mass of the solar system.
• Inner planets (Mercury, Venus, Earth, and Mars) are terrestrial, rocky worlds.
• The asteroid belt lies beyond the inner planets.
• Outer planets (Jupiter, Saturn, Uranus, Neptune) are gas and ice giants, much larger than Earth.
• The solar system also includes the Kuiper belt and Oort cloud.

Meteorites and Age of the Solar System

• A meteorite is a piece of rock or metal from space that falls to Earth.
• Antarctica is ideal for finding meteorites due to ice ablation zones concentrating them.
• Over 20,000 meteorites recovered from Antarctica show considerable material falls to earth
• Meteorite types include pure metallic iron (5%), silicates or rocky material (94%), mixtures of stone and iron (1%), stony (chondrites) and metal="iron" (achondrites).
• Carbonaceous chondrite meteorites are carbon and water-rich and contain high-temperature ceramic minerals (CAI), being the least altered materials.
• Cooling down gas in the solar system leads to the formation of calcium-aluminum inclusions (CAI) at high temperatures, followed by rocks and metals, and then volatile materials.
• The solar spectrum has dark lines, indicating it is an absorption spectrum.
• Atoms absorb specific wavelengths, creating gaps in the spectrum.
• The sun's composition matches that of the solar system (based on spectroscopy).
• STARDUST Mission collected debris from outer space and trapped particles in fluffy materials.
• Showed how meteorites in outer space compared to those found on earth.
• Earth consists of oxygen, carbon, and magnesium, which are heavier elements compared to the hydrogen and helium in the sun.
• Measuring element isotopes helps determine the radioactive decay and age.
• Ages of meteorites indicate the age of the solar system.
• Radioactive decay is emission of ionizing radiation from nuclear decay, including alpha, beta, and gamma decay.
• Energy is released during decay, with parent and daughter atoms indicating age.
• Half-life is the time for 50% of an unstable element to decay.
• Primitive meteorite materials formed shortly after heavy elements, indicated by product of radioactive decay.
• The solar system is approximately 4.568 billion years old (Gy).
• The composition of meteorites reflects that of the early solar system.
• Isotopic age dating uses over 40 techniques.
• Energy of decay causes radioactive heating.

Building a Planet and Journey to the Center

• Radioactivity occurs naturally.
• Radioactive isotopes are used to date rocks.
• Rock mantle
• Pressure increases from the surface to the center of earth Uses sound wave to help see what is on the inside
• The interior of Earth consists of a rocky mantle with an iron alloy “steel” core.
• Natural soundwaves help indicate density and movement.
• Density and pressure increase towards the Earth’s center.
• At the surface of the earth are rocks and the mantle.
• Going Inward there is a outer liquid core before a solid inner core
• Pressure = density x depth.

Active surface dating

• Some craters have fluid-like responses .impact velocity very high
• Object hitting a planetary surface creates a pressure wave, zone of very high pressure just underneath pressuring object, behind object is vacuum.
• Crater formed not by impact but by explosion of all materials coming out of high pressure zone direction of impact doesn't matter.
• More craters → older surface (relative timing)
• Relative surface age can be told by number of crater.
• Smaller impacts occur more often, collect over time.
• Can compare crater density to age – can calibrate age vs crater density.
• Rate of crater formation is slower now – cratering is an intrinsic process of planet formation.
• Our planets id dynamic: “solid” Earth moves like a fluid over geological time

Atmospheres and the Coriolis Effect

• Earth's structure results from large-scale separation by density; informs structure and composition.
• Planetary properties and processes are governed by gravity over strength, with time determining deformation and flow over geological timescales.
• Newton's laws of motion hold in an inertia reference frame
• The coriolis effect helps explain how straight lines appear curved to a frame in motion
• The Stratosphere is heated by UV light
• Troposphere: temp decreases with height
• The earth's atmosphere consists of ; nitrogen, then oxygen, then argon, carbon dioxide
• Earth's global wind patterns are driven by atmospheric heating and planetary rotation:
• With the coriolis effect, winds on northern hemisphere are deflected to the right
• Stronger coriolis effect at poles
• Warm air rising at the equator is deflected bc coriolis effect

Explore astronomy with notes on planetary characteristics, the universe's scale, and gravity. Understand the structure of the solar system, meteorites, Earth, atmospheres, and climate. Discover details about planets like Mars and the composition of giant planets.