When one thinks of a satellite it is usually in the form of a man-made object orbiting the Earth. However, by definition a satellite is a moon, planet or machine which orbits a planet or a star. From our vantage point here on Earth, the Moon is the predominant satellite. Long before Sputnik 1 (the first man-made satellite launched by the Soviet Union) the Moon was our one and only satellite.
Long, Long Ago
When the Solar System first formed it consisted of a star surrounded by a disk of gas. Eventually this gas gathered into dust, rocks, asteroids and finally planets. Each planet also had its own disk of gas, which in turn would follow a similar process. Some of the debris was pulled into the planets, but not all. Over time some of the gas eventually turned into moons. Some moons could have formed independently from their host planet, and later were captured by gravity as they drifted through space.
Our Moon is believed to have been created by a different manner. The early Solar System was a very violent and chaotic place. As planets and moons were born, they were bombarded by asteroids and small planets. The Moon’s many craters is clear evidence of this early chaotic period. In the 1970s a theory was proposed: about 4.5 billion years ago the Moon was formed by a gigantic collision between the early Earth and another planet. Recently a new theory has surfaced which tweaks the original 70s theory. I’ll begin with the established theory first, then get back to the revised theory later.
The original theory states that a mars-size planet on a similar orbit as Earth struck the Earth on an angle. The collision created the Moon and quite possibly the tilt of the Earth’s axis of 23 degrees. This rouge planet is sometimes referred to as Theia, named after the mother of the ancient Greek moon goddess, Selene. The impact generated intense heat in both planets. The Earth absorbed part of Theia along with her heavy iron core, the lighter rocky material ended up in a ring around Earth’s orbit. From this debris our first satellite would from. Interestingly, the Moon may have been intact after only several decades. Over billions of years both bodies cooled, but not entirely; the Earth still has a largely molten core. The smaller Moon may have completely cooled or perhaps still retains a tiny molten core.
Evidence for the ‘Giant Impact Theory’ (70s theory)
- The Moon is large for a satellite in comparison to the size of the Earth. Most moons are much smaller in ratio to the planet they orbit. Models for how moons are usually formed place a limit on how big a moon can be in relation to its host planet. Our Moon appears to be too big to have formed by surrounding gas in the early solar system or captured by the Earth’s gravity.
- By examining the surfaces of both Mercury and Mars we are able to see what the early solar system must have been like. Virtually unchanged for about 4 billion years, these planets are dotted with craters. Some of which are as large as six hundred miles wide. The Earth has no such markers due to climate and erosion, but by deduction, we can assume that the early Earth was also hit by large objects (such as Theia).
- In six trips to the Moon the Apollo astronauts collected rock samples and for the first time they were able to see what the Moon was made of. Remarkably, the Moon samples were found to have a similar chemistry to Earth. This discovery is in line with a Theia and Earth collision. Such an event would have blasted parts of the Earth into space which coalesced with bits of Theia to form the Moon.
- The impact hypothesis was also put to the test with computer simulations. The impact suggested, was applied to software that recreated the conditions of the early Solar System. After running several simulations of a Mars-size object colliding with the Earth at the angle predicted, everything worked. The end result was the Earth/Moon system we have today.
The ‘big Whack’ (new theory)
This is where the new revised theory comes in; modern computer simulations suggest a much more intense collision at a significantly sharper angle. Such an intense impact would have vaporized Theia and much of the Earth. This accounts for why the Earth and Moon are so similar in their chemistry. In fact, new research is finding increasing chemical similarity. This points to a much more violent impact which would have thoroughly mixed both bodies before they separated.
Also, the impact forced the Earth to spin much faster (about once every 2 hours) and tilt as much 60 to 80 degrees on its rotational axis. The Earth’s present rotational tilt of 23 degrees is though to have been arrived at later by complex interactions with the Moon and the Sun. Another interesting fact, which the original theory left unexplained, is the 5 degree tilt of the Moon’s orbital plane. The Moon’s orbit is tilted 5 degrees in relation to the Earth’s orbit around the Sun. The Earth orbits the Sun on what is called the ecliptic plane; this plane is where most bodies orbit the sun. The early Moon’s orbit is though to have matched the severe tilt of the Earth and did not transition smoothly to match the ecliptic plane. The revised theory proposes that the 5 degree orbital tilt of the Moon is but a relic of a much steeper orbital tilt from the distant past.
A Match Made in Heaven?
The two prominent heavenly bodies are the Sun and the Moon. Much of the Sun’s influence on the Earth is clearly recognizable; the Moon, however, affects us in more subtle ways. The warmth of the Sun (or lack of it on some days) is an everyday experience. In ancient times the Sun was worshiped by some cultures as godlike. It would have been clear then, as it is now, that without the Sun the Earth would be void of heat and most likely without life.
As it turns out the Moon’s presence might also be fundamental to life. However, for a large part of human history the Moon remained mysterious. Today scientists speculate that the Moon may have contributed to life in various ways. What follows are plausible explanations for how our Moon influenced life:
- When the Moon was first formed it was much closer to the Earth than it is today. It is still receding by a minuscule amount every year. Over 4 billion years ago the Moon exerted a greater gravitational pull on the Earth, which may have set plate tectonics in motion. Plate tectonics are believed to be necessary for a living planet.
- Shortly after the Earth’s post impact formation it rotated about once every 5 hours (70’s theory) or once every 2 hours (new theory). Either way, the Moon’s presents gradually slowed down the Earth’s rotation, diminishing the severity of the weather. The Moon may also have stabilized the earth’s rotation on its axis.
- Nocturnal animals behave differently at various times during the monthly lunar circle, depending on the brightness of the Moon. If not for the influence from varying moon light, who knows how the course of evolution would have been altered.
- The greatest influence the Moon has on the earth is in generating tides. This would have allowed life from the ocean (where life began) to spend short intervals of time on land. This may have provided the ideal training ground for life to gradually adapt to the land.
The Earth and the Moon have been united by gravity for over 4 billion years. It is hard to know for sure what the Earth would be like without the Moon. Would there be life? If so, what would it look like? Nevertheless, if there was no Moon and life did manage to evolve, it would almost certainly be different.
References: Jim LeBans, The Quirks & Quarks Guide to Space.
Did We Need The Moon For Life? Fraser Cain, Published on Nov 20, 2015, https://www.youtube.com/watch?v=KulEmr7X1HM
Origin of the Moon, tonyweston9, Uploaded on Nov 27, 2008, https://www.youtube.com/watch?v=m8P5ujNwEwM
What is a Satellite? Dan Stillman, Feb 12, 2014, http://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-a-satellite-k4.html
Scientists propose new theory about how Earth got its moon, By Sheena Goodyear, CBC news, Posted: Nov 1, 2016. http://www.cbc.ca/news/technology/moon-theory-1.3830623
Violent Impact That Created Moon Mixed Lunar and Earth Rocks, By | January 28, 2016 02:28pm ET. http://www.space.com/31763-moon-creating-impact-mixed-lunar-earth-rocks.html
Did Early Earth Spin On Its Side? Monday, October 31 2016. http://www.seti.org/seti-institute/press-release/did-early-earth-spin-its-side
New Model Explains the Moon’s Weird Orbit, October 31, 2016, http://cmns.umd.edu/news-events/features/3680
THE LANDSCAPE OF REALITY 
indeed are approached many situations as precised by prof dr mircea orasanu and prof drd horia orasanu and so followed for the situations with THE THREE BODIES PROBLEM that given thus equation must be satisfied for all possible small perturbations .
Integrating the second term in the integrand of the above equation by parts, we get
(680)
Now, if the end points are fixed then at and . Hence, the last term on the left-hand side of the above equation is zero. Thus, we obtain
(681)
The above equation must be satisfied for all small perturbations . The only way in which this is possible is for the expression enclosed in square brackets in the integral to be zero. Hence, the functional attains an extremum value whenever
(682)
This condition is known as the Euler-Lagrange equation.
Let us consider some special cases. Suppose that does
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here can be mentioned that problem of MOON must include in large domain of TWO BODIES PROBLEM and THE THREE BODIES PROBLEM that still not solved observed prof dr mircea orasanu and prof drd horia orasanu and followed that must applied important relations as studying the differential equation for a given function that resembles linear fractional transformations with real coefficients. When perturbed to have slightly complex coefficients, this yielded a group of linear fractional maps with complex coefficients that act on the Riemann Sphere. called the ones with real coefficients fuchsian groups after Fuchs and the ones with complex coefficients kleinian groups, though neither Fuchs nor Klein had much to do with the groups they are named after. Allegedly, Klein was offended when Poincare declared the fuchsian group, claiming it had been he, not Fuchs, who had thought about it. So to appease Klein, Poincare named the next group after him. Nonetheless, these are groups of isometries on the hyperbolic plane, Originally, he began his studies in differential equations, then stumbled upon hyperbolic geometry naturally in his work. He wrote in his book Science and Methods that:
The incidents of travel made me forget my mathematical work. When we arrived at Countances, we got into a break to go for a drive, and, just as I put my foot on the step, the idea came to me, though nothing in my former thoughts seemed to have prepared me for it, that the transformations I had used to define Fuchsian functions were identical with those of non-euclidean geometry
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to observed that existence of the MOON appear in THE TWO oR THREE BODIES PROBLEMS observed prof dr mircea orasanu and prof drd horia orasanu followed laws of Newton and ELLIPTICAL orbits given by KEPLER Equations and thus the results for thus equations ,are used LAGRANGIAN OPERATORS and The answer is no, since some correspond to irrational numbers (e.g., the cut consisting of {x:x22} corresponds to 2–√). In this explicit, precise sense, the system of rational numbers is not continuous, i.e. not line-complete.integers, can then be added, multiplied, and hence factored. By means of this theory of ideals, he allowed the process of unique factorization—that is, expressing a number as the product of only one set of primes, or 1 and itself—to be applied to many algebraic structures that hitherto had eluded analysis.CONSTRAINTS OPTIMIZATIONS , so
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