Introduction






Gravity plays a central role in physics for several reasons. Every particle in the universe attracts every other particle. The gravitational force is one of very few fundamental forces between interacting particles. The others are the electromagnetic force between electrically charged particles, the weak interaction force that governs the slow decay of certain unstable particles, and the strong interaction force that dominates the interaction between particles in an atomic nucleus. It is now believed that all may be special examples of a single universal force in a grand unified theory of forces. One of the most extraordinary intellectual achievements of all time is originating, developing, and applying the law of gravitation. Sir Isaac Newton contributed this to the world. He saw that single universal force of gravity could account equally well for the motion of a dropped apple, of the moon about the earth, and of the planets about the sun. The laws of physics are universal. Gravity is still a lively topic in present day physics and astronomy. The general theory of relativity is basically a comprehensive theory of gravity. Shifts to longer wavelengths of light emitted by massive stars are gravitational red shifts. Black Holes are an extreme example of gravitational attraction. [1]



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History


Johannes Kepler was the first one who came up with some ideas about gravity, even though he did an unsatisfactory experience. He calculated the distance from Mars at each and every degree around an eccentric circular orbit and used the sum of those distances as a measure of the time it took to get from one place to another. He had used a similar trick with sums of distances to calculate the area of a circle. Johannes Kepler worked out the details of how the orbits of the moon and planets can be described mathematically, but he doesn't explain that what is gravity or how it works. This is known as the Kepler laws of planetary motion. In 1605, he came up with his three laws of planetary motion by referring the measurement of the orbits of the planets by Tycho Brahe. Kepler's three laws of planetary motion are:
1. The planets move in elliptical orbits, with the sun at one focus.
2. The line connecting the planet and the Sun sweeps out equal areas in equal intervals of time.
3. The squares of the orbital periods of planets are directly proportional to the cubes of the major axis of the orbits.
Almost a century later, Sir Isaac Newton deduces Kepler's laws of planetary motion using his invention of calculus and from his laws of motion and law of universal gravity. After that everybody realize the physical explanation of the behavior of planets. Then he modified Kepler's 3rd Law to read,
phys._equation.PNG




  • P is the planetary orbital period
  • m1 is the mass of Sun (in solar mass)
  • m2 is the mass of the planet (in solar mass)
  • d1 is the distance the Earth travels between the winter and summer solstices (in astronomical units)
  • d2 is the distance the Earth travels between the summer and winter solstices (in astronomical units)
  • R is the distance between the centers of the two objects (in astronomical units)
In 1687, Sir Isaac Newton included his famous three laws of motion and the law of universal gravitation in his book 'Mathematical Principles of Natural Philosophy'. They are:
1. Everybody continues to be in its state of rest or uniform motion in a straight line unless an unbalanced force acted upon it.
2. The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, and it is inversely proportional to the mass of the object.
3. To every action there is always an equal and opposite reaction.
4. The force magnitude varies inversely proportional with the square of the separation distance and is directly proportional to each of the two interacting masses. [2]




What is Gravity or Gravitational force?


Gravity is one of the four fundamental forces of the universe and is considered a non-contact force. It is what holds the planets in orbit as well as the very universe itself. It is what keeps us from floating off into space and plays a crucial role in almost every nature process from the ocean tides to the body's circulatory system. It is a force pulling together all matter. It is the force that causes two particles to pull towards each other. The more mass they have and how closer they are, it has greater the force of attraction. Sir Isaac Newton is the one who came up with an equation for calculating the force of gravity:
force_of_gravity.PNG



G is the universal gravitational constant.m1 is the mass of one of the objects.m2 is the mass of the other object.
r is the distance between the centers of masses of each object.
FG is the force of attraction between the two objects [3]
The vertical motion of objects thrown into the air or of objects falling through the air, if it were not for the resistive force of air on these objects, their acceleration would be constant. This acceleration is caused by the gravitational force of the earth pulling down on the objects. This force and their weight cause them to accelerate toward the center of the earth with gravitational acceleration. Any free object dropped from the rest or thrown near the earth's surface has the same gravitational acceleration, 9.8m/s^2 toward the center of the earth. The value of this gravitational acceleration varies slightly with elevation and the latitude and also depends on the geographical formations at different parts of the earth's surface. This gravitational acceleration is constant only if we ignore air resistance. The gravitational force is the weakest of the fundamental forces in physics; yet it is the only fundamental force we experience directly. [4]



The earth is round, it's because of gravitation. According to Newton's Law of Universal law of gravitation, everything pulls everything else with a force that depends upon the masses of the objects and the distance between their centers of mass. So, the earth attracted itself before it become solid. Earth is a giant sphere because any corners of the earth have been pulled in. [5]

Some Facts about Earth and Moon


Earth is the largest terrestrial planet in the Solar System. It has a diameter of seven thousand nine hundred and twenty six miles which is twelve thousand seven hundred and fifty six kilometers. Some scientists believe that Earth may be the only place in the universe that life exists. It is because earth only has the oxygen and nitrogen gases in the atmosphere. Nickname for the Earth is the blue planet; it's because of the water amount in it. What makes Earth so special from other planets is that its unique relationship with the moon, it's own natural satellite. Earth's gravity is the thing that keeping the moon in the orbit around the earth. Moon also has some influence on the earth. Like, Moon affects the weather and ocean tides on the earth. That made the life possible on the earth. Other planets also have moons; earth is not the only one. Some have more than one moon; some do not have any moon. Venus and Mercury don't have any moon. In the solar system, there are at least one hundred and sixty six moons circling around it. Earth's moon is the fifth largest moon in the Solar System. Earth's moon has the greatest size and greatest mass compared to the planet it orbits. Moon has only 1.2 percentage of earth's mass. But because of its closeness to the earth, its small amount of mass has an enormous powerful influence on the earth. [6] The earth is the fifth largest planet in the solar system. It orbits the sun in an elliptical path. Earth is the third planet from the sun and it is about 149.6 million kilometers away from the sun. The inner core of the earth is made up of solid iron and nickel and it has a temperature of about three thousand six hundred and seventy seven degrees Celsius. The next two layers also had the effect of this inner core. The outer core of the earth is made up of iron and nickel; it is in the molten form. And it has a thickness of two thousand and three hundred kilometers. The next layer is made up of mantle; it has the silicate rock in it. It has a thickness of about two thousand and eight hundred kilometers. The layer of the earth at and just below the surface of the earth is the crust, it is made up of silicates and it has six to forty kilometers of depth.[7][8]

How the Moon formed?


Moon is the second brightest object in our sky. It looks like a round shaped. But, it bulges on the side nearest to us. Scientists find out that how the moon is formed, by working out different things. They come up with the idea that: "Around 4.6 billion years ago, before the earth was really solid, a slightly smaller but similar object bumped into it. It was not a head - on collision but a glancing blow, after which the smaller object spun off into space. The debris created by this galactic accident went into an eccentric orbit about 238,855 miles which is 384,400 kilometers from the earth. Over time it came together to form the moon." [9]
When a Mars sized object collided with the earth, enough matter was thrown into space to form the Moon. The newly formed moon began to move farther away from the earth. About one hundred million years after the creation of moon, it was already half way to its present distance. [10]
The bits and pieces that formed the Moon came from the outer layers of the Earth and the object that hit it. That's why in the moon contains little iron. Iron is the main ingredient of the earth's core. There is a tiny amount of water on the surface of moon in the form of ice. It's probably arrived with the meteoroids and the incoming comets. Moon is the only celestial object besides Earth that human beings have visited. There are still questions about moon that are unanswered for human beings. [11]




Structure of Earth and Moon



The moon's structure is very similar to the earth's structure. It has a small inner core with about one thousand four hundred and eighty two degree Celsius. Next layer is made up of some semisolid rock. Next layer is the mantle, which has a thickness of nine hundred and sixty six kilometers. The outer layer is the crust, it is known as the regolith. On the two sides of the moon, it has different thickness. The one we are seeing is only about sixty four kilometers deep. The other side has ninety seven kilometers depth. Still, we didn't get an answer for what's the reason for these differences. Size and distance of Moon and earth also is reason for the gravitational interactions. The moon is much smaller than the earth. The volume of the moon is 2.199 x 10^10 km^3 and the volume of the earth is 1.08321 x 10^12 km3, which is fifty times greater than the moon's volume. The mass of the moon is 7.349 x 10^22 kg and the mass of the earth is 5.9736 x 10^24 kg, which is eighty times greater than the moon. The moon's diameter is 3,476 km and the earth's diameter is twelve thousand seven hundred and forty two kilometers, which is approximately four times greater than the moon. The surface gravity of the earth is 9.78 m/s^2 and the surface gravity of the moon is 1.62 m/s^2, which is one sixth of the earth's gravity. It's because moon has only a small core but the earth has other large core and other metallic elements. The ellipticity of the earth is 0.0034 and the moon's ellipticity is 0.002. Average density of the earth is three hundred and forty four pounds per cubic foot, 5,515 kg/ m^3 and the average density of the moon is two hundred and ten pounds per cubic foot, 3,341 kg/ m3. The acceleration due to gravity on the surface at the equator of the earth is thirty two feet per square seconds, which is 9.78 m/sec^2 and the acceleration due to gravity on the surface at the equator of the moon is 5.32 feet per square seconds, which is 1.62 m/sec^2. The magnetic field strength at the surface of the earth varies from 2.2 * 10-5 to 6.6 * 10-5 T and the surface of the moon varies from 6 to 313 * 10^-9 T, it is about thousand times weaker than Earth's magnetic field strength. [12]

earth_and_moon.jpg
http://www.freemars.org/jeff/planets/Luna/Luna.htm





What would happen if the earth and moon were twice as far apart?


Suppose there were two bodies a thousand miles apart. What would happen if the bodies were twice as far apart? By the Newton's Law of gravitation, we can say that if the bodies were twice as far apart, then the gravitational attraction will be one-fourth as great. It's because Newton's Law of Gravitation states that every particle of matter attracts every other particle with a force proportional to the square of the distance between them. So the force varies inversely with the square of the distance. One of the problems that created after the discovery of Law of Universal Gravitation was how and why the moon goes around the earth. If we apply the Newton's Law to the earth - moon system, we know that there will be a gravitational attraction of Earth's mass upon mass of the moon. It is a force and the direction of this force is along the line of those masses that connects the two bodies. If the distance between the two bodies increases, the force will decrease and if the distance between the two bodies decreases, the force will increase. But the force will never become zero, because of that; the moon is always pulled toward the earth. As long as the moon moves in a circular orbit, the distance between earth and moon will remain unchanged. Therefore, the force will not change. [13]



Why the Moon stays in Orbit, not falling down?


Other question will rise on our mind is "If earth is pulling on the moon, why does the moon not fall into earth?" But the Newton's first Law of Motion can answer this question. It states that a body at rest will stay at rest until a force exerted on it or a body in motion stays in motion until a force exerted on it. It means that if no force exerted on a body, the body will remains still or moves in a straight line. If several forces are exerted, and if the forces are balanced, the same thing happens. For example, if you were pushing a table one way, and if someone else were pushing it the other way with equal force, the effect would be zero and it will not move. To move that table, one force must be greater than another, the forces should be unbalanced. Suppose a steel ball were rolling along. There were two magnets, one in the right and one in the left of the steel ball. Left magnet pulls the steel ball to the left and the right magnet pulls the steel ball to the left. If these two magnetic forces are equal, they will cancel the force each other and so the steel ball will move in a straight line. If we want the steel ball to move in a curved path, the force must get unbalanced - one force must be greater than another. So, if something moves in a curved path, the force exerted upon it must be unbalanced and if the forces were balanced, then it will move in a straight line. The Moon moves in a curved path, so the force exerting on it must be unbalanced. The force exerted upon the moon is gravitational attraction of earth and it is not balanced by any other force. The unbalanced force of earth's attraction on the moon causes the moon to fall toward earth, to pull away from a straight line. So it may cause the earth to fall constantly toward earth. The amount of that falling must be 1/19 each second. Suppose, if the moon did not fall toward earth, the moon would go in a straight line and will not see again. Likewise, the earth moves in a curved path about the sun. Earth falls 1/8 inch toward the sun each second. What makes the earth to move in a curved path is the gravitational attraction of the sun deflects it from a straight path.
Gravitational attraction is related to mass. If we know the mass of a body, we can find its density. If we know the density, then we can find that how much mass there in a certain volume. Suppose we give a value of 1 for the earth's gravity. Then the gravitational attraction at the surface of moon is one sixth that at the surface of earth.
[14]



Results of the gravitational interaction between Earth and Moon


Tides are one of the results of gravitational interaction between sun, moon and the earth. The height of the tides is related to the changes in the position of the moon. The highest tides occur when the moon and sun are on the same side of the earth and lunar eclipse also occurs at this time. These tides are called the spring tides. And the other relationship between earth and moon is that the highest tides occur when the moon is closest to the earth. The lowest tides occur when the sun, earth and moon form a right angle. And it occurs when the Earth lies exactly between the Sun and the Moon. The lower tides are called neap tides. Both of them occur twice a month. The moon attracts the ocean at the moon-side of earth more strongly than it does the solid earth directly below it. So the water is piled up there. The ocean at other side of earth is not pulled toward the moon as much as the solid earth because it is farther away from the moon. So the earth is pulled away from the water. And therefore during this part of the tidal cycle, the water is deeper. Therefore, the high tides occur at the ocean on the moon-side of earth and the ocean on the farthest side of earth. And low tides occur at the top and bottom side of earth, where the locations removed 90 degrees. [15] [16] [17]
Gravitational attraction between Earth and Moon produces a tidal force on each of them. The tidal force of the moon is very small when comparing with the force of gravity. The tidal force of moon is about 1/9,000,000 that of earth's gravity. The tidal force causes each to become slightly oval shaped. The bulges on the earth are the result of the gravitational attraction of the moon. But the tidal bulge will not be stable forever because, if either the earth or moon is rotating relative to the other, the tidal bulge is not stable. The rotation of the body will cause the long axis of the bulge to move out of alignment with the other object. And what works to reshape the rotating body is the gravitational force. Because of the relative rotation between the earth and moon, the tidal bulges move around the rotating body to stay in alignment with the gravitational force between the two bodies. The ocean tides on Earth rise and fall with the rising and setting of its moon. [18] [19]

Eclipses are also one of the results of the gravitational interaction between Earth and the Moon. Solar and Lunar eclipse are the result of the interaction between the shadows of the Earth and Moon. A lunar eclipse can happen only during the full moon phase. It occurs when the moon moves into earth's shadow. But there will not be a lunar eclipse occurs during each full moon. Earth goes around the sun in a certain plane and the moon goes around the earth, but the moon's path is tilted a little more than five degrees to the plane of earth's orbit. The earth always casts a shadow, but we are not aware of it because the moon usually passes above or below the shadow of earth. During the full moon, if the moon is near to the orbit of the earth, then eclipse occurs. When the sun and moon appear near the nodes of moon's orbit, a lunar eclipse occurs. To the astronomers lunar eclipses are not valuable as solar eclipses. Lunar eclipses can be used to determine the dates when events of long ago occurred. One example for this is that the bible says that there was a lunar eclipse the night before the King Herod's death. This information helped the historians to fix the date of his death. The solar eclipse occurs when the moon is new, when the moon is between the earth and sun. Every twenty nine days, twelve hours, forty four minutes and three seconds, the Sun, Moon and Earth are in direct alignment. New moon officially occurs when our satellite passes between our line of sight and the Sun. The moon passes either above or below the Sun from our angle of view. Solar eclipses only lasts for a few minutes. The longest solar eclipse can last is seven minutes and forty seconds. It can be this long only when viewed it only from the equator. There is an average of four eclipses occurs each year. Always, there are at least two solar eclipses in a year. There may be sometimes as many as seven eclipses occurs per year, five solar and two lunar or four solar and three lunar. Anyway, there are more solar eclipses in a year than the lunar eclipses. It's because of a lunar eclipse can be seen considerably more than one half of earth, while solar eclipses can be seen from only a very limited area. [20]




Conclusion


The law of conservation of angular momentum works perfectly for the Earth-Moon system. For the last 4.5 billion years, the total angular momentum has stayed almost the same. The angular momentum of the Earth-Moon system is 3.5 * 10^42kg/m2sec. The tidal bulge of water pulled up from the earth's surface by the gravitational attraction of the moon. And the moon exerts a gravitational torque on the bulge. Torque is a tendency of a force to rotate an object in an axis, also called it as a moment of force. The earth's tidal bulge is at a small angle to the Moon. And the forming torques by the moon causes to slow the rotation of Earth and the Moon to recede from the earth. The tidal bulge exerts a torque on the moon, and it results for the acceleration of the orbital speed of moon. And it causes the Moon to move away from the Earth in order to preserve angular momentum. Based on different analyses, scientists have determined that 2.45 billion years ago, a day on earth was only about nineteen hours long. This means that the earth is rotating in a period of nineteen hours. When the Earth first formed, the rotation of the earth has slowed down and days have gotten longer. Because of the conservation of Angular Momentum, days are still getting longer. Moon pulls the tides around the earth. By tidal fraction, earth's rotation gets slow down. According to conserve angular momentum, the rotation slows and the Moon moves slightly farther from the Earth. By measuring the distance from the moon to the earth by laser ranging, it is known that the Moon is receding from the Earth at a rate of 1.5 +/- 0.03 inches per year. There are still more effects that caused by the interaction between the earth and moon. We find that the earth's day is growing because of the interaction between the earth and moon. And we also talked about the tidal forces, how it formed and how it is effecting on the earth. We find that the Earth and Moon has a close relationship, without the moon, earth can't stay like now and without the earth, moon can't also stay like now. There are still discussions going on about the Earth-Moon system because we can't say that it will be stable forever. Because it changed from the beginning, still it is changing, it will continue this changing process until the end of the world. [21] [22]





Reference


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