Lecture 6: Orbital Mechanics / Meteors, Asteroids and Comets (CONTINUED)

Introduction to Orbital Mechanics

• Overview of the chapter topics:

  • Orbital Mechanics

  • Meteorites, asteroids, and comets

• Finish Chapter 7, begin Chapter 9

• Eros image reference: Link (Courtesy of European Space Agency/Halley Multicolor Camera Team).

Units of Measure and Density

• Importance of tracking units of measure:

  • Example: Density of water

    • Standard: 1 g/cm³ = 1000 kg/m³

    • Explanation of conversions:

      • 1 m = 100 cm, therefore,

      • 1 m³ = (100 cm)³ = 1,000,000 cm³ = 10⁶ cm³

      • 1 cm³ of water = 1 g, therefore

      • 1,000,000 cm³ of water = 1,000,000 g = 1000 kg, thus

      • Can represent as (10⁶ g)/(10³ g/kg) = 10³ kg.

Time Conversion

• Calculation of seconds in a year:

  • (365 days/year) × (24 hours/day) × (60 minutes/hour) × (60 seconds/minute)

    • Result: Approximately 31,536,000 seconds/year

    • Alternatively expressed as 3.15 × 10⁷ seconds/year (to three significant figures).

Cannonball and Gravity

• Theoretical scenario of a cannonball:

  • Initial velocity determines travel distance.

  • If sufficient: will orbit the Earth.

  • If fired faster, can escape Earth's gravity.

  • Conceptual illustration: Newton’s cannonball.

Orbital Mechanics and Gravitational Influence

• Gravity's role in orbital mechanics:

  • Orbital period dependence on:

    • Mean orbital distance

    • Mass of the object being orbited

  • Formula:

    • P² = (4π² * a³)/(G * M)

    • G: Gravitational constant = 6.67 x 10⁻¹¹ m³ kg⁻¹ s⁻²

    • a: Semimajor axis (meters)

    • M: Mass (kg) of the planet/star

  • Kepler’s 3rd Law representation: P² ∝ a³.

Orbital Resonance

• Gravitational interactions between objects:

  • Orbital resonance defined.

  • Effects:

    • Stabilize orbits (e.g., Galilean satellites)

    • Cause instability leading to orbital changes.

  • Reference for more details: Wikipedia on Orbital Resonance.

Kirkwood Gaps

• Definition and implications:

  • Gaps in the asteroid belt caused by:

    • Orbital resonance with Jupiter.

  • Result: Asteroids can become unstable and are ejected from these orbits.

Characteristics of Asteroids and Comets

• Orbital characteristics:

  • Both can exhibit highly elliptical orbits.

  • Comet orbits may be inclined relative to the Ecliptic plane.

  • Caused by gravitational interactions, particularly with giant outer planets (Jupiter, Neptune).

Evolution of Orbits and Earth-Crossing Objects

• Impact of gravitational interactions:

  • Continuous interaction leads to changes in smaller body orbits.

  • Possibility of crossing orbits of inner Solar System planets, including Earth.

Earth-Crossing Asteroids

• Identification of significant numbers:

  • Over 7,000 identified asteroids with Earth-crossing paths.

  • Most large ones (>1 km) found; currently no immediate threat detected.

  • Ongoing search for smaller objects with unknown impacts.

Asteroid 99924 Apophis

• Notable near-Earth asteroid:

  • Initial 2004 predictions suggested a 2.4% chance of collision in 2029.

  • Further observations ruled out this threat.

Importance of Comets and Asteroids

• Leftover building blocks of the Solar System:

  • Vital for understanding Solar System's formation.

  • Potential risks posed by rogue bodies.

Asteroid Belt Overview

• Location and composition:

  • Situated between Mars and Jupiter.

  • Consists of thousands of bodies, ranging from <1 km to nearly 1000 km in size.

  • Source of most meteorites.

Characteristics of Asteroid 4 Vesta

• Profile of Vesta:

  • 2nd largest asteroid in the belt (diameter = 525 km).

  • Surface composition akin to a specific class of meteorites (Eucrites).

  • Initially hot and partly molten, leading to a differentiated structure.

Differentiated Structure of Vesta

• Evidence for Vesta’s structure:

  • Suggested layers: core, mantle, and crust.

  • Indication of past geological activity and heating processes.

Reflectance Spectra of Asteroids

• Spectral analysis significance:

  • Different materials absorb varying light wavelengths.

  • Diverse reflectance spectra show a range of compositions among asteroids.

Comparison of HED Meteorites with Vesta

• Reflectance matches indicate:

  • Similar composition between HED meteorites and asteroid 4 Vesta.

Comet Characteristics

• Definition of comets:

  • Typically small (<10 km), composed of ice and rock.

  • Represent planetesimals contributing to giant planet cores.

• Significance:

  • Offer insights into the formation of the outer Solar System.

Historical Comet Observations

• Highlight on historical records:

  • 1066 AD comets noted by William of Jumièges.

Comet Coma Formation

• Process when approaching the Sun:

  • Heating sublimates ice, creating a coma (transient atmosphere).

  • Composition of gases largely water (≈90% H2O) with other trace gases.

Comet Tail Dynamics

• Gas and dust tail features:

  • Gas tail fluoresces from sunlight ionization, oriented away from the Sun.

  • Dust tail follows orbit of the comet.

Meteor Showers and Comet Intersections

• Relationship between comets and meteor showers:

  • Comet debris creates meteor showers when intersecting Earth's orbit.

  • Examples: Perseids (Swift-Tuttle), Orionids (Comet Halley).

Comet Nucleus Characteristics

• Description of the nucleus:

  • Solid center, ranging from ~100 m to >40 km.

  • Composed of rock, dust, water, and various ices, including organic compounds.

Philae Lander Mission

• Historic event:

  • On November 14, 2014, Philae was the first robotic lander on a comet.

  • Challenges of landing on a low-gravity surface.

Conclusion and Future Topics

• Upcoming content to cover:

  • Meteorites, asteroids, and comets continuation.

  • Finish Chapters 7 and 9.

• Eros image reference: Link (Courtesy of European Space Agency/Halley Multicolor Camera Team).