by Ammon Piatt
Here are some things running around in my head at the moment. Is the force of gravity the same everywhere on the earth?
The earth isn’t perfectly round so does that mean that gravity isn’t always pulling straight down? Would this then mean that some places on earth where gravity isn’t pulling straight down you could jump higher?
How about the distance you are from the center of the earth? If gravity is weaker as you move further away from the earth does that mean you can jump higher at higher elevations?
What about the fact that the planet is spinning. Centrifugal force would be greater around the middle of the pivotal plane verses the axis in which it is spinning. Does this mean that you can jump higher at the equator then you can the North Pole because you have centrifugal force working with you?
Now how does your brain feel?
Friday, September 5, 2008
How does your brain feel?
Subscribe to:
Post Comments (Atom)
4 friends stopped by:
I think you have opened a can of worms on this one. But my head OFTEN hurts when David starts talking about things like this!
Great minds work alike. Many great and important physicists have asked these very questions. It takes great intelligence to understand enough of the physical world to even comprehend the existence of such questions. Keep thinking!
Some of the greatest minds of science have designed experiments try to answer some of these questions. We know unbelievably little about gravity. My dad studied a little of this stuff as part of his astrophysics degree at Berkeley in the late 1940's. Everyone is stumped by gravity and its properties. Yes, even Einstein couldn't figure it out.
Experiments using the spacelab, space station, and orbiting satellites have shown that yes, gravity does indeed vary around the world, albeit slightly.
It would be more accurate to say that "gravity's pull" or "gravity's effective force" varies around the world, because gravity itself is not the force, but the name we give to the effect of the force.
Gravity's pull varies not so much due to altitude, but mainly due to the earth's density. In other words, gravity's pull varies in different parts of the world as the magma lumps and tectonic plate composition varies around the world. There are "lumps" in the mantle, some thicker and heavier than others, and as you get over a dense area, your weight (gravity's pull) increases. These lumps were actually discovered and mapped by (!) measuring the variations in gravity above them.
So can you jump higher on mountains than on the seashore? It depends more on what's under the mountain or under the seashore than on how high the mountain is.
So can you jump higher at the equator than at the pole? This is where Einstein's relativity comes in.
Centrifugal force (and its counterpart, centripetal force) are called "fictitious forces" because they are completely dependent upon a frame of reference, not action or reaction or other objects. When something is moving, if you are on that something, you can't tell that it is moving unless you have a reference point of something that "isn't" moving. If you are in a car, and another car goes by you from left to right, you can't tell whether you are moving right to left or the other car is moving left to right, unless you have a third reference point (such as the ground or a telephone pole) to serve as a frame of reference.
Physicists refer to either an "inertial" frame or a "rotating" frame of reference, and Newton's laws of motion differ based on which type of frame of reference you adopt. This is another reason why gravity is so hard to understand.
Gravity therefore acts as the centripetal force to keep you on the rotating surface of the earth, and the gravitational force far surpasses the centrifugal force attempting to pull you off. And since your jumping is in reference to the mountain which is also moving at the same speed you are moving (making your frame of reference inertial, e.g., you appear to be standing still with respect to the surface of the earth) your "jumping" at the equator is relatively unaffected by centrifugal forces compared to jumping at the poles.
Centrifugal forces come into play, however, in orbital mechanics, where the apparent vector of motion places the trajectory (and the acceleration inherent in the vector's directional change) in a different frame of reference, and the motion appears to "overcome" gravity from the perspective of the inertial frame of reference of the earth's surface.
In other words, gravity in space is not the same as gravity on the surface of the earth. This is one of the points of Einsteins theory of relativity.
Few people realize it, but in reality, an orbiting satellite and the "weightless" astronauts on it are subject to just as much gravity pull as the rest of us while they are in low earth orbit... it's just that their lateral motion is so fast that by the time they've "fallen to earth", their lateral motion has taken them sideways so far that the earth is no longer beneath them, and they "go around" to the side of it, continuing their "fall" as they go.
This is why spacecraft "re-enter" the earth by "braking" their speed. Gravity exerts the same pull on them regardless of their speed, so as they slow their speed, they no longer "miss" the earth by going to the side of it... they appear to fall back to the surface.
But this gravity force is based on a rotating frame, e.g., the spacecraft is in motion relative to the earth, whereas on a mountain, you are "standing still" relative to the earth.
This is why gravity appears to be a violation of other laws of physics. For example, it is well known that energy diminishes with the square of the distance. As you double your distance from an energy source, you diminish the energy's force by four times. If you triple your distance, you decrease the force by nine times. But hey, gravity doesn't work this way! And only part of the anomaly can be explained by the problem of figuring out where the base location is. (Is it at the center of the earth, or the earth's surface? It doesn't matter because the formula doesn't appear to work for gravity! Why not? No one knows!)
It is this counter-intuitive result (e.g., by living on earth, most of us unconciously adopt the inertial frame and have trouble imagining the rotating frame) which makes understanding Keplerian orbital mechanics so difficult to comprehend without a thorough grounding in the concepts of Newton's calculus.
And because of this difficulty and the apparent "breaking of the rules of Newtons laws of motion as we know them", this is why we know so darn little about gravity. We need some genius to come up with some replacements for Newton's and Kepler's and Copernicus' laws before we can figure out what's going on.
(And yes, even Einstein and Hawking's works are insufficient to explain why gravity behaves the way it does!)
So keep thinking about it, and keep inspiring others to think about it. The mind is like any other part of the human body... the more you exercise it, the stronger it becomes, and the more it can accomplish.
(This post illustrates the danger of letting just anyone comment on your blog... you never know when some jerk is going to go off on a tangent like this. And speaking of tangents, did you know that tangents, cosines, sines, and other trig functions were the inspiration for Newton's discovery of calculus? It wasn't the apple falling on his head, it was "thinking" about how things go around in circles and fly off at certain angles that prompted his asking questions which helped progress mankind.
Keep on thinking! and keep on asking questions, even if no one knows the answer. Maybe you might become the next Newton or Einstein! Einstein was no Einstein in school, he was a simple patent clerk who started thinking about some of the inventions he was seeing cross his desk, and relating them to his question as a five-year-old as to what was moving the needle on the compass his daddy had given him! Asking questions, even ones that don't have an answer yet, is the best way to push man's understanding forward.
You asked! Thanks for letting David comment. He loves this stuff and loves to explain it.
I read somewhere about the mass and gravity idea. If that is true that each atom has some minuet pull toward another it makes since that where the earth has higher density the "gravitational" pull is higher. More atoms in a given amount of space would mean more pulling. This means that if we could some how make the earth bigger we would be spreading out the atoms in a bigger area and creating less of a pull e.g. we could jump higher! (keeping the amount of mater in the earth the same). I guess if we could ever get the density of atoms above us great then the amount below us we would in a since fly, being pulled to the greater density of atoms. Kind of like how and air plain wing creates lift.
I don’t think I have heard of Keplerian’s orbital mechanics but the way you explained it I think it makes since. I mean everything is relative right… so when someone goes into space it doesn’t mean they stop moving. Think about it if someone is space “stopped moving” the earth would leave them in the dust and be gone so fast they would never get back to it. Thinking about a path from here to the moon for example you can draw two circles on a paper and a line connecting them. This is what it would be like with out motion. This isn’t the case and because there is motion, as in the earth is moving and the moon is moving and you will be moving going from one to the other.
Sure the closer you get to earth the more the density of the earth pulls you to it. The same goes for the moon. As you get closer to the moon the pull of it’s atoms over powers the other atoms, whether from the earth or the sun.
So back to the idea of jumping higher if we created something that was extremely dense, 10 times the density of the earth, and put that above where we were jumping we could jump higher. I vaguely remember something about block wholes and the density that they have. Something about they are so dense and having so much of a “gravitational pull” they not even light can escape.
The key to jumping higher is to decrease the density below you or increasing the density above you, holding all other thing constant. Would this mean that if you went into a cave miles into the earth that the more earth you got above you the higher you could jump?
Ok must do some work, I’ll think more later.
PS Thanks for the post.
Post a Comment