# Gravity and Gravitation

## Newtonian Gravity

Newton's universal law of gravitation states that all objects in the Universe attract all other objects. Thus the Sun attracts Earth, Earth attracts the Sun, Earth attracts a book, a book attracts Earth, the book attracts the desk, and so on. The gravitational pull between small objects, such as molecules and books, is generally negligible; the gravitational pull exerted by larger objects, such as stars and planets, organizes the Universe. It is gravity that keeps us on the Earth, the Moon in orbit around the Earth, and the Earth in orbit around the Sun.

Newton's law of gravitation also states that the strength of the force of attraction depends on the masses of the two objects. The mass of an object is a measure of how much material it has, but it is not the same as its weight, which is a measure of how much force a given mass experiences in a given gravitational field; a given rock, say, will have the same mass anywhere in the universe but will weight more on the Earth than on the Moon.

We do not feel the gravitational forces from objects other than the Earth because they are weak. For example, The antenna (cylindrical bar, bottom center) of the gravitational wave detector Auriga under construction at Legnaro, Italy. Auriga is one of the first ultracryogenic antennas in the world. Gravitational waves will be detected by the 10 ft (3 m) long bar which will be suspended in the shell seen in the background on the left. The shell will shield it from external vibrations. The bar will also be cooled to a temperature of -459.2°F (-272.9°C [0.1K]) to minimize its own atomic vibrations. Auriga will be detecting gravitational waves from supernova explosions within the galaxies of the Local Group. Photograph by Tommaso Guicciardini. Photo Researchers, Inc. Reproduced by permission.
the gravitational force of attraction between two friends weighing 100 lb (45.5 kg) standing 3 ft (1 m) apart is only about 3 = 10-8 N = 0.00000003 lb, which is about the weight of a bacterium. (Note: the pound is a measure of weight—the gravitational force experienced by an object—while the kilogram is a measure of mass. Strictly speaking, then, pounds and kilograms cannot be substituted for each other as in the previous sentence. However, near Earth's surface weight and mass can be approximately equated because Earth's gravitational field is approximately constant; treating pounds and kilograms as proportional units is therefore standard practice under this condition.)

The gravitational force between two objects becomes weaker if the two objects are moved apart and stronger if they are brought closer together; that is, the force depends on the distance between the objects. If we take two objects and double the distance between them, the force of attraction decreases to one fourth of its former value. If we triple the distance, the force decreases to one ninth of its former value. The force depends on the inverse square of the distance.

All these statements are derived from one simple equation: for two objects having masses m1 and m1 respectively, the magnitude of the force of gravity acting on each object is given by:

where r is the distance between the objects' centers and G is the gravitational constant (6.673 × 10-11N m2/kg2.) Note that the gravitational constant is an extremely small number; this explains why we only feel gravity when we are near a large mass (e.g., the Earth).

Newton also explained how bodies respond to forces (including gravitational forces) that act on them. His Second Law of Motion states that a net force (i.e., force not canceled by a contrary force) causes a body to accelerate. The amount of this acceleration is inversely proportional to the mass of the object. This means that under the influence of a given force, more massive objects accelerate more slowly than less massive objects. Alternatively, to experience the same acceleration, more massive objects require more force. Consider the gravitational force exerted by the Earth on two rocks, the first with a mass of 2 lb (1 kg) and a second with a mass of 22 lb (10 kg). Since the mass of the second is 10 times the mass of the first, the gravitational force on the second will be 10 times the force on the first. But a 22-lb (10-kg) mass requires 10 times more force to accelerate it, so both masses accelerate Earthward at the same rate. Ignoring the Earth's acceleration toward the rocks (which is extremely small), it follows that equal falling rates for small objects are a natural consequence of Newton's law of gravity and second law of motion.

What if one throws a ball horizontally? If one throws it slowly, it will hit the ground a short distance away. If one throw sit faster, it will land farther. Since the Earth is round, the Earth will curve slightly away from the ball before it lands; the farther the throw, the greater the amount of curve. If one could throw or launch the ball at 18,000 mi/h (28,800 km/h), the Earth would curve away from the ball by the same amount that the ball falls. The ball would never get any closer to the ground, and would be in orbit around the Earth. Gravity still accelerates the ball at 9.8 m/s2 toward the Earth's center, but the ball never approaches the ground. (This is exactly what the Moon is doing.) In addition, the orbits of the Earth and other planets around the Sun and all the motions of the stars and galaxies follow Newton's laws. This is why Newton's law of gravitation is termed "universal;" it describes the effect of gravity on all objects in the Universe.

Newton published his laws of motion and gravity in 1687, in his seminal Philosophiae Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy, or Principia for short). When we need to solve problems relating to gravity, Newton's laws usually suffice. There are, however, some phenomena that they cannot describe. For example, the motions of the planet Mercury are not exactly described by Newton's laws. Newton's theory of gravity, therefore, needed modifications that would require another genius, Albert Einstein, and his Theory of General Relativity.