An Introduction to Gravitation

     You probably already have an idea of what gravitation and gravity refer to. Gravity is what pulls a ball towards the ground when it is released. Gravity is what makes the moon orbit the earth, and is also what causes the nine planets of our solar system, along with all of their moons, to orbit the sun. It is basically what holds our whole universe together. According to Isaac Newton, gravitation is a type of force. In physics, force is simply a measure of push or pull. The greater the push or the pull, the greater the force.

     Whenever you are referring to the term force, acceleration also comes into the picture. This is because applying force causes acceleration. Acceleration tells us how fast an object's velocity changes. Velocity tells us how fast something is moving, and in what direction it is moving. So, the bigger the acceleration is, the more the velocity changes. For example, when you are riding in a car and push the gas pedal, the car accelerates because the burning fuel in the engine causes it to do so. If you look at the speedometer (which shows you how fast you are going), you will see that your speed is increasing. This means that you are accelerating, since the car's speed is changing. The following equation, Newton's Second Law of Motion, shows us the relationship between force and acceleration:

     Mass is another term you are probably familiar with. Basically, the heavier something is, the more the mass it has. If you increase the amount of force, or "push", you put on an object, the bigger the object's acceleration will be. The mass of an object also affects acceleration: if you apply a force onto a heavy object, its acceleration will be less than it would be if the object were lighter. This simply means that heavy objects are harder to move than light objects, because you need more force to move the heavy objects. You definitely knew this!

     As mentioned earlier, gravity is a type of force. Let us add to that description: gravity is an attractive force that affects everything in the universe. In other words, gravitation is the force that pulls all things towards each other. You can see gravitation acting in our solar system, for example through the Moon's circling of Earth. This is because the Earth and the Moon are pulling towards each other. Even you and the computer monitor that you are looking at are pulling towards each other, but since both you and the monitor have very small masses (meaning that you both are very light) you cannot really feel the force between you. However, you can definitely feel the Earth pulling on you; this is because the Earth is so massive.

     There are two properties that affect how strong the gravitational force between two objects is, one of which was already hinted at in the last paragraph: mass and position. You can explore the effects of changing both mass and position using the Creator applet if you have a java-enabled browser. Click here to go to the Creator applet to see the gravitational effects between the Earth and the Moon. Instructions for using the Creator are included with the applet. Gravitation is a force that acts over a distance, and as the distance between two objects increases the force decreases. So, when the moon is closest to the Earth, the force is the greatest, making the moon's speed increase more. Remember, the greater the acceleration, the greater the object's speed will change. The relationship between gravitational force and distance is an inverse-square relationship, which means that if you double the distance between two objects, the force will be one-fourth as strong; if you triple the distance, the force will be one-ninth as strong. You can try this out in the applet and see that this holds true; increase the distance between the Earth and the moon, and look at the acceleration. Remember, force causes acceleration, so if you see the acceleration go up by a certain factor, the force also goes up by the same factor. You can use Newton's Law of Universal Gravitation to calculate gravitational force. You should note, however, that Newton's theory of gravitation is not perfect. It has its flaws, but it is still applicable for gravitational fields that we here on Earth are used to, and is also a good way to introduce and learn about gravitational motion and the effects of gravity.

     This may be a little confusing, but the force that the Moon exerts on the Earth is the same as the force that the Earth exerts on the moon. Now you are probably asking yourself, "How could that be?" If you look at the Earth and the Moon in the Creator applet, you can see that the Moon's velocity keeps changing, you will see that the moon's acceleration is greater than the Earth's acceleration. It certainly seems that the Earth is pulling on the Moon more than the Moon is pulling on the Earth. However, this is not true. The reason for this is that since the Earth has a bigger mass than the Moon, it will be moved less by the force between the Earth and the Moon. This same force, however, will cause the Moon to accelerate more because it has a smaller mass. You can see this in the equation Force = Mass * Acceleration. The force is the same between the Earth and the moon, but the masses are not. Since the Earth is more massive than the moon, it will have a lower acceleration for the same amount of force. Lower acceleration means less change in velocity. This principle is known as Newton's Third Law of Motion, and is very important to know in order to understand gravitation. It may be confusing at first, but you will get to understand it.

     Now is a chance to use the Creator again. Observe what happens when the mass of the Earth is more than twice its actual mass, and then go to the moon and look at its acceleration and velocity during orbit. If the mass of the Earth were to suddenly increase, it would mean that the force between the Earth and the Moon would increase (remember that this force is that the Earth exerts on the Moon the same as the force that the Moon exerts on the Earth). That means that the moon is going to be pulled harder by the Earth, which brings it closer to the Earth during its orbit. An orbit is the path taken by an object as it travels around another object. The Earth will be pulled harder by the moon as well, but since the Earth's mass will have increased, its acceleration will stay the same with the increased force. However, since the Moon's mass will stay the same, its acceleration will increase due to the increased force. You can check this out using the Creator applet by clicking here. This also means that the moon's period will be shorter, meaning that it will take less time for the moon to orbit the Earth.

     As the Earth's mass increases, the orbit of the moon will be less like a circle and will become more eccentric, or more elliptical and flatter. This is the result of the increased force between the Earth and the Moon. When an object is travelling in an elliptical orbit, it means that the distance between it and the object is constantly changing. Remember that gravitational force depends on the distance between objects, and so when objects travel in an elliptical orbit the gravitational force between the two objects will be constantly changing as well. When using the Creator you should notice that the moon's acceleration is the greatest when it is closest to the Earth, and the least when farthest from the Earth. You should also notice that the moon's speed is the greatest when it is the closest to the Earth. You now have an idea of how mass and position affect the orbit of objects in space; now it is time to look at velocity. In the Creator applet, increase the magnitude of the moon's velocity. The moon's orbit does become more elliptical, but also becomes larger. If moon's velocity were to decrease, then the orbit would become smaller and shorter. To try it yourself in the Creator, here.

     If you use the Creator applet to experiment with the orbit of the moon, you could see how much the velocity of the moon fluctuates if the moon's starting velocity is changed. A slight change in the velocity makes the orbit non-circular. Although we cannot actually change the velocity of the real moon, we can change the velocity of satellites that we put into the orbit of Earth. It is important for these orbits to be circular. One reason is that these satellites transmit information to the Earth and must remain a constant distance from a point on the Earth (these satellites are called geosynchronous satellites). Sometimes these satellites need to repaired, as was the case with the Hubble Telescope, and must be easy to dock with by spacecraft. It is much easier to approach and dock a satellite that is in a circular orbit than a satellite with a highly elliptical orbit. Try it yourself in the Docking Game by clicking here. You will be able to adjust the satellite's velocity so that the satellite's orbit is not circular.

     In order for an object to orbit another object in a circular path, it must have a certain velocity. This velocity must be perpendicular to the direction of the force applied to it. (see diagram). The magnitude of the object's velocity, or speed, can be calculated by the following:

     Where V is the speed, A is the acceleration of the orbiting object, and R is the distance between the two objects. The acceleration of the orbiting object is caused by the gravitational force between it and the object it is orbiting around. Use Newton's Law of Universal Gravitation to find out how to calculate acceleration. By solving the equation, you will calculate the force; in order to find acceleration, divide the force by the mass of the object that you wish a satellite to orbit, which in this case would be the Earth. Try putting new objects into the orbit of the Sun using the Creator applet and the data for the Solar System with this new knowledge.

Gravitation in the Solar System

     In the previous section you learned about gravitational effects with two bodies. The solar system is made up of many more bodies (satellites, planets, asteroids, comets, etc.), but by far the Sun is the most massive of them all. The Sun causes all the planets to orbit around it, and because it dominates the Solar System in terms of mass (99.9% of the entire mass of our solar system is taken up by the moon), it brings a level of stability to our solar system. Compared to the Sun, the mass of each planet is insignificant. This is why all the things in our Solar System move in orbits around the sun, and is also why the Sun barely moves by the force that exists between itself and each of the planets. Only an object with a mass comparable to that of the Sun could disrupt the orbits of the planets in our Solar System. To see the Solar System in the Creator applet, click here. If you wish to read about the Solar System, click here.

Evolution of Gravitational Theory

     Several theories about the force that caused objects to fall to the earth were developed by Greek philosophers. In the 4th century BC, Aristotle suggested that all things were composed of four elements: earth, fire, air, or water. His viewed gravity as a force that drew objects of like elements together. The philosopher’s views on cosmology consisted of a geocentric, or earth-centered universe. The Greek views on the force that holds the solar system together and the force that pulls objects towards the center of the earth were in no way related.

     In the early 17th century, the Italian physicist and astronomer Galileo discovered that all objects fall toward the earth with the same acceleration, regardless of their weight, size, or shape, when gravity is the only force acting on them. Galileo adopted a theory about the universe based on the heliocentric ideas of the 16th century Polish astronomer Nicolaus Copernicus. Galileo disagreed with Copernicus’s idea that the planets orbited in elliptical orbits. The Italian favored the idea that orbits were circular, and like the Greek philosophers before him, he saw no connection between the force behind planetary motion and gravitation on earth. In 1609, Galileo observed moons orbiting Jupiter. This observation destroyed the theory of geocentricity, and by the mid 17th century, the heliocentric idea gained acceptance. The telescopic observations of the Danish Tycho Brahe and his German student Johannes Kepler revealed noncircular orbits, and calculations proved that the planets traveled in ellipses.

     The heliocentric theory changed scientific views of the universe and man’s position in the universe. However, it was not until the late 17th century that Isaac Newton’s theory of gravitation encompassed both the attraction of objects on the earth and planetary motion. Newton developed a science of forces and motion, now known as Newtonian Mechanics. He proposed that the natural motion of an object is motion at a constant speed on a straight line, and that it takes a force to slow down, speed up, or change the path of an object. His branch of mathematics, known as calculus, became an important tool in studies of the universe.

     Newton’s law of gravitation, proposed in 1687, is still widely used in study of planetary motion. The theory stated that every particle in the universe attracts every other particle in the universe with a force that depends on the product of the two particles' masses divided by the square of the distance between them. The gravitational force between two objects can be expressed by the following equation:

     where F is the gravitational force in newtons, G is a constant known as the universal constant of gravitation (later defined by English chemist and physicist Henry Cavendish as 6.670 x 10^-11 Nm²/kg²), M and m are the masses of each object in kilograms, and d is the distance separating them in meters. The Newtonian theory employs the idea that force acts on a straight line between the centers of the given spheres. Irregular objects are more complicated, since every bit of matter in one object attracts every bit of matter in the other. For these objects, the center of gravity is used in calculations. Newton’s theory applies to every bit of matter in the universe.

     Newton’s theory was the first theory of gravitation that was used in describing the motion of the planets. Scientists used it extensively in studying the motions of the earth, moon, and the other bodies in our solar system. It was these Newtonian calculations that led to the 1884 discovery of the planet Neptune when variations in Uranus’s orbit could not be explained.

     As scientific studies expanded in the 19th and 20th centuries, several problems with Newton’s theory arose. Newton’s observations were based on relative observations of velocity. Different observers may see one object moving at different speeds. Under the tradition theory about space and time, there can be no reference speed to which all others may be compared. However, towards the end of the 19th century, Scottish physicist James Clerk Maxwell proposed a reference speed of c, or 300,000 km/sec. This speed was the approximated speed of electromagnetic waves, and Maxwell’s suggestions about c led to a crisis in physics dealing with relativity.

     In 1905, the German physicist, Albert Einstein, proposed the idea that speed c is the fastest speed at which anything can travel. Neither particles nor information can travel at a speed faster than c. From this idea, Einstein developed his Theory of Relativity. This theory, which views the effects of gravity not as a force but as a deviation in the curves of spacetime, encompasses an idea of a four-dimensioned universe. These dimensions include three space dimensions and one time dimension. Einstein’s ideas, complex to all but the most intelligent physicists, have been tested to a small extent and proven correct. Einstein carried scientific theory and study of gravitation from the 1600s into the third millennium.