Astrophysics: Trigonometric Parallax and Kepler's Laws

Trigonometric Parallax

• A method to measure distances to nearby stars
• Measures the apparent shift in a star's position as Earth orbits the Sun
• Distance is inversely proportional to the parallax angle
• Formula: d (in parsecs) = 1 / p (in arcseconds)
• Smaller parallax angles indicate greater distances
• Effective for stars within a few thousand light-years

Kepler's Laws of Planetary Motion

• Describe the motion of planets in our solar system
• First Law (Ellipses): Planets orbit the Sun in elliptical paths, with the Sun at one focus
• Second Law (Equal Areas): Planets move faster when closer to the Sun and slower when farther away
• Third Law (Orbital Periods): A planet's orbital period squared is proportional to its average distance from the Sun cubed. (P^2 ∝ a^3)

Light and Matter Interactions

• Light interacts with matter in fundamental ways
• Emission: Matter emits light when atoms/molecules transition from high to low energy states, releasing photons
• Absorption: Matter absorbs light, increasing its energy
• Transmission: Light passes through matter, potentially altering intensity or direction but not composition
• Reflection/Scattering: Light bounces or scatters off surfaces, depending on surface properties and wavelength

Measured Spectra of Light

• Spectra provide information about matter
• Thermal (Black-body) Spectrum: Continuous spectrum of light based on an object's temperature; intensity follows a curve, with peak wavelength depending on temperature (Wien's law)
• Emission Spectrum: Bright lines at specific wavelengths corresponding to specific energy emissions from excited atoms/molecules
• Absorption Spectrum: Dark lines superimposed on a continuous spectrum, resulting from absorption of light by cooler gases

Proto-planetary Disks

• Rotating disks of gas and dust surrounding young stars
• Birthplaces of planets and stars
• Material coalesces through gravity and angular momentum
• Form planetesimals and eventually larger objects like protoplanets
• Crucial role in planet formation

Planet Formation

• Starts with small dust grains sticking together (coagulation)
• Larger bodies (planetesimals) form through collisions
• Gas giants require rapid growth to capture hydrogen and helium
• Process influenced by solar nebula's temperature, density, and chemical composition

Planetary Cooling

• Larger planets cool more slowly due to retaining internal heat longer, with insulating layers
• Smaller planets cool more quickly

Heat Sources

• Radioactive decay is a primary heat source for planets
• Releases energy, contributing to planetary heating, and maintaining internal processes like volcanic activity and tectonics

Magnetic Fields and Atmosphere Retention

• A liquid, conducting core and rapid rotation generate a magnetic field
• This field shields the atmosphere from solar wind
• Without a magnetic field, atmospheric erosion can occur and surface pressure can decrease

Tidal Heating in Gas Giant Moons

• Gravitational forces from a planet or another moon cause a moon's shape to deform
• Friction within the moon generates heat
• Important heat source for moons of gas giants (e.g., Io, Europa, Ganymede)

Best Places to Search for Liquid Water

• Europa (moon of Jupiter): subsurface ocean beneath its icy crust
• Enceladus (moon of Saturn): plumes of water vapor suggest a subsurface ocean
• Titan (moon of Saturn): possible liquid water beneath the surface
• Ganymede (moon of Jupiter): potential subsurface ocean

Significance of Plumes on Europa and Enceladus

• Plumes of water provide direct evidence of subsurface liquid water
• Allow for indirect sampling of subsurface materials, facilitating exploration without drilling

Titan's Methane Cycle

• Titan has a thick nitrogen atmosphere and a methane cycle (instead of water)
• Methane exists in liquid and gaseous forms due to extremely cold temperatures
• Resembles Earth's water cycle with methane evaporation, cloud formation, precipitation, and collecting in lakes/rivers

Exoplanets

• Planets orbiting stars outside our solar system
• Difficult to observe directly due to their small size and proximity to bright host stars
• Detection methods include radial velocity and transit methods

Number of Discovered Exoplanets

• Nearly 6,000 exoplanets discovered to date
• More expected with improved observational techniques

Radial Velocity and Transit Methods for Detecting Exoplanets

• Radial Velocity: Measures star wobble caused by orbiting planets; determines minimum planet mass
• Transit: Detects the dimming of a star as a planet passes in front; determines planet radius

Radial Velocity Technique and Doppler Shift

• Detects star wobble caused by an orbiting planet via Doppler shifts in the star's light
• Blue shift: moving towards us, red shift: moving away from us
• Measures star's radial velocity, inferring planet presence

51 Pegasi b and Planetary Migration

• Hot Jupiter, challenging early theories of planet formation
• Planetary migration: gas giants can form at greater distances and migrate inward through interactions with the protoplanetary disk or other planets