Astrophysics: Trigonometric Parallax and Kepler's Laws

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Questions and Answers

What causes tidal heating in gas giant moons?

Chemical reactions within the moon's crust

Gravitational forces leading to shape deformation (correct)

Direct sunlight on the moon's surface

Solar winds impacting the moon's atmosphere

Which moon of Saturn is known for its plumes of water vapor suggesting a subsurface ocean?

Enceladus (correct)

Rhea

Titan

Tethys

What unique feature does Titan have compared to other moons in the solar system?

Direct evidence of microbial life

A surface covered in liquid water

An atmosphere rich in methane (correct)

Active volcanoes creating tidal heating

How do astronomers typically detect exoplanets?

Through changes in star brightness and wobbles Signup and view all the answers

Which one of the following moons is NOT suggested to have conditions suitable for liquid water?

Titan Signup and view all the answers

What is the significance of the plumes discovered on Europa and Enceladus?

They provide indirect sampling of subsurface materials. Signup and view all the answers

What is the approximate number of exoplanets discovered to date?

Nearly 6,000 Signup and view all the answers

What does the Radial Velocity Method measure in the context of exoplanets?

The wobble of a star caused by orbiting planets Signup and view all the answers

What is the relationship between parallax angle and distance to a star?

Distance is inversely proportional to the parallax angle. Signup and view all the answers

According to Kepler's First Law, how do planets move in relation to the Sun?

In elliptical orbits with the Sun at one focus. Signup and view all the answers

Which of the following best describes the purpose of Kepler's Third Law?

To calculate the distance of planets based on their orbital period. Signup and view all the answers

What happens to light when it is absorbed by matter?

Absorbed light excites electrons to higher energy levels. Signup and view all the answers

How does the change in speed of a planet related to its distance from the Sun, according to Kepler's Second Law?

Planets move faster when they are closer to the Sun. Signup and view all the answers

What type of spectrum is produced by objects based on their temperature?

Thermal (Black-body) Spectrum Signup and view all the answers

What is the effect of transmission on light as it passes through matter?

Light's intensity or direction may alter but not its composition. Signup and view all the answers

What aspect of light does reflection/scattering depend on?

The surface properties and the light’s wavelength. Signup and view all the answers

What does the peak wavelength of radiation depend on, according to Wien's Law?

Temperature of the emitting source Signup and view all the answers

What is the primary process through which planetesimals are formed?

Coagulation of dust grains Signup and view all the answers

Which of the following factors does NOT influence planet formation?

Astrophysical turbulence Signup and view all the answers

What is the main heat source for most planets today?

Radioactive decay Signup and view all the answers

What is required for a planet to generate a magnetic field through the dynamo effect?

A liquid, conducting core and rapid rotation Signup and view all the answers

How do larger planets cool compared to smaller planets?

They cool more slowly due to heat retention Signup and view all the answers

What effect does a magnetic field have on a planet's atmosphere?

It protects the atmosphere from solar wind Signup and view all the answers

What happens to a planet without a significant magnetic field over time?

The atmosphere may be stripped away slowly Signup and view all the answers

Study Notes

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

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Description

This quiz covers essential concepts in astrophysics, including the method of trigonometric parallax for measuring star distances and Kepler's laws of planetary motion. Participants will explore how these principles describe the motion of celestial bodies and the interactions between light and matter. Test your understanding of these foundational topics in the study of the universe!