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Unformatted text preview: Newton ’ s laws of motion and gravity 1. Every body continues in a state of rest or uniform motion (constant velocity) in a straight line unless acted on by a force. (A deeper statement of this law is that momentum (mass x velocity) is a conserved quantity in our world, for unknown reasons.) This tendency to keep moving or keep still is called “inertia.” (Nobody really knows what it means.) 2. Acceleration (change in speed or direction) of object is proportional to: applied force F divided by the mass of the object m i.e. ⇒ a = F/m or (more usual) F = ma This law allows you to calculate the motion of an object, if you know the force acting on it. This is how we calculate the motions of objects in physics and astronomy. ⇒ You can see that if you know the mass of something, and the force that is acting on it, you can calculate its rate of change of velocity , so you can find its velocity, and hence position, as a function of time. 3. To every action, there is an equal and opposite reaction , i.e. forces are mutual. A more useful equivalent statement is that interacting objects exchange momentum through equal and opposite forces. What determines the strength of gravity? The Universal Law of Gravitation: 1. Every mass attracts every other mass. 2. Attraction is directly proportional to the product of their masses. 3. Attraction is inversely proportional to the square of the distance between their centers. Newton’s Law of Gravity : Every object attracts every other object with a force ⇒ F (gravity) = (mass 1) x (mass 2) / R 2 (distance squared) Notice this is an “inverse square law” (right illus.). Orbits of planets (and everything else) are a balance between the moving object ’ s tendency to move in a straight line at constant speed (Newton ’ s 1st law) and the gravitational pull of the other object (see below). Now we ’ ll see how all this can be combined to calculate the motion of any object moving under any force (gravity or otherwiselike a magnetic force, or friction, or anything. But first: more on the Newton’s law of gravity How is this “force” transmitted instantaneously , at a distance? (“Gravitons” translation: we don ’ t know). Today, gravity is interpreted as a “field” that is a property of spacetime itself, or even stranger interpretation. Nobody really knows what gravity “is,” we just see things falling… But for most applications, Newton ’ s law of gravity is sufficient to calculate the orbits of nearly all astronomical objects. We only need to combine it with Newton ’ s 2nd law ( a = F/m , where F is the expression for the force of gravity). Then we can solve for the acceleration , which is the change of velocity with time. This gives us the velocity (you have to solve a “differential equation” a = dv/dt = force/mass); since v is just the change in position of the object, we can calculate the position of the object as a function of time....
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 Fall '07
 Harvey
 Mass, General Relativity

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