8.1.7 Non-Circular Orbits

• What are non-circular orbits also known as?

  Elliptical orbits
• What are the two main types of orbits?

  • Circular Orbits: Path is a perfect circle around a central body.
  • Elliptical Orbits: Path is an elongated circle (ellipse).
• What is an elliptical orbit?

  An elliptical orbit is an elongated, oval-shaped path followed by a celestial body around a focal point.
• What are Kepler's Laws of Planetary Motion?

  1. First Law (Law of Ellipses): All planets move in elliptical orbits with the Sun at one focus.

  2. Second Law (Law of Equal Areas): A line connecting a planet to the Sun sweeps out equal areas in equal times.

  3. Third Law (Law of Harmonies): The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.
• What does Kepler's First Law state?

  All planets move in elliptical orbits with the Sun at one focus.
• What does Kepler's Second Law describe?

  A line connecting a planet to the Sun sweeps out equal areas in equal times, meaning planets move faster when closer to the Sun.
• What is the implication of Kepler's Third Law?

  The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.
• What defines an ellipse?

  An ellipse is defined by its two foci, with the sum of the distances from any point on the ellipse to these two foci being constant.
• What are the key parameters of an ellipse?

  • Semi-Major Axis (a): The longest radius of the ellipse.
  • Semi-Minor Axis (b): The shortest radius of the ellipse.
  • Eccentricity (e): A measure of how elongated the ellipse is, calculated as \( e = \frac{c}{a} \).
• What is the semi-major axis of an ellipse?

  The semi-major axis is the longest radius of the ellipse, stretching from the center to the furthest edge.
• What is the semi-minor axis of an ellipse?

  The semi-minor axis is the shortest radius of the ellipse, perpendicular to the semi-major axis.
• How is eccentricity defined in relation to an ellipse?

  Eccentricity is a measure of how elongated the ellipse is, ranging from 0 (a perfect circle) to 1 (a highly elongated ellipse).
• How is eccentricity calculated?


  Eccentricity is calculated as \( e = \frac{c}{a} \), where \( c \) is the distance from the center to a focus.
• What are perihelion and aphelion in an orbit?

  • Perihelion: The point in the orbit where the celestial body is closest to the Sun.
  • Aphelion: The point in the orbit where the celestial body is farthest from the Sun.
• How does orbital speed vary in an elliptical orbit?

  A body moves faster when it is closer to the Sun (perihelion) and slower when it is farther from the Sun (aphelion).
• What is Kepler's Third Law equation?


  For any orbiting body:

  \[

  T^2 \propto a^3

  \]

  where \( T \) is the orbital period and \( a \) is the semi-major axis of the ellipse.
• What role does gravitational force play in orbital motion?

  The gravitational force provides the centripetal force needed to keep the body in orbit.
• What is the formula for gravitational force according to Newton's law of gravitation?


  The formula is \( F = \frac{G M m}{r^2} \).
• What are practical examples of elliptical orbits in our solar system?

  • Earth’s Orbit: Closest to the Sun in January (perihelion) and farthest in July (aphelion).
  • Cometary Orbits: Typically highly elliptical, bringing them close to the Sun and then far out into the Solar System.
• What are the key characteristics of elliptical orbits?

  • Oval shape
  • Described by Kepler’s laws
  • Key parameters include semi-major axis, semi-minor axis, and eccentricity
  • Variations in orbital speed based on distance from the central body
• Why is understanding non-circular orbits important in astrophysics?

  Understanding non-circular orbits helps explain a wide range of astronomical phenomena and is fundamental to both classical and modern astrophysics.