Originally posted by: liquid51
The original topic of the thread was a discussion of shedding g forces. I said that astronauts are not accelerating, simply maintaining orbital velocity, because that is what is required to negate the gravitational pull of the earth. Because forces are acting apon the astronauts in a perfect balance, they feel nothing. Therefore, because we are speaking reletively, reletive to the astronauts bodies, there is no force. They are not currently being smashed or ripped apart. Those are the magnitudes of force which place limits on our rates of acceleration.
liquid51
Velocity is a vector; it has magnitude AND direction.
Simply because the astronauts are changing direction, their velocity is changing.
Change in velocity is called acceleration.
The astronauts are.... (drum roll) accelerating.
There is no room for debate on this. Circular motion is not possible without acceleration.
Acceleration is the result of unbalanced forces, so the forces are, in fact, not balanced.
Furthermore, if you do F=Gmm/r^2 for the orbit of astronauts, you may be surprised to find out how high their acceleration actually is.
Question: If a high diver is standing on top of a 100 foot cliff, does the earth exert a force on him? Yes. If the high diver jumps over the cliff, does the earth exert a force on him? Yes. If it didn't, he would float in mid-air. The force (gravitational) accelerates him downward. Now, if someone drove a car off a cliff, does the frame of the car magically block the gravitational force acting on the driver? Of course not. The force of attraction between the earth and car, and between the earth and driver cause both to accelerate at the same rate toward the earth (9.8m/s^2). When you're in an amusement park ride that experiences "0 g's", is it because somehow Disney has figured out how to turn gravity on and off (by pushing a button??) No, it's because you and the vehicle are in freefall. (Although, if you have a forward velocity, freefall will follow a parabolic path; much the same way a rock thrown upward at an angle falls back to the earth along the path of a parabola (ignoring air resistance.)
Now, the astronauts are in fact accelerating, somewhere around 7 or 8 m/s^2. (It's been a year since I had students calculate the gravitational force acting at that distance) This acceleration is free-fall toward the center of the earth. There *IS* a force acting on those astronauts. However, they are accelerating toward the earth in free fall *at the same rate their spacecraft is accelerating toward the earth.* Thus, they're in the equivalent of riding on a rollercoaster that experiences "0 g's" Now, on the roller coaster, if you're moving forward at 20 m/s relative to the ground, by the time your altitude has changed from 45 meters to 0 meters, (about 3 seconds in freefall), you will have moved forward about 60 meters, relative to the ground, following a parabolic path. However, the astronauts are accelerating just a little bit slower. BUT, they're moving so fast that by the time they've fallen 45 meters in altitude, they've moved far enough forward that the curvature of the earth causes the land to have dropped away by 45 meters as well.
Now, I think a few people are confused about the g-forces a body can stand; how it is that the body can't stand them. Try this: Cut about a 1/4 inch hole in the bottom of a 2-liter bottle. Cover it with your hand and fill the bottle with water. Leave the cap off.
Now, when you remove your hand, what happens to the water? Answer (captain obvious) - it runs out the hole in the bottom.
Now, suppose we cover the hole with some sort of thin membrane. Just strong enough so that it won't break... right on the verge of breaking though. Now, get in the worst elevator you've ever been in (one that accelerates so fast at the beginning that you think you're stomach is in your feet.) Oh no. The membrane is going to break. Think of it as the elevator is applying a force to the bottle (causing the acceleration). Since you're accelerating upward, the bottle is experiencing more than 1 "g" of force, and the membrane breaks. This could represent your blood vessels, or whatever tissue you want in your body, not to mention your blood rushing from your brain to your feet.
Now, the fun part. Find a nice 10 story building where they'll let you throw stuff off the roof or out an upper floor window. Fill the 2 liter bottle with water, keep the hole covered with your hand and keep the cap off. Now, throw the 2-liter bottle out the window (obviously, letting go of the hole.) You'll notice that as the bottle accelerates toward the earth that NO water is coming out the top or out the hole in the bottom. That's because gravity is pulling on the bottle and water at the same time and causing both to accelerate at the same rate. Back to the elevator. The elevator was applying the force to the bottle (but not to the water) The bottle was applying the force to the water. Likewise (Newton's 3rd law) the water was applying a force to the bottle. It is in this case where the human body can only stand so much force. Not in the case of freefall where all the parts of the body are being pulled on to accelerate at the same rate. (Silverpig or someone else above noted that the gravitational field can't be changing rapidly as in the case of black-holes. In the case of black holes, if you fell in feet first, the difference in the force acting on your feet and the force acting on your head is so large, that it would rip you in half)
One more attempt at an analogy. Imagine 2 large toy cars, connected by a piece of thread. Push on just the car in front, causing it to accelerate, and the thread is going to break. However, if you push on each of them, causing each to accelerate at the same rate, the thread isn't going to break, regardless of the acceleration. You could accelerate both cars at 100m/s^2, and as long as they start at the exact same time and accelerate at the same rate, they're going to stay the same distance apart and the thread isn't going to break. Such is the case of a human in free-fall. They can accelerate at any rate, and as long as each little piece of their body is accelerating at the same rate, they're not going to break (like the thread.) But, just push on one of the cars, and the thread breaks. Put a person an elevator and accelerate them vertically at a very high rate, by just pushing against their feet, and their head is going to wind up at their feet (call it inertia if you will.)
I hope that makes some sense of it for you.