GravityWhat is gravity?Gravity is an attractive force, one that attracts all of the matter in theUniverse towards all of the other bits of matter in the Universe. On the sizescale of moons, planets, stars, and galaxies, it is an extremely importantforce, and governs much of the behavior of these objects. Gravity keeps ourfeet firmly on the ground, keeps the Moon in orbit around the Earth, keeps theEarth in orbit around the Sun, keeps the Sun in orbit around the center of ourMilky Way galaxy, keeps the Milky Way and Andromeda galaxies orbiting theircommon center of mass, and so on, and so on ... for matter, gravity reallymatters!When dealing with the force of gravity between two objects, there are only twothings that are important – mass, and distance. The force of gravitydepends directly upon the masses of the two objects, and inversely on thesquare of the distance between them. This means that the force of gravityincreases with mass, but decreases with increasing distance between objects.We are drawn towards the most massive objects, and towards the closestobjects. Even though the Sun is far more massive than the Earth, the Earth"sclose proximity insures that our feet stay planted on terra firmarather than zooming off toward the Sun. A space craft docked on Earth actsthe same way; but if we fire it off toward the Moon, there will come a time atwhich the Moon"s weak gravitation attraction outweighs that of the moredistant Earth, and the space craft will begin to drift toward the lunarsurface.By how much does gravitational attraction increase with increasing mass(M1 and M2) and by how much does it decrease with increasingdistance (R)? For a gravitational force, F,
where G is a constant factor (the gravitational constant), which doesnot vary.Since the distance term is squared (the exponent is a two), the force ofgravity falls by a factor of four when the distance is doubled (as two squaredis four), and by a factor of nine when it is tripled (as three squared isnine).However, the exponent on the mass terms is one. This means that if one of theobjects suddenly became ten times more massive, the gravitational attractionbetween the two objects would grow by ten times as well.
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What is the difference between force and acceleration?You may have noticed that the gravitational force equation is symmetric forour two objects – does this mean that the gravitational force that youexert on the Earth is as strong as that exerted on you by the Earth? Yes!This may seem puzzling at first, so let"s take care to distinguish betweenforce, F, and acceleration, a.Your gravitational acceleration is the rate at which your speedincreases as you are drawn toward another object (how quickly you becomeattracted to it).Your gravitational force is the product of your acceleration and yourmass, m.
Let"s consider the gravitational force between you and the Earth. As above,your mass is m and your acceleration is a. The Earth"s mass andacceleration are M and A, and the distance between you and theEarth is R. (You can think of R as the Earth"s radius.)
It is clear that the force that you exert on the Earth is a large as the forcethat the Earth exerts on you. However, how does your acceleration toward thecenter of the Earth compare to the Earth"s acceleration toward you?
Because your mass is much less than that of the Earth (m M),your experience a much greater acceleration than the Earth does (a >>A)! This is why if you toss a ball into the air, it is pulled back toEarth rather than pulling the whole Earth to it.In a certain sense, the force tells you how hard you are being pulled,and the acceleration tells you how much you move in response.
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The moremassive an object is, the harder one must pull to move it. (As anyone who hasever tried to help a friend arrange, and re-arrange, their living roomfurniture set knows well.)On the surface of the Earth, the gravitational force is what we call your weight, and the gravitational acceleration is equivalent to the surface gravity, g, equal to 980 centimeters per second squared.