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Direction of Force of gravity on two people, concept?

  1. Oct 19, 2014 #1
    I know that there exists a force of gravity between person A and person B that are action reaction pairs.

    My question is, is this gravitational field inherent in matter(i think higgs boson) look like an electrostatic field between matter? I ask this because, it seems that the moon and the Earth from our point of view, the gravitational force is straight up and down, but the gravitational force between two people, or even electrons, is side to side...
     
  2. jcsd
  3. Oct 19, 2014 #2

    davenn

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    what makes you think that ?
    it is, only if the moon is high in the sky above you

    what if the moon is on the horizon ? ;)

    Dave
     
  4. Oct 19, 2014 #3
    Realize that our notions of "up and down" having meanings precisely because of the direction of the terrestrial force of gravity.
     
  5. Oct 20, 2014 #4

    CWatters

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    Lie on the ground. Now gravity is acting sideways.
     
  6. Oct 20, 2014 #5
    Your first question seems to have gone unanswered. Yes gravity is an inherent feature of matter.

    Anything with a mass will have a gravitational influence. Before Newton, gravity as a concept was not very well understood, it was not clear that astronomical objects moved the way they do due to the same force that holds us to the surface of the Earth and make things return to the surface of the Earth when elevated and let go (I tried to phrase this carefully because if things are elevated quickly enough they can keep going away from Earth forever.)

    I think it is this pre-Newtonian lack of understanding that your "up/down" versus "side/side" might be referring to. It seems odd that an apple will fall straight down to Earth when if detaches from a branch, whereas the Moon appears to move around us in a circle also due to gravity. You've probably noticed that even if you toss an apple quite fast parallel to the Earth surface it falls down eventually, and might wonder what is "keeping the Moon up"? At least I struggled with this when I was young.

    What Newton gave us which helped us understand gravity is a whole box of wonderful tools. First of all he defined that it is forces which affect the motion of things. He tells us that without forces acting on something the thing will either be at rest or move with unchanging speed in a straight line (first law). Also he gives us a relation between the strength and direction of a force and the resulting "change in speed and direction" (acceleration) of the thing the force is acting on (second law). He also noted that forces seem to always come from "things", which he calls bodies, and that when one thing is affecting another with a force, the opposite is also always happening; the other is affecting the first thing (third law).

    The old Greek philosophers understood that the Earth was round. Their conclusion was that while it appears that things fall "straight down" to Earth, they are really falling towards the center of the Earth. Otherwise stuff on the other side of the planet would have fallen into space long ago, and indeed Earth would probably fall in that direction too (not true, but this was their line of thought.) Things falling towards the center of the Earth fitted very well with their view that Earth was at the center of the Universe.

    When Newton started thinking about motion in general terms, he wanted to put all types of motion into the same framework. Forces turned out to be the right way to accomplish this. Like the Greek, Newton arrived at the notion that gravity appears to be directed towards the center of the Earth. In fact he went on to show that as each part of the Earth contributes a bit of gravity (including people on the surface), the net result when seen from a distance (for example as the Moon would experience it), works as if all of the gravitational force was placed in the center of the Earth. This works very well to describe falling apples and what happens when we step onto a bathroom scale to weigh ourselves; objects are drawn towards the center of the Earth with a force that is proportional to the mass of the Earth.

    While Kepler had done a great job at writing down laws that documented what we can expect to observe when looking at planets and moons, there was no real sense of understanding where his laws came from. Newton considered what would happen if Earth would instantly disappear, and how that would affect the motion of the Moon. Would it keep going in circles, or would it fly off into the distance? (I say circles but the orbits are really ellipses as Kepler had shown.) According to Newton's first law the Moon would continue moving in a straight line in the direction it was moving the instant Earth vanished.

    Imagine tying a rock to a piece of string and swinging it around above your head. The rock is moving in a circle. If you let go of the string, the rock flies off in a straight line. Gravity between the Moon and Earth works like the string; it pulls on the Moon with exactly the force needed to keep it in orbit. So in that sense the Moon is falling towards Earth, but it simply keeps missing because it has a velocity pointing in the "sideways" direction. If the Moon would "stand still" next to Earth at its current distance, it would immediately start falling straight towards us, which would be unfortunate.

    The force of gravity from Earth is obviously affecting the Moon, keeping it in orbit. But it is not keeping Mars or any of the other planets in orbit around Earth. This is because the strength of gravity weakens over distance. The two facts (that gravity is proportional to mass, and that it weakens over distance) are combined in Newton's law of gravitation: Fg = G(M1*M2) / r^2; where Fg is the force due to gravity, M1 and M2 are the masses of two objects, r is the distance between them, and G is a constant that makes the units of force, distance and mass proportional. So G is different depending on whether we use pounds and feet or grams and meters for example.

    The r^2 in the denominator is the reason we call the force law an inverse square law. Newton showed that this is what causes planets and moons to move in elliptical orbits, thus providing a model that explained Kepler's laws. The combination of the force diminishing with the square of the distance and the fact that the force can be considered to act from the center of a distributed mass is why we call it a central force. In this aspect gravity has a lot in common with electric and magnetic forces, which have been described so well using the concepts of fields. Gravity can also be described using fields, which is actually quite useful.

    We can add Newton's second law to the mix, it is written as F=m*a. Let's call the mass of Earth 'M' and the mass of an apple 'm'. Then Fg=G(M*m) / r^2. If we then ignore all other forces and only focus on the acceleration due to the gravitational pull (F = Fg), we can rewrite the second law as a=F/m. Inserting the gravitational law into this equation we get a = (G(M*m)/r^2) / m. The two 'm' will cancel out, giving us a = G*M/r^2. If we take r to be the radius of the Earth, then this is what we call 'g' the acceleration due to gravity. Since the actual mass of the small object has been eliminated, we get the interesting fact that both light and heavy objects are accelerated the same by gravity.

    A small apple and a large apple should fall at the same rate, or even an apple an a feather should fall at the same rate (technically be under the influence of the same acceleration.) Indeed without air resistance they do, as Armstrong demonstrated on the Moon by dropping a hammer and a feather; (I hope I am not violating policy by posting this video.) Indeed it was good that his experiment confirmed Newtonian gravity, otherwise their plan for returning home would be in jeopardy.

    Further to the above, it is also worth noting that if we would want to determine G from the derived equation we would have to know the mass of the Earth quite accurately. Alternatively, if we could determine G without knowing the mass of the Earth, the derived equation can be used to figure out the mass of the Earth. Cavendish set up an experiment which measured G very carefully using the gravitational force between two known masses. When asked what he was doing his answer was "I am weighing the Earth", or at least that is how the anecdote goes. Note that he probably phrased this very differently though (http://en.wikipedia.org/wiki/Cavendish_experiment)

    Newton explicitly noted that he was offering a model for how gravitational forces could be calculated precisely, he underlined the fact that he gave no mechanism for how this force was propagated. In other words; it is a mathematical description of what happens, my says nothing about HOW it happens. It was not until Einstein that we got a good model for "how", and it involves some modifications to Newtons model that are important in extreme situations. Einstein also informs us that the gravitational force propagates at the speed of light, and not instantaneously as Newtons law implies.

    Under central forces, the forces due to each object can be added up individually. So when considering the forces of several "bodies" you can calculate the forces between pairs of bodies and add them all up (I am not talking about the equations of motion here, simply the forces present at a given instant). Your question of gravity between two people can now be answered. There is a gravitational force between person 1 and Earth which is very strong (because Earth has a very large mass), the force points towards the center of Earth. The same holds for person 2. Between the two persons there is also a force, drawing them towards each other, but due to the tiny mass of a person, it is unnoticeable compared to the force imposed by Earth. The force is not zero, it can be (and has been) measured, but you do not feel this force in your daily life. If Earth was not there at all (two people are floating in empty space, hopefully wearing appropriate suits) then you would see a slow acceleration of the people towards each other. A large cheese or a grain of dust would likewise experience the gravitational force.

    When it comes to electrons, there is also a gravitational force. But the electromagnetic forces between them are so much stronger that we usually completely ignore the gravitational forces. In fact, the gravitational force is 10^36 times weaker than the electromagnetic force. So only if we need to know a result to more than 36 decimal places would it make a difference to neglect gravity!

    In summary; people and apples fall towards Earth due to gravity. It is exactly the same "falling towards Earth" that keeps the Moon in its orbit rather than seeing it fly off at a tangent straight off towards infinity. Gravity depends on the masses of the objects considered as well as the distance between them.


    I hope you might find this at least entertaining if not a helpful answer to your questions.

    Michael
     
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