Date: Tue, 1 Nov 1994 20:03:21 -0500 (EST) From: Boats Subject: Gravity Hello Dr. Math, I teach a course titled The Non-Western World. Across the hall from me there is a class of Math Superstars and I'm going to pass on your service to them. Meanwhile, I have a question. When space ships get close to earth, gravity seems to effect the occupants really fast. Why isn't the effect of gravity a gradual occurence? Does it have anything to do with that law about any two bodies in the universe affect each other... and does it have to do with inverse relationships? Thank you Fred Hunt Internet: email@example.com Raleigh, North Carolina West Millbrook Middle School
Date: Tue, 1 Nov 1994 20:28:10 -0500 From: The Swat Team Subject: Re: Gravity Hi! I'm Heather, and I'm a member of the swat team. Thanks for writing. I'm not entirely positive, because it's been a while since I've taken physics, which is what your question refers to, but I'm thinking that the answer to your question is that the force (F) between two objects is equal to the mass of the first (M1) times the mass of the second (M2) divided by the distance between the two(r) squared, all times some defined constant that I can't remember (G)... (M1*M2) F = (G) -------- r^2 Gravity would affect the occupants quickly because of the r^2 in the bottom. As the distance between the two objects decreases, the force increases exponentially. I'm sending this to the other Swat team members, so if there's a problem with this explanation, someone will help. Date: Wed, 2 Nov 1994 09:20:50 -0500 Subject: Re: Gravity The inverse square law has little to do with this effect. Let r be the distance of the rocket from the center of the earth. The gravitational force on the rocket is GMm/r^2, as you say. At the surface of the earth we have r^2 = (6.37x10^3 km)^2 = 4.06x10^7 km^2. In an orbit 200 km above the surface of the earth, which is well above the point where atmospheric heating is important, we have r^2 = (6.57x10^3 km)^2 = 4.32x10^7 km^2. The difference between the two is only about 6%. The real reason (I think) has to do with the exponential increase in density of the atmosphere as the rocket approaches the earth. The force the astronauts feel comes from the rapid deceleration of the rocket as it descends due to the exponentially increasing frictional force of the atmosphere. A very important point: When you are inside a rocket, as long as it is in free fall you cannot tell that you are in a gravitational field -- you feel weightless. (Note that a rocket in orbit beyond the atmosphere is in free fall.) The only time you feel heavy is when the rocket is accelerated in a way the gravity would not produce; i.e., when the rocket fires its engines, when the rocket encounters a frictional force, or when the rocket is sitting on the earth and thereby being prevented from falling through it. Nice question! Josh
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