Beyond the Reach?

Question

Is it possible to get beyond the earth's gravitational field if you go far enough away from the earth?

a) Yes, you can get beyond the reach of the earth's gravity.

b) No, you cannot get beyond the reach of the earth's gravity.

The answer is: b. Newton's vision of gravity is that "lines of flux" or "tentacles" reach out from the earth (or from any mass) into space. The lines of flux NEVER END. They go on forever. But, as they reach further and further into space they get more and more spread out so the force of gravity, which they produce, gets weaker and weaker but never diappears completely. It is like the light rays which come out from a candle, or radiation particles emanating from a piece of radioactive ore. They spread into space. The radiation gets weaker and weaker, but the rays go on forever.

How much weaker? That depends on distance. Visualize a paint spraying can. The can sprays a little square on the wall. Now suppose the wall is twice as far from the can. How much lighter or thinner is the paint spray on the more distant wall? That depends on how much more area the same spray must cover. How much larger is the area of the second square? Twice as large? No.

The second square is twice as high and twice as wide, so its area goes up FOUR times. So the spray is only one fourth as dense in the second square. Likewise, the intensity of gravity, or heat, sound, or light from any such point-like source is reduced to one fourth if the distance of the source is doubled. If the distance of the source is increased three times, the square is three times higher and wider, so spray density is reduced nine times. In general, for any stuff spreading through space from a point source: Intensity~1/(distance)^2. This results in a very sudden rise in intensity as you get close to the source. Thus, children get the notion that heat is "in" a flame and that the surrounding space is cold.

Back to gravity. Surrounding every bit of matter in the universeis a gravity field. You are matter, and you are surrounded by your own gravity field. How far does it reach? To the far ends of the universe. Your influence is everywhere...really!

Answer 1

a) Yes, you can get beyond the reach of the earth's gravity.
A gravitational field is denoted by the formula, E= G*Mass/((distance)^2)
So we find that the field is zero only at infinite distance. But imagine a vacant Earth. It's gravitational field attracting any thing and every thing massive. The things are attracted towards it and with time, rush towards the planet, gaining kinetic energy. Therefore if I give exactly the amount of energy that it had gained in coming, it would reach back to the point from which it had started. If I give a little more, it would go farther, more, farther and so on. Finally i can get a speed with which if it is thrown from the planet, earth will never be able to stop it. But as it is clear the body will reach out of the field but only in infinite time. So you indeed can escape the field theoretically but practically it is senseless. The distance would be infinite, i e. as long as you can measure distance you will always yourself in the field. Hence the answer should be a) and b) both. You can get out of the field given all the time, a lot of energy and a vast space to travel. No you cannot get out of the field because you will never be able to. Whenever you will think, 'It's been long since I have traveled, I should measure the field.' you will find a measurable field.
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This is an edit. As has been pointed above, it is different thing to be out of the field and not being affected by it. If a force equal to the gravitational force by the earth is applied on you, you will not feel the effect of the field. However I feel that the question wishes to ask about getting out of the field. Even at the center of the planet, all the particles are still attracting you, but the net effect is zero.
Yours,
D

Answer 2

strictly speaking, you will always experience the earth's gravity... but it is pretty irrelevant once you get to the distance of the moon.

if you're somewhat further along the physics learning curve,
the potential energy of a mass in a gravitational field is

U = -GMm/r which only goes to zero at infinity. Since F = -grad(U), the force never quite vanishes either.

and if even further, you can't experience the earth's gravity field at a point that is beyond the edge of the light cone that corresponds to the range that the earth's field has permeated space - around 4.5 billion light years.

so there you have three answers... they are all different and they are all correct :-) ain't physics fun?
hth.

Answer 3

I'm taking the position that the answer is "A." (I know, the answer Dr. H would like is "B" for the reasons set forth in my para 2 & 3, below, but it is more interesting to explore contrary ideas). I note that being beyond 'earth's graviational field' and beyond the 'reach or earth's gravity' are quite different than being beyond where earth's gravity has no effect.

Imagine you are a space traveler. How would you define "Earth's gravitational field"? You would define being out of Earth's gravitational field by when the gravitational pull of other objects exceed that of Earth's.

Gravitational fields are like a landscape. Earth's gravity creates a 'valley' or 'basin' in the fabric of space. Once you get out of the basin, you are beyond the effective range of earth's gravitational field. Even though earth's gravity continues to have a minor effect on the topology of the space you are travelling through, you are literally beyond the reach of earth's gravity. You are no longer being accelerated towards earth.

When the gravitational field slopes to an object other than earth, as a traveler in space, you would say that you are beyond the reach of earth's gravitational field. You can travel farther to get beyond the Sun's gravitation field and beyond the galaxy's gravitational field using the same principal.

Kirchwey, Lynlions and Noisejammer all make good points. I have my own take on the same subject-matter.

1. As for Kirchwey's answer, all you have to do is hollow out a cavity at the center of the earth instead of shrinking yourself to a point. This cavity could be as big as you want. (In a hollowed sphere, only matter located closer than you to the center effects you). Then you could live quite comfortably -- if you can get the air conditioning to work -- floating around in your hollowed shell at the Earth's center and beyond its gravitational field.

2. I note that, in support of "B" it is not possible for any of us, as earthlings, to get beyond the effect of Earth's gravity (even though we are in the gravitational field of another body, see above). According to Einstein's theory of general relativity, the gravitational field travels at the speed of light. Since none of us can travel as fast, let alone faster, than the speed of light, we can never get to a point beyond which Earth's gravity has no effect.

3. Lastly, Newton's law of gravity states F=G *m1*m2/r^2. and the field will never go to zero, because r never goes to infinity -- or at least, we can never get to a point that is infinitely far away.

(Although, if the universe is finite and closed, Under the Newonian concept of gravity, there will be a point where earth's gravity, from all directions balances. However, if we apply the concept of the Big Bang and relativity, this point [or expanse of space] has not felt the effects of the matter that currently makes up the earth since the Big Bang itself -- when someone there looks towards earth, he or she sees the Big Bang)

Answer 4

Generally no, as the 1st answer says. However instead of going far away, you can zero the effect of earth's gravity by the simple expedient of digging a 4000 mile hole straight down to the earth's center, going there, and shrinking yourself to a point. If you can do that in less than 4.5 billion years, you win the race!