The roots of orbital mechanics can be traced back to the 17th century when astronomer Johannes Kepler (1571-1630) published three laws relating to orbital motion. Nearly 60 years later, Sir Isaac Newton (1642-1727) confirmed Kepler's work with his laws of motion.
While Kepler believed his laws applied only to celestial bodies orbiting the Sun, Newton proved that Kepler's laws applied to any satellite in orbit around any celestial body.
Keplerian Elements
Our studies into modern orbital mechanics include the following applications:
- Ascent/Re-entry Trajectories -- Calculating ascent/descent guidance to establish optimized flight dynamics with emphasis on angle of attack and lateral/axial loading.
- Orbital Maneuvers -- Determining optimal thrust vectoring and fuel consumption parameters for orbital insertion, circularization, transfer, rendezvous, and re-entry phases of a flight.
- TransLunar/Interplanetary Transfers -- Calculating velocity expenditures and departure velocity vectors for heliocentric transfer orbiting thresholds.
Through formulaic computations and software simulations, we gather detailed elemental trajectory data for Earth-orbiting satellites. Our on-going research provides statistical analysis in determining orbital perturbations, fuel consumption rates, atmospheric drag, and decay calculations.
Keplerian Orbital Elements
Real Time Satellite Tracking
View current Earth orbiting satellite trajectories
Johannes Kepler (1571 - 1630)Building on Tycho Brahe's work, Kepler formulated three laws of planetary motion:
I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse, and the other focus empty.
II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.
III. The square of the planet's period of revolution is directly proportional to the cube of its mean distance from the Sun.
Isaac Newton (1643 - 1727)
In 1687, Newton published the single greatest work in the history of science, the Principia Mathematica. He described the three laws of motion and the law of universal gravitation:
I. Every object in a state of uniform motion tends to remain in that state unless acted upon by an external force.
II. Force is equal to the change in momentum per change in time.
III. For every action, there is an equal and opposite reaction.
The law of universal gravitation states: Every object attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.