Gravity

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Gravitation Summary

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Gravity

The term "gravity" implies to many the notion of weight. Since antiquity, objects have been observed to "fall down" to the ground, and it therefore seemed obvious to associate gravity with Earth itself. Earth pulls all material bodies downward, but some appear to fall faster. For example, a rock and a feather fall to the ground at appreciably differing rates, and the logical conclusion of such great intellects as Greek philosopher Aristotle (384-322 B.C.E.) was that heavier objects fall faster than lighter ones. In fact, many erroneously believe this today, but it is found not to be true when tested in a controlled experimental manner. Air resistance is the confusing culprit and, when removed or minimized, all bodies are observed to hit the ground in the same amount of time when dropped from the same height.

Newton's Law of Universal Gravitation

In 1687, English physicist and mathematician Isaac Newton examined the laws of motion and universal gravitation in a classic text, The Principia, making it possible to explain and predict the motions of the planets and their newly discovered moons. Gravity is not just a property of Earth but of any matter in the universe. The essence of Newton's law of universal gravitation is demonstrated by imagining a "point mass," which is a certain amount of matter concentrated into a space of virtually zero volume. Now, suppose there is another point mass located some distance away from the first mass. According to Newton, these two masses mutually attract one another along the straight line drawn directly between them. In other words, the first mass feels a "pull" towards the second mass and the second mass feels an equal amount of "pull" towards the first. Of course, the universe contains far more than just these two isolated masses. The gravitational interaction is between any given mass and any other mass. A particular mass has a total gravitational force acting upon it that is the vector sum of all the attractions from every other mass paired with it. Every other mass will attract the mass in question independently, as if the others are not present. Intervening matter does not block gravity.

The more massive and closer neighbors to our imaginary test mass will exert a larger gravitational force on it than less massive, more distant objects. The force between the test mass and any other point mass is directly proportional to the product of these masses and inversely proportional to the square of the distance between them. Expressing the statement in the form of an algebraic equation yields: F_grav is the gravitational force existing between point masses m₁ and m₂, and d is the distance between the two masses. G is a constant making the units consistent. Its value was unknown to Newton and was later experimentally determined.

Real objects are not point masses but occupy a volume of space and have an infinite variety of shapes. Newton's law applies here by assuming that any object is composed of many particles, each of which is a close approximation to the ideal point mass previously described. Since gravitation is a very weak force compared to electrical or nuclear interactions, small objects that are normally encountered are not held together by self-gravitation. Instead, the electrically based chemical and molecular bonds are responsible. Nonetheless, the object behaves gravitationally like a collection of point particles each pulling independently on any other separate object's collection of point particles.

Fortunately, most large celestial bodies, such as planets and stars, are nearly spherical in shape, have mass that is symmetrically distributed, and are fairly distant from each other compared to their diameters. Under these assumptions, we can treat each object as a point particle and use Newton's formulation. Near Earth, an object's weight is the combined attraction of every particle in it with every particle that makes up the planet. Since Earth is a rather symmetrically distributed sphere, the net attraction of all its mass points on the object is directed (more or less) toward its center, and the object accelerates or "falls" straight down when released. The attraction is mutual, as Earth accelerates "upward" towards the falling object. But Earth is very massive compared to the object, so its inertia or resistance to acceleration is much greater. Its acceleration is immeasurable and we simply observe objects falling "down" to the ground. Heavier objects accelerate downward at the same rate as lighter ones (neglecting air resistance) because of their correspondingly greater inertia.

Einstein's General Theory of Relativity

Throughout the 1800s, Newton's law of gravitation was applied with increasing precision to the observed orbits of planets and double stars. The planet Neptune was discovered in 1846 from the gravitational disturbance it created on the orbit of Uranus. Even modern space science relies on Newton's law of gravitation to determine how to send spacecraft to any place in the solar system with pinpoint accuracy. To better understand gravity's fundamental nature and account for observable departures from Newton's law, however, an entirely new approach was needed. German-born American physicist Albert Einstein provided this in 1915 with the general theory of relativity.

Rather than the "action-at-a-distance" concept inherent to Newton's formulation, Einstein reasoned that a mass literally distorts the shape of the "space" surrounding it. If a beam of light is sent through empty space, it will define a "straight-line" path and hence the shortest distance between two points. The presence of mass, however, will cause the beam to bend its direction of propagation from a straight line and therefore define a curvature to space itself.

To visualize this, imagine a stretched rubber sheet onto which a large mass is placed. This mass creates a depression in the area surrounding itwhile the membrane is essentially "flat" farther out. The larger the mass, the larger and deeper the depression. If another smaller mass is placed on the sheet, it will "fall" into the dimple well created by the heavier object and appear to be "attracted" to it. Likewise, if friction could be eliminated, it is possible to project the lighter mass into the edge of the well at just the right speed and angle to cause it to circle the massive object indefinitely just as the planets orbit the Sun. The Sun is massive enough, Einstein calculated, to cause a measurable deviation in the direction of distant starlight passing near it. The accurate positional measurement of stars appearing near the Sun's edge was successfully made in 1919 during a total solar eclipse, and Einstein's predictions were verified.

Astronauts and cosmonauts prepare to share a meal in the Zveda Service Module on the International Space Station (ISS). The absence of gravity can turn the simple act of opening a can into a challenge.