Kepler's Laws and Orbital Mechanics

• Planets orbit the sun in elliptical paths, with the sun at one focus point.
• A line from the planet to the sun sweeps out equal areas in equal time intervals.
• The square of a planet's orbital period is proportional to the cube of its semi-major axis.

Eccentricity of an Ellipse

• Eccentricity measures deviation from a perfect circle
• Eccentricity is defined as e=c/a, where c is the distance from the center to the foci and a is the semi-major axis
• Eccentricity satisfies 0≤e<1
• If e=0, the ellipse is a circle where the foci coincide with the center
• As e approaches 1, the ellipse becomes highly elongated

Conservation of Energy

• Energy cannot be created or destroyed, only transformed from one form to another.
• The total energy in a closed system remains constant over time
• E total = E initial = E final

Forms of Energy and Indicators

• Kinetic: object in motion
• Gravitational potential energy: height above ground
• Elastic potential energy: stretched or compressed material
• Chemical energy: energy stored in bonds
• Thermal: heat, temperature change
• Electrical: flow of electricity
• Nuclear: atomic reactions
• Electromagnetic: light, radiation waves
• Sound: vibrations, waves in a medium
• Mechanical: motion or stored energy

Photon Wavelengths

• Shorter wavelength = higher frequency = higher energy
• Longer wavelength = lower frequency = lower energy

Emission Spectrum

• Atoms absorb energy.
• Electrons move to higher levels, then emit photons as they return to lower levels.
• This process forms a unique bright-line spectrum.

Absorption Spectrum

• Atoms absorb specific wavelengths of light.
• The spectrum shows dark lines where those wavelengths are missing.

Observed Light and the Doppler Effect

• Wavelength of the observed light changes due to the doppler effect
• Blueshift occurs when object approaches the observer
• Light waves get compressed
• Redshift occurs when object moves away from the observer
• Light waves get stretched

Atoms vs Molecules

• Atoms have only electric energy levels, while molecules have electronic, vibrational, and rotational energy levels
• Atoms have sharp, well-defined spectral lines, while molecules have broader lines due to multiple transitions
• Atoms absorb/emit visible and UV light, while molecules absorb/emit visible, UV, infrared, and microwave light

Solar Emission Spectrum

• Broad spectrum of electromagnetic radiation, including a blackbody spectrum and hydrogen, helium, oxygen, calcium, and iron absorption lines.

Galileo's Observations Supporting Heliocentric Model

• Phases of Venus: Venus has full and gibbous phases
• Moons of Jupiter: Discovered 4 large moons orbiting Jupiter in 1610, contradicting the idea that all celestial bodies orbit Earth

Angular Resolution

• Smaller angular size = more detail resolved.
• On Earth: Atmospheric turbulence limits resolution (~1 arcsecond), while diffraction depends on aperture. Adaptive optics can improve resolution.
• In Space: No atmospheric turbulence, resolution is limited by diffraction. Larger apertures and space interferometry can further improve resolution.

Telescope Size and Light Collection

• The telescope's aperture size affects its light-gathering ability
• The area is proportional to the square of the aperture diameter A = πr²
• Larger apertures collect more light
• Enabling the telescope to observe fainter objects and capture more detail
• Bigger telescopes can observe dimmer and more distant objects

Processes Responsible for Surface Geology

• Crater Impacts
• Tectonism
• Volcanism
• Erosion

Surface Characteristics

• Rough surface: scatters light, appears matte, and shows texture
• Smooth surface: reflects light uniformly, appears glossy or mirror-like
• Microscopic features: roughness reveals material structure and how it interacts with light.
• Functionality: roughness can indicate grip (rough) or aesthetic appeal (smooth)

Earth's Interior

• Density & Composition: Seismic data indicate the core's density and the mantle's semi-solid nature.
• Magnetic Field: It suggests a liquid, iron-rich core.
• Gravity: Gravitational measurements show mass distribution inside Earth.

Criteria for Planetary Differentiation

• Heat: Internal heat from decay, compression, or impacts melts the planet's interior.
• Density Differences: Denser materials (iron, nickel) sink to form the core
• Lighter materials (silicates) rise to form the mantle and crust.
• Gravitational Forces: Gravity helps separate materials into layers.
• Size: Larger planets retain more heat, aiding differentiation.

Greenhouse Gases

• Absorb Infrared Radiation: Trapping heat by absorbing infrared radiation from Earth's surface.
• Re-radiate Heat: Gases re-radiate heat, including back to Earth, maintaining warmth.
• Regulate Temperature: They help keep Earth's temperature stable.
• Global Warming: Excess GHGs (e.g., CO2, methane) trap more heat, contributing to global warming.

Volcanism on Inner Planets and the Moon

• Venus: Volcanic activity likely contributes to a thick atmosphere and high surface temperatures; some volcanoes may still be active.
• Mars: Evidence of ancient volcanic activity with massive volcanoes, but little current volcanism.
• Earth: Active plate tectonics and volcanism shape the surface, contribute to the atmosphere, and support life.
• Moon: Volcanic activity in the past created maria (dark plains), but there is no current volcanism.

Venus and Earth Comparison

• Size and Composition: Both are similar in size, mass, and rocky composition
• Orbital Position: Both are inner planets near the Sun.
• Atmosphere: Venus has a thick CO2 atmosphere, causing extreme heat, while Earth has a balanced atmosphere supporting life.
• Surface: Venus is extremely hot with no liquid water, while Earth has liquid water and moderate temperatures.
• Rotation: Venus has a slow, retrograde rotation, while Earth has a standard day/night cycle
• Venus' Greenhouse Effect traps heat, whereas Earth's atmosphere supports life and moderates temperature