Originally posted by fscott:
For Jimdandy only,
Your equations are correct. I tend to go with HT's explanation that the elliptical orbit is what keeps the moon from falling into the earth. What you are explaining is what I already know. You haven't explained though that an object in a vacuum, such as the moon, steadily accelerate at the gravitational rate. The moon apparently DOES accelerate when the orbit is closest to the earth. The reason is gets closer is because ALL objects accelerate at the gravitational rate. However, the forward momentum of the moon, as you pointed out, keeps it from hitting the earth. What is does do is creates an elliptical orbit.
Here's what i was getting at originally. If you drop a ball in a vacuum with gravity being 10 ft/sec...that ball will be dropping at that rate. Faster and faster, faster until it reaches the just near the speed of sound. This is what I have learned from asking. That was my first question. Now YOU tell me, what are the obvious factors that limit an objects maximum speed in the real world? Drag comes to mind right away as it is probably the single most important factor. However there is no drag in space.
I am _NOT_ concerned with the moon's forward velocity at all! I understood all that stuff from the beginning. My question was since the rate of gravity upon the moon is a constant, it will continue to fall, what keeps it from falling faster and faster and faster rate until it finally hits the earth? And now I think I have a good grasp on it. The elliptical orbit was formed BECAUSE the moon accelerated towards the earth, but JUST missed it. The moon passes by, but the earth's pull is too much to allow the moon to just pass out into space, so it brings it back for another pass, and it just repeats and repeats.
fscott
fscott I want to make this clear that I'm not trying to be a know it all or a smart bellybutton or anything like that. But if you really want to get to the bottom of this question I think I better make sure I understand what your saying.
"...If you drop a ball in a vacuum with gravity being 10 ft/sec...that ball will be dropping at that rate. Faster and faster, faster until it reaches the just near the speed of sound..."
I assume your using 10ft/sec/sec as an example. I think your saying that in a vacuum a ball will reach a maximum speed near the speed of sound. If this is what your thinking it is not correct. The ball will accelerate to near the speed of light. The speed of sound is dependant on the material the sound is traveling thru. If it is in a vacuum there is no material for the sound to travel thru. Sound is a product of friction between the molecules in the material you might say. The more closely packed the molecules the easier it is for them to bump into each other. Light speed as far as we know is the limiting factor in a vacuum (fiction free) environment because the equations show that the mass of an object becomes infinite at the speed of light. E=mc^2, m is the mass of the object, c is the speed of light. (Please Please don't anyone bring in the discovery of faster than light particles. E=mc^2 is still the gospel at the moment.
"...I am _NOT_ concerned with the moon's forward velocity at all!..."
You have to be that is the key to the relationship between the orbit radius and the opposing centripetal force. Look at the equation above and you will see that the key factors are the radius of the orbit and the velocity of the orbital.
"...Now YOU tell me, what are the obvious factors that limit an objects maximum speed in the real world? Drag comes to mind right away as it is probably the single most important factor. However there is no drag in space..."
Yes the atmosphere of earth (air) is what causes the drag. Simple example is putting your had out of the window of a moving car. Yes space is EXTREMELY low drag but there is some. It is a vacuum.
"...My question was since the rate of gravity upon the moon is a constant, it will continue to fall, what keeps it from falling faster and faster and faster rate until it finally hits the earth?..."
The moons velocity as I have said has EVERYTHING to do with your question. It is what creates the counter acceleration because of the constant change in the direction of travel of the velocity vector at the radius of orbit. The moons orbit isn't a perfect circle as you know. But for your question that really doesn't matter at all. It is possible that do to some outside force that the moons orbit about the earth could take on a shape that DOES put it on a collision course with the earth. Let us assume that the moon is in a circular orbit and that your driving the moon. You have a speedometer on the dash of the moon. Think of it as always trying to fly off from the earth's orbit in a straight line tangent to the circle. A simple example is a car going through a curve. If you quit in putting the force on the steering wheel (the earth's gravity in our case) it will take a straight path off of the corner tangent to the curve. Also if you go faster (on the speedometer) and don't turn harder you will go straight off the road. It equal balance that you keep on the wheel of the car that keeps it turning the corner. If you turn tighter (add more gravity) you will turn into the center of the curve and off the road. But you have to go slower (the speedometer) to turn a tighter corner or you will slide off the road (the centripetal force of the moon trying to throw it out of orbit). The speedometer on a car reads tangential velocity. It doesn't see the changing direction of the vector (the centripetal acceleration). If your accelerating it is measuring the instantaneous change in the size of the velocity vector tangent to the curve. Add a stop watch to the speedometer and you can figure out average acceleration over the distance tangent to the curve. If the tangential velocity (the speedometer on the moon) slows down the force acting to oppose the earth's gravity decreases so the moon is pulled into the earth (turning a tighter corner). As I said just take a ball and tie it to a rubber band and swing it around over your head. The rubber band simulates the pull of gravity on the moon (the ball). The rubber will stretch if you spin the ball faster and contract is you spin it slower. It is a simple model of the relationship between the earth and the moon. If you want to escape the gravity (break the rubber band) of the earth the kinetic energy of you ball has to be greater than the gravitational pull on the earth. Kinetic energy is produced by movement: KE=(1/2) mv^2. There is the critical velocity again. I gave the escape velocity example already.
"...The elliptical orbit was formed BECAUSE the moon accelerated towards the earth, but JUST missed it. The moon passes by, but the earth's pull is too much to allow the moon to just pass out into space, so it brings it back for another pass, and it just repeats and repeats..."
The elliptical orbit of the moon is do to several things. The earth isn't a perfect sphere and the mass of the earth isn't distributed equally over the earth. In the above examples that was the assumption and it works just fine to explain most thing about orbitals. There are also other planets in the solar system all of which act on the moon. In the above example that was ignored because the earth is by far the greatest factor. The fact that other forces act on the moon, the earth and the moon are not perfectly round or have a perfectly even distribution of mass cause the other than circular orbit. On top of that you can think of adding this. If you captured the moon into the earth's gravitational field as it was moving past how would it look. Back to the ball and the rubber band. The ball comes flying up and you lasso it with the rubber band. The ball will start to slow down. Then it will stop as the KE of the ball and the force of the rubber band equalizes. Then it will reverse direction and speed up. If there were no friction in the rubber band and no friction of any kind that cycle would repeat over and over forever. That along with the other factors mentioned is what places the moon in a non circular orbit. If the path of the moons obit were made tight enough by some outside force (something hitting the ball for example) it could run into the earth. It is just chance that put it in the orbit we see. Comets and asteroids are in BIG orbits about the sun. If there orbit becomes small enough or happens to cross ours when we are there they run into the earth. Never forget that there can not be acceleration with out something moving (having a velocity). Acceleration is the rate of change in the movement. The earth and the moon want to come together do to the gravitational attraction. The velocity of the orbit prevents that. If the velocity of the moon drops to zero (and I'm sure it wont in my life time
) gravity will take over and pull the two together like a satellite falling back to the earth.
I'm only trying to clarify. I wanted to make sure you knew that the velocity of the moon was the key to the orbit and not secondary. I like talking about this stuff and I like it when people are interested. So if what I just said is what you were trying to tell me than that's great and I apologize for the reply. Thank you for posting something though provoking. <S>
[This message has been edited by Jimdandy (edited 01-30-2001).]
