8-1 Gravitational Force Answers

[Siri]

Gravityholds us firmly on the ground and keeps the earth circling the sun. This invisible force1 also draws down rain from the sky and causes the daily ocean tides. It keeps the earth in a spherical shape, and prevents our atmosphere from escaping into space. It would seem that this everyday gravity force should be one of the best understood concepts in science. However, just the opposite is true. In many ways, gravity remains a profound mystery. Gravity provides a stunning example of the limits of current scientific knowledge.

Therefore every particle in the entire universe actually attracts every other particle. Gravity is a long-range force in contrast to the strong and weak forces (Table 1).2 Magnetic and electric forces are also long-range, but gravity is unique in being both long-range, and always attractive, thus never cancelling out (unlike electromagnetism, where the forces may either attract or repel).

What really is gravity? How is this force able to act across the vastness of empty space? And why does it exist in the first place? Science has never been very successful in answering these most basic questions about nature. Gravity cannot somehow slowly arise by mutation or natural selection. It was present from the very beginning of the universe. Along with every other physical law, gravity is surely a testimony to a planned creation.

Attempts to explain gravity have included invisible particles, called gravitons, that travel between objects. Cosmic strings and gravity waves have also been suggested, but none have been confirmed. We simply do not know how objects physically interact with each other over vast distances.

Two Bible references are helpful in considering the nature of gravity and physical science in general. First, Colossians 1:17 explains that Christ is before all things, and by Him all things consist. The Greek verb for consist (sunistao) means to cohere, preserve, or hold together. Extrabiblical Greek use of this word pictures a container holding water within itself. The word is used in Colossians in the perfect tense, which normally implies a present continuing state arising from a completed past action. One physical mechanism used is obviously gravity, established by the Creator and still maintained without flaw today. Consider the alternative; if gravity ceased for one moment, instant chaos surely would result. All heavenly objects, including the earth, moon and stars, would no longer hold together. Everything would immediately disintegrate into small fragments.

General relativity also predicts that if a body were dense enough, its gravity would curve space so strongly that light could not escape at all. Such a body would absorb light and anything else caught by its intense gravity, and so is called a black hole. Such a body could be detected only by its gravitational effects on other objects, strong bending of light around it, and by intense radiation emitted by matter falling in.

There is good evidence that a very massive star, after most of its nuclear fuel runs out, would have nothing to counteract a collapse under its own huge weight into a black hole. Black holes with the mass of a billion suns are thought to exist in the centres of galaxies, including our own, the Milky Way. Many scientists believe that the super-bright and extremely distant objects called quasars are powered by the energy released as matter falls into a black hole.

The main danger to an astronaut near a black hole is tidal forces, caused by the fact that gravity is stronger on the parts of the body closer to the black hole than on the parts away from it. The tidal forces near a black hole with a mass of a star are much stronger than a hurricane, intense enough to stretch an onlooker into tiny pieces. However, while gravitational attraction decreases with the square of the distance (1/r2), the tidal effect decreases with the cube of the distance (1/r3). So contrary to popular imaginings, large black holes have weaker gravitational (including tidal) forces at their event horizons than small black holes. So the tidal forces at the event horizon of a black hole the mass of the observable cosmos, for example, would be less noticeable than the most gentle breeze.

As discussed earlier in Lesson 3, Isaac Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other objects is inversely proportional to the distance separating the earth's center from the object's center. But distance is not the only variable affecting the magnitude of a gravitational force. Consider Newton's famous equation

Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.

But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as

Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.

Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.

The constant of proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. (This experiment will be discussed later in Lesson 3.) The value of G is found to be

Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem.

Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center.

Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.

Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student (a.k.a. the student's weight) is less on an airplane at 40 000 feet than at sea level. This illustrates the inverse relationship between separation distance and the force of gravity (or in this case, the weight of the student). The student weighs less at the higher altitude. However, a mere change of 40 000 feet further from the center of the Earth is virtually negligible. This altitude change altered the student's weight changed by 2 N that is much less than 1% of the original weight. A distance of 40 000 feet (from the earth's surface to a high altitude airplane) is not very far when compared to a distance of 6.38 x 106 m (equivalent to nearly 20 000 000 feet from the center of the earth to the surface of the earth). This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.

The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity (or weight) yields the same result as when calculating it using the equation presented in Unit 2:

3a8082e126