Short history of astrodynamics

What is astrodynamics? Several definitions could be given (each textbook has its own), and I personally prefer the following, taken from Griffin, Space vehicle design:

Astrodynamics is the study of the motion of man-made objects in space subject to both natural and artificially created forces

If we totally rely on the definition above, from the historical point of view we should limit the historical background from the ' 50 of last century. Nevertheless, for a complete comprehension of the phenomenon that characterize the matter, it is essential to take a look into the astrodynamics predecessor: astronomy and celestial mechanics.

Nicolaus Copernicus (1473-1543)

Among the famous ancient astronomers a very important place is occupied by Nicolaus Copernicus, whose main merit was the formulation of the hypothesis that the Earth is not in the center of the universe, but instead that it, together with all the other celestial bodies, turns around the Sun that occupies the reference position. Copernicus published this revolutionary work only just before his dead - that happened in 1543 - due the huge difficulties that such hypothesis would bring to his life. Its name is De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres).

The Copernicus assumptions were so strong that all the philosophical and religious convictions had changed after they influence, even if the last Copernicus work contains several inaccuracies: we can think for example that he guessed the orbits as circular instead of elliptical. Despite of such inaccuracies, Copernicus started its own "revolution" whose consequences arrived till to us.

Galileo Galilei (1564-1642)

Galileo is certainly one of the most eminent personality that italian scientific history can remember. Even if he started in studying medicine, shortly after he started his travel into applied science through hydraulics and mechanics. He was named professor is Pisa and Padova universities and astronomy became his principal interest. He shared the Copernicus theories about the Solar System, and started direct observation by introducing the utilization of the telescope for scientific purposes.

Between 1610 and 1615 his works started to irritate the Roman Catholic Church, that considers them as contradictor respect to the Holy Scriptures. The relationships between Galileo and the Church made worse in a short lapse of time and finally they broke in 1630, after the publication of "Dialogo sopra i due massimi sistemi del mondo" where the Copernicus thesis was supported to the detriment of the geocentric one. In 1632 he was judged by the Inquisition for its positions and was condemned to the abjuration of the Copernican thesis; he was also put in prison and his "Dialogo" was put aside. At the end of the time passed in prison, he was exile in Arcetri, where its health status dropped quickly till he became blind. He died in exile in 1642. In 1992 (after 359 years) the Catholic Church rehabilitated Galileo, recognizing his true faith and his sincere honesty.

Johannes Kepler (1571-1630)

Fortunately, the fertile soil of that period gave to the humanity other exceptional minds. Kepler, together with Tycho Brahe (a Danish astronomer known for his very accurate observations), contributed in a very significant way to the modern astrodynamics. In 1601 he became the mathematician of the emperor Rudolph II's Court and inherited a large set of data relevant to the planet's position. Mars was the most observed planet due the high eccentricity of its orbit; after many years of work he published in 1609 the book "Astronomia nova", which contains the first two laws about the motion of the planets. The third law was published only in 1619, in a book named "Harmonices mundi".

 The three Kepler's laws of planetary motion are here reported:

1) The orbit of every planet is an ellipse with the Sun at a focus

2) The line joining a planet and the Sun sweeps out equal areas during equal intervals of time

3) The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

Law #1 states that, contrary to the Copernicus hypothesis, every planet follows an elliptical path (very close to a circular path, to be honest). This leads to the definition of a certain amount of elements directly from the plane geometry. One of the most important is the semimajor axis that gives an immediate idea about the dimension of the orbit.

Law #2 gives the rule that drive the velocity of the planet respect to the Sun: lower is the distance, higher is the speed. The figure below (source Wikipedia) shows in green the velocity vector: its size is maximum when the point is close to the focus and is minimum when is far away from it. The swept area (the blue one) is constant over time.

Law #3 means that the largest is the orbit, the greatest is the period of time needed to travel it. It put in relation the orbital period with the semimajor value.

The Kepler's laws allowed the formulation of the gravitation's law that made Isaac Newton a legend of the human history.

Isaac Newton(1642-1727)

There are few men in the human history whose works changed the course of the events and that can be appointed as "universal genius": Sir Isaac Newton is certainly one of them. Philosopher, mathematician, physicist and alchemist, in the early phases of his career he approached the basis of the differential calculus that would become of paramount importance for the demonstration of his assumptions about gravitation. Some of his efforts were also spent in the field of the optic where he demonstrate that a prism breaks down the white light into the colors of the optical spectrum, but the reason for which Newton will remain into the history is of course for his exceptional discoveries in the field of classical mechanics. The legend tells about an apple that fell in his head during a nap in his country house: for which reason the Moon does not fall in the same manner? To answer to that question, Newton will publish, in 1687, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), a masterpiece that became for more than 300 year the absolute reference book for any science or mechanical scholar.

The "Principia" contains also the three laws (equations) of motion, carrying pillars of the entire classical mechanic that each student sooner or later faced during his/her scientific studies:

1) Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force

2) A body of mass m subject to a force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F = ma

3) The mutual forces of action and reaction between two bodies are equal, opposite and collinear

However, the immortal mark leaved by Newton of astrodynamics is contained into the third book of the "Principia", well-know as law of universal gravitation:

Two bodies whose mass is respectively M and m attract each other with a force proportional to their product and inversely proportional to their distance.

The consequences of this relation are extraordinary: Newton contributed to the development of modern vision of the world; he was at the height of a marvellous period and can be collocated among the main personality of the human history, even if he wrote in a famous letter to his colleague Hooke: "if I have seen further it is by standing on the shoulder of the giants".

... and yes, Pink Floyd is my favorite rock band. And when you think of them, you cannot avoid to think their most famous record's cover, that is exactly what Newton saw during his optical experiments...a cool scientist...