satellite

Page 1: Introduction to Astronomy and Early Theories

Ancient Observations

  • Early humans observed the night sky, documenting star patterns.

  • Beliefs: Earth was flat.

Key Figures

  • Aristotle: Proved Earth is round (ca. March).

  • Ptolemy: Introduced the geocentric theory; Earth at the universe's center.

  • Nicholas Copernicus: Developed the heliocentric theory (15th century), proposing Earth orbits the Sun.

Evolution of Astronomy

  • Transition to orbital mechanics as a detailed study of planetary motions.

Page 2: Kepler's Laws of Planetary Motion

Overview

  • Johann Kepler (Early 1600s) used Tycho Brahe's observations to formulate laws of motion.

Kepler's Laws

  • First Law: Planets in elliptical orbits with the sun at one focus. (applies to Earth and satellites).

  • Second Law: Law of areas; planets cover equal areas in equal time. Speed varies with distance from the Sun (or Earth).

  • Third Law: Square of orbital period is proportional to the cube of mean distance from the sun. Applies to satellite orbits—further out means longer periods and slower speeds.

Page 3: Newton and Classical Mechanics

Isaac Newton's Contributions

  • Integrated Kepler's work to formulate principles of classical mechanics.

Universal Gravitation

  • Objects attract each other based on mass and distance.

Laws of Motion

  • First Law: Objects maintain motion in same path without external force.

  • Second Law: Acceleration of an object is dependent on net force (F = ma).

  • Third Law: For every action, there is an equal and opposite reaction (e.g., rocket propulsion).

Page 4: Projectile and Satellite Motion

Projectile Motion

  • Horizontal firing vs. Earth curvature; sufficient velocity achieves orbit.

  • Escape Velocity: Approx. 7 miles/sec to surpass Earth's gravity.

Orbital Elements

  • Six key numbers describe an orbit's characteristics:

    • Semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, time of perigee passage.

Semi-major Axis

  • Defines size of the orbit; for circular orbits, half the diameter.

Page 5: Orbit Definition and Orientation

Eccentricity

  • Indicates orbit shape (0 is circular, between 0-1 is elliptical).

Coordinate System

  • Geocentric Equatorial Coordinate System: Non-rotating reference system with Earth’s center as origin.

    • X-axis: Points to the vernal equinox.

    • Z-axis: Aligned with Earth's spin axis.

    • Nodes: Points where the orbit crosses the equatorial plane.

Page 6: Launch Dynamics

Launch Considerations

  • Ideal conditions affect launch windows (lighting, orbit timing, etc.).

Rocket Design

  • Most rockets are multi-stage to optimize payload by discarding weight.

Space Shuttle Launch

  • Requires precise timing of thrust applications for effective orbit insertion.

Page 7: Satellite Operations and Delta V

Adjusting Orbits

  • On-orbit burns are vital to maintain or change satellite orbits.

  • Delta V: Measure of change in velocity, critical for mission planning.

Types of Burns

  • Posigrade Burn: Increases altitude and velocity.

  • Retrograde Burn: Reduces speed and lowers orbit.

Page 8: Hohmann Transfer and Maneuvers

Hohmann Transfer Orbit

  • Most fuel-efficient transfer method between two orbits (perigee and apogee burns).

Plane Change Maneuvers

  • Changing satellite inclination is fuel-intensive and special maneuvers must be executed.

Page 9: Satellite Design and Field of View

Satellite Tasks

  • Field of View: Area visible from the satellite strongly influenced by altitude.

    • High-altitude satellites have a larger coverage area.

Geosynchronous vs. Geostationary Orbits

  • Geosynchronous: Appears to hover above a fixed point.

  • Geostationary: Fixed above the equator for constant communication.

Page 10: Specialized Satellite Orbits

Other Satellite Orbits

  • Molniya Orbit: Highly eccentric, ideal for northern communications.

  • Sun-Synchronous Orbit: Precesses with Earth’s rotation for consistent light conditions.

Page 11: Orbital Perturbations

Effects on Orbits

  • Small forces causing deviations: solar winds, gravitational pull of other celestial bodies.

Maintaining Orbit

  • Adjustments and thruster firings may be necessary to keep satellites in serviceable paths.

Page 12: Conclusion and Launch Considerations

Spacecraft Lifecycle

  • Satellites may be left in orbit or deorbited depending on their operational life.

  • Retrograde burns for spacecraft return processes.

Final Thoughts

  • Understanding these principles illuminates the intricacies of satellite motion and space exploration, leading to informed perspectives on launches.