How far from the earth's surface do you need to be to experience weightlessness?

Question

OK, we all know that astronaults in orbit experience weightlessness because they are in free-fall, not because of their distance from the earth. Here's my question: What if you were not in a free-fall. Let's say that you were standing on a little platform which was resting on the ground in your back yard. Now, imagine that the platform rises slowly like an elevator. OK, now you are 20 miles up, standing on your platform which is hovering. You are still experiencing 1 G.
Let's slowly increase it's altitude in 20 mile increments, pausing each 20 miles. What gravitational effect would you notice at 60 miles up? (Did I remind you to wear your spacesuit?) How about 160 miles up? 10,000 miles up?
At what point to you effectively experience weightlessness??

Answer 1

Gravitational force goes down like 1/r^2. So you never escape it completely, no matter how for away you go.

Centrifugal force, however, counteracts it goes up like r.

At some point, if you are on the equator, the forces are equal (opposite) and you are effectively weightless. That point is the height of a geostationary orbit. It's where you can park a satellite in orbit above the equator and have it not move relative to the surface.

Gm/r^2 = m(omega^2)r

r = cube root (G/omega^2)

Look up newton's G.

Omega = 2 pi radians / (sidereal day).

Or just look up "geostationary orbit" on wikipedia.

Note: if your backyard isn't on the equator, you will never be able to be weightless this way because the gravitational and centrifugal forces don't push in the same line, so they can't cancel. As others noted below, there are other ways to be weightless like parking yourself at a carefully chosen spot between the earth and some other body.

Ultimately, you will be weightless in any spacecraft that is travelling through space that doesn't have its thrusters on. Gravity from various sources will effect you, but just as when you are in freefall, you won't feel it.

Answer 2

I guess it would depend upon the sensitivity of the individual's body to downward pressure as to where they'd sense it against the platform. The actual effect of gravity is based upon the square of the distance, but I'm not sure that one's perception of downward pressure against the platform is well enough understood to answer your specific question about the "experience" of weightlessness by any given individual. Darned interesting question from that perspective. Is our sense of downward pressure linear? Logarithmic?

The physics part is easy.

Newton's law of universal gravitation states that bodies of matter in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. According to this law, even a small increase in the distance between bodies will produce a large decrease in the gravitational force, since the force decreases with the square of the distance. As a body moves from the Earth's surface to a location an infinite distance from the Earth, the gravitational force approaches zero and the body approaches weightlessness. In the true sense, a body can be weightless only when it is an infinite distance from all other objects.

So it's easy enough to calculate the "weight" that will be there to sense -- but at what point do we cease to sense it? Obviously, the slightest twitch of a leg muscle could overcome light gravity that would keep a person in a stable postion on the platform at sufficient altitude. Hmmm... you've really opened up a kinesthesia question that's probably never been carefully considered. Not that many folks have the opportunity to have the experience, and are no doubt usually too busy to notice the point of "feel it" / "don't feel it".

Answer 3

The moon gravitational pull is about 1/6 the earth. So, to make things easy, If you were exactly between the moon and the earth, and about 5/6 the way to the moon, the moon and earth gravity will cancel out. However, you will still have a little sun gravity acting on you.
Or you could go the other way. If you could get to the center of the earth, you would be weightless.

Answer 4

After a distance of 18 earth diameters from the earth the gravitatianal force relative to the earth's center is very minimal. However that does not mean that eventually you will not be brought back to earth by gravitational power.

Answer 5

What form of transportation would you use? Are we walking, riding a bike, driving a car, going through in a super fast jet? Just take the miles per hour and figure out with the diameter. It would take about the same amount of time as it takes to drive across the US and back.

Answer 6

the formual you use is F=GMm/R^2
where;
F=Gravitational force
G=gravitational constant
M=Mass of the earth
m=mass of person
R= radius or distance of m from M.

to figure this out set F=0 and solve for R

Answer 7

you cant because gravity is everywhere. the moon would start to pull you, then the other planets, then the astreoids...