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Unformatted text preview: AST 2002 Sec 0004 Fall 2009 Extra info about gravity relevant to Chapter 4 Introduction In class we went over the law of gravity. On page 98 of the textbook you are shown the equation F g = G M 1 M 2 d 2 , where F g is the gravitational force between the two objects you are worried about. The masses of those two objects are given by M 1 and M 2 . The distance between the objects is given by d . The variable G is a universal constant that you dont need to worry about. The important thing to understand is how mass and distance change the strength of the force. We can use this equation to understand what the gravity would be like if you were standing on other objects, both hypothetical ones and real ones in our Solar System. The gravity youd feel depends on your mass, the mass of the thing (planet/comet/asteroid) youre standing on, and the distance you are from the center of the thing. Let your mass be M 1 , let the mass of the thing youre standing on be M X (where we will replace X with the name of the thing), and let the distance you are from the center be d . This last point about d can be confusing: the distance in the equation is not meant to represent the distance between the outer boundaries of the two objects in question. Its the distance between the centers of the objects in question. So the gravitational force you feel here on Earth doesnt depend on the distance between your feet and the ground, it depends on the distance between the center of your body and the center of Earth. Changing Distance Lets explore a bit what would happen to gravity if a fiendishly clever alien race visits Earth and decides to change the properties of Earth. Note that this is the same as asking how your weight would change if the properties of Earth change. The two questions are equivalent. Anyway Im going to explain this by using math but at the end of each part Ill tell you the tricks you can use so that you wont have to do the math at this level. Ill show you how to solve the problem and just use first-grade arithmetic. Suppose that the aliens double Earths radius (and therefore its radius) but keep the mass the same. So all of a sudden were on a much bigger planet that has the same mass. How does the gravity change? Well before we had F g before = G M 1 M Earth d 2 Earth , but now we have As an aside, if you recognize this distinction, this will help you keep straight in your head the fact that there is still gravity in space. The radius of earth is almost 4000 miles. When youre standing on the ground, the d in the force equation is equal to about 4000 miles. Orbiting astronauts are approximately 150-200 miles off the ground, which means that d for them is 4150-4200 miles. Thats only 5% different than d for us here on the ground not much! Astronauts feel only slightly weaker gravity than we do. The reason they appear weightless has other reasons....
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- Fall '08