Celestial mechanics: Kepler’s laws, Orbit nomenclature, orbit motion and orbit transfer
Kepler’s Laws
Originally formulated from observations, but obtainable and provable through Newton Gravitational
Theory
1. Planets move in elliptical orbits with the Sun at one focus of the ellipse.
2. The line joining the Sun to a planet sweeps out equal areas in equal times.
3. The square of the orbit period, τ, is proportional to the third power of the semi-major axis of
the orbit, a, i.e. t 2∝ a 3
Kepler’s laws were formulated for the Sun-Earth system but they apply to all bounded orbits, e.g. All
the planets of the solar system, all the satellites orbiting around a planet, etc…
1st Kepler Law
Planets move in elliptical orbits with the Sun at one focus of the ellipse.
Nomenclature
1. Period of the orbit is the time taken by the orbiting body to go around the orbited body
once.
2. True Anomaly is the angle swept by the line connecting the orbiting and the orbited objects.
It is measured from the line connecting the orbited object to the periapsis.
3. Periapsis is the point of the orbit with the smallest distance between the orbiting and the
orbited object
4. Apoapsis is the point of the orbit with the largest distance between the orbiting and the
orbited object
, Celestial mechanics: Kepler’s laws, Orbit nomenclature, orbit motion and orbit transfer
Are all orbits elliptical? NO
Kepler’s Laws
Originally formulated from observations, but obtainable and provable through Newton Gravitational
Theory
1. Planets move in elliptical orbits with the Sun at one focus of the ellipse.
2. The line joining the Sun to a planet sweeps out equal areas in equal times.
3. The square of the orbit period, τ, is proportional to the third power of the semi-major axis of
the orbit, a, i.e. t 2∝ a 3
Kepler’s laws were formulated for the Sun-Earth system but they apply to all bounded orbits, e.g. All
the planets of the solar system, all the satellites orbiting around a planet, etc…
1st Kepler Law
Planets move in elliptical orbits with the Sun at one focus of the ellipse.
Nomenclature
1. Period of the orbit is the time taken by the orbiting body to go around the orbited body
once.
2. True Anomaly is the angle swept by the line connecting the orbiting and the orbited objects.
It is measured from the line connecting the orbited object to the periapsis.
3. Periapsis is the point of the orbit with the smallest distance between the orbiting and the
orbited object
4. Apoapsis is the point of the orbit with the largest distance between the orbiting and the
orbited object
, Celestial mechanics: Kepler’s laws, Orbit nomenclature, orbit motion and orbit transfer
Are all orbits elliptical? NO
