1 1 Introduction

Chapter 1 Introduction

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Introduction

Galileo Galilei (1564-1642). Italian natural Philosopher, Astronomer and Mathematician who made fundamental contributions to the development of the scientific method and to the sciences of motion, astronomy and strength of materials.

The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the Universe to do.

Galileo Galilei (1564-1642)

1.1Why is Space So Amazing and So Attractive?

Getting into space is tremendously expensive and associated with many challenges and even risks. Recall, for instance, the most recent tragic space shuttle accidents, in which the entire crews of Challenger and Columbia were lost in 1998 and 2003 respectively¹. So why do humans bother the cost and take the risk? The answer to this question is several folds. Space offers human kind several compelling advantages which have been exploited in modern societies. It provides a global perspective - Space provides the highest post for surveillance and resource monitoring. Space also provides a universal perspective - un-obscured view of the heavens above all metropolitan, weather and pollution effects which obscure Earth telescopes. In addition, space offers a unique environment - a free-fall environment which can be used to perform unprecedented material and biological experiments. Finally, space has an abundant storage of resources which can be used to replace depleting Earth resources. Human eminent curiosity and intrinsic longing for knowledge has always been a strong drive for exploration in land, sea and space.

1.2What is Space Mechanics?

Space mechanics is the branch of mechanics, which studies the motion of objects traveling into space – subject to all possible forces. These objects may be celestial or heavenly bodies created by God such as the Earth, the Sun, and the Moon; or vehicles made by man such as satellites, space shuttles and space probes. The branch of the subject studying the former objects is usually referred to as celestial mechanics, whereas the branch studying the latter is usually referred to as astrodynamics². Orbital mechanics may be considered as a synonym for space mechanics.

Claudius Ptolemaeus (83–168), known in English as Ptolemy. Greek-Egyptian mathematician, astronomer, geographer and astrologer. He was born, lived and died in Roman Egypt. He was the author of several scientific treatises, which had great importance to later Islamic and European science. His most famous treastise on astronomy is now known as the Almagest, or “The Great Treatise. The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world.

The Hubble Space Telescope's launched in 1990. Its position above the atmosphere, which distorts and blocks the light reaching Earth, gives it a view of the universe that far surpasses that of ground-based telescopes.

Astronomy is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation). It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the formation and development of the universe. Therefore, in a correct sense, space mechanics may also be considered as a branch of astronomy. Old or even ancient astronomy is not to be confused with astrology, the belief system that claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin and a part of their methods (namely, the use of ephemerides), they are clearly distinct³.

1. Historical Background

As a child of astronomy, the historical roots of space mechanics may be traced back in the history of astronomy and even tangled in some ancient periods with the false science of astrology. In the following historical overview, we will focus on the achievements made to astronomy with no mention to astrology even if such achievements were in fact intended to serve the need for better astrological prediction.

1.2.1Ancient Astronomy

Early cultures identified celestial objects with gods and spirits. They related these objects (and their movements) to climate and weather changes such as rain, drought, seasons, and tides.

Naṣīr al-Dīn al-Ṭūsī, or Tusi (1201-1274). Persian astronomer, philosopher, physician, mathematician, physician, physicist, and theologian. Tusi made very accurate tables of planetary movements as depicted in his book Zij-i ilkhani. Tusi invented a geometrical technique called Tusi-couple, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy's problematic equant.

Omar Khayyam (1048-1131). Persian poet, mathematician, and astronomer. Khayyam measured the length of the year as 365.24219858156 days, which shows an incredible confidence. For comparison the length of the year at the end of the 19th century was 365.242196 days, while today it is 365.242190 days.

Calendar systems were developed usually based on the Sun and Moon apparent motion and were of great importance to agricultural societies. Babylonian astronomy was the basis for much of the astronomical traditions that later developed in Greek and Hellenistic astronomy, in classical Indian astronomy, in Sassanid, Byzantine and Syrian astronomy, in medieval Islamic astronomy, and in Western European astronomy. Babylonians invented a sexagesimal (base 60) number system which is still used in the modern practice of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians.

Beginning around 600 BC, Greek philosophers and scientists developed a number of important astronomical ideas. The early Greek astronomers knew many of the geometrical relationships of the heavenly bodies. Pythagoras, who lived during the 500s BC, argued that the earth was round.

He also tried to explain the nature and structure for the universe as a whole. He developed an early system of cosmology. In about 370 BC, Euxodus of Cnidus had developed a mechanical system to explain the motion s of the planets. Euduxos taught that the planets, sun, the moon, and the stars revolved around the earth. In 300s BC, Aristotle incorporated this earth centered or geocentric, theory into his philosophic system.

Ptolemy was the author of several scientific treatises including the astronomical treatise, Almagest. His Planetary Hypotheses went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1210 Earth radii while the radius of the sphere of the fixed stars was 20,000 times the radius of the Earth.

1.2.2Islamic Astronomy

In the history of astronomy, Islamic astronomy or Arabic astronomy refers to the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (8th-16th centuries), and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Islamic Spain, North Africa, and later in China and India.

Astrolabe is a sophisticated tool for observing the position of the stars which was invented in ancient Greece and vastly improved in early Islam. Through Islamic Spain, the new astrolabe was introduced to Europe.

Muhammad ibn Jabir al-Batani (858–929) Latinized as Albategnius, Albategni or Albatenius. Arab astronomer, astrologer, and mathematician. One of his best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds.

It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science that was essentially Islamic. These included Indian, Sassanid and Hellenistic works in particular, which were translated and built upon. In turn, Islamic astronomy later had a significant influence on Indian and European astronomy (see Latin translations of the 12th century) as well as Chinese astronomy. ⁴

It is really interesting to note that Muslims were in fact the first to differentiate and separate the science of Astronomy from the pseudo science of astrology. A significant number of stars in the sky, such as Aldebaran and Altair, and astronomical terms such as alhidade, azimuth, and almucantar, are still today recognized with their Arabic names.

A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world, many of which have not been read or cataloged. Even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed.

An important area in Astronomy is optics. It is very relevant in the development of tools for observation like telescopes that employ lenses or mirrors. Ibn al-Haytham (the Latin Alhazen) studied the property of lenses, discovered the camera obscura, explained correctly the process of vision, studied the structure of the eye, and explained for the first time why the sun and the moon appear larger on the horizon (very simply put, it is because the thicker layer of atmosphere at the horizon acts as magnifying lens compared to overhead).

Other Muslim mathematicians such as Khayyam and al-Tusi examined Euclidean geometry that is the geometry of flat surfaces. The Muslim mathematicians, especially al-Battani, Abu'l-Wafa', Ibn Yunus and Ibn al-Haytham, also developed spherical Astronomy. Euclidean and spherical geometry are particularly useful in studying the overall geometry of the Universe in the study of cosmology.




Nicholas Copernicus (1473-1543). Polish astronomer and mathematician. He began to believe that the earth went round the sun about 1507 and from that time until his death worked, more or less intermittently, on his exposition of his theory. He delayed the publication of this exposition because of fear of being accused of heresy.




Johannes Kepler (1571 - 1630). German mathematician and astronomer who discovered that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. He also did important work in optics and geometry.

The Muslims also applied their astronomical knowledge to questions of time-keeping and the calendar in making almanacs, this word too being Arabic in origin. The most exact solar calendar existing to this day is the Jalali calendar which was developed under the direction of Omar Khayyam in the 12th century. This is still in use in Persia and Afghanistan⁵.

Many people think that “the Arabs gave us (the) zero”. It is more appropriate to look at the phenomenon of Islamic science within its own cultural context. Then, if we want to compare, we discover that actually, as far as astronomy is concerned, little was achieved in Europe until ca. 1550 that had not been achieved previously by Muslim scholars at some time between the 9th and the 15th century.⁶

1.2.3 Medieval European Astronomy

Nicholas Copernicus (1473 – 1543)

Copernicus was the first astronomer to formulate a scientifically-based heliocentric cosmology that displaced the Earth from the center of the universe. His epochal book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), is often regarded as the starting point of modern astronomy and the defining epiphany that began the Scientific Revolution. The book was published the year of Copernicus’ death, 1543, though he had arrived at his theory several decades earlier.

Although Greek, Indian and Muslim savants had published heliocentric hypotheses centuries before Copernicus, his publication of a scientific theory of heliocentrism, demonstrating that the motions of celestial objects can be explained without putting the Earth at rest in the center of the universe, stimulated further scientific investigations and became a landmark in the history of modern science that is known as the Copernican Revolution.

Galileo Galelei (1564-1642)

Galileo Galelei provided the crucial observations that proved the Copernican hypothesis, and also laid the foundations for a correct understanding of how objects moved on the surface of the earth (dynamics) and of gravity. (Valado, 2007: 7 – 9)

Sir Isaac Newton (1642-1727). British mathematician and physicist, one of the foremost scientific intellects of all time. He was elected a Fellow of Trinity College in 1667 and Lucasian Professor of Mathematics in 1669. During two to three years of intense mental effort he prepared Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia, although this was not published until 1687.

Johanns Kepler (1571-1630)

The greatest achievement of Kepler was his discovery of the laws of planetary motion. There were such three laws, but here we shall deal only with the first two - those that govern the motion of an individual planet. These are found in Astronomia Nova (New Astronomy, 1609), underpinned by important work in Epitome (of Copernican Astronomy) Book V (1621). The laws are:

First Law: The orbit of a planet/comet about the Sun is an ellipse with the Sun's center of mass at one focus.
Second Law: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time.
Third Law: The squares of the periods of the planets are proportional to the cubes of their semimajor axes.

Isaac Newton (1643 – 1727)

According to the well-known story, it was on seeing an apple fall in his orchard at some time during 1665 or 1666 that Newton conceived that the same force governed the motion of the Moon and the apple. He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and the problems of planetary motion.

Correspondence with Hooke (1679-1680) redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance; he determined it to be an ellipse, so informing Edmond Halley in August 1684. Halley's interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write the Principia.

Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centers of force. Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles. The three laws of motion are stated below.

First Law of Motion: Every object remains in its state of rest or motion in a straight line unless a force is exerted upon which.
Second Law of Motion: The rate of change of (linear) momentum of a body is proportional to the force exerted on which and is in the same direction.
Third Law of Motion: To every action there is always an equal and opposite reaction.

Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the revolutions of the six known planets, including the Earth, and their satellites. However, he could never quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter, already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation.

Universal Gravitational Law: Any two bodies attract one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Sputnik I (which means traveling companion) is the Earth's first artificial satellite, which was launched by the former Soviet Union on October 4, 1957. This launch of that 18-lb, 22-inch-diameter sphere sent a dramatic shockwave through the west, which resulted in a series of ground-breaking events including the establishment of NASA itself.

Ulysses (named after the Latin translation of Dantie’s Odysseus) was a robotic space probe designed to study the Sun, launched on October 6, 1990 as a joint mission of NASA and ESA to study the Sun at all latitudes. As one of the longest and most successful space missions ever, it has finally ended, with ground shut-down commands on June 30, 2009.

1.2.4Astrodynamics

The birth date of astrodynamics may be marked with the successful launch of the first man-made Earth satellite known as Sputnik I by the former Soviet Union on October 4, 1957. Only few months later, to be followed by the launch of the second man-made satellite Explorer I on January 31, 1958 by the United States. Thousands of satellites have been launched since then to serve numerous applications ranging from purely civil to purely military. In addition to Earth satellites missions, many interplanetary space exploration missions have been successfully accomplished to the Moon, Mercury, Mars, Saturn and other planets in the solar system. From Sputnik to Ulysses (the joint ESA/NASA solar orbiter mission and one of the longest and most successful space missions ever conducted, which has finally ended on June 30, 2009), space utilization has become an integral and crucial part of the modern human life.

Due to the highly ambitious programs in NASA and ESA, in recent years, it has become evident that there is piling interest innovative space missions which require collaborative scientific and engineering efforts from different disciplines. Recent advances in modern orbital mechanics, space propulsion systems, and orbital and attitude control techniques paved the way to realize missions which used to be unfeasible. New space mission concepts such as formation flying have gained much of the space community interest. Such progresses were supported by peer advances in orbital determination methods and maneuver techniques which constitute what is referred as modern astrodynamics.

1.3Where Are We in Space?

The following plate illustrates the relative sizes of the planets belonging to our solar system. Jupiter is the largest and Ceres is the smallest.

Fig. 1. The Solar system.

1.4References

Kit, S. T. (2007). Astrodynamics Premier.

Unsöld, A., Baschek, B., & Brewer, W. (2001). The New Cosmos: An Introduction to Astronomy and Astrophysics. Berlin: Springer.

Albrecht Unsöld; Bodo Baschek, W.D. Brewer (translator) (2001). The New Cosmos: An Introduction to Astronomy and Astrophysics. Berlin, New York: Springer.

Satellite Tool Kit Tutorial. STK version 8.0

1^ Verify the years.

2^ Vallado, 2007: chapter 1.

3^ Albert et al., 2001: through www.wikipedia.com

4^ Saliba, George (1999), Whose Science is Arabic Science in Renaissance Europe?, Columbia University, http://www.columbia.edu/~gas1/project/visions/case1/sci.1.html, retrieved on 26 December 2008

5^ www.moonsighting.com/articles/roleofislam.html

6^ Prof. David A. King in his lecture titled “ASTRONOMY IN THE BAGHDAD OF THE CALIPHS” at the Institute of the History of Science, Johann Wolfgang Goethe University.