Astronauts are weightless when they’re less than 130 miles above the earth. But i was wondering. When does weightlesness first start?
Let’s say i have a very well anchored 130 mile long ladder pointing skyward. I’ll be carrying a very accurate scale that i can stand on. I will also have a platform that can be attached to the ladder wherever i want that i can stand, rest, etc. On. And, of course, i’ll be taking my trusty laptop. The physical elements will have no effect on me, so i don’t have to wear a space suit. And my body won’t loose any weight from the exercise i’ll be doing.
I’ll start off by weighing myself and recording this on my computer. I’ll then put everything on my back and start to climb the ladder. The rungs of the ladder are one foot apart and are numbered, with number 1 being the bottom one. Every so often i’ll stop, set up the platform, put the scale on it and weigh myself, always recording the weight and rung number on the laptop.
My question is… About how high will i be when the scale starts to show a lower reading? When the effect of earth’s attractive force (gravity) on me is less?
If this is true, then you would theoretically see the effects anywhere along the ladder. The force of gravity changes per the square of the distance between the two objects. So if your scale were that accurate, then you would see a difference anywhere along your ladder.
(However, what would be even more impressive about your scale is that it was designed and calibrated to work with gravity varying from that at earth’s surface to 130 miles above the earth’s surface).
Weightlessness is produced by being in free fall. If you’re dropping in an elevator you can be momentarily weightless. Your height above earth doesn’t matter. Only the duration of the period of free fall matters. The “Vomit Comet,” the airplane that takes a series of dives that produces weightless conditions, does so for about half a minute because of the length of its dive.
Astronauts in orbit are in a perpetual state of freefall. Their orbit drops off at the exact rate the curvature of the earth drops off underneath them. They are always falling toward the earth and never reaching it. That orbit can be of any height.
Now, your weight under the pull of gravity does depend on the distance you are from the center of the earth and instruments can easily detect a difference between your weight at the poles and your weight at the equator. (The earth bulges slightly at the equator because of its rotation and so the equator is farther away from the center.) I’ve no doubt that we have instruments sensitive enough to detect variations from the first floor of your house to the second.
I’m not going to do th math at this time of night. I assume someone will come along shortly and provide exact numbers.
I just wanted to make sure that you immediately were told that the question “When does weightlessness first start?” is the wrong way to think about the situation. Weightlessness is freefall. That’s a different thing.
Even 130 miles up on your ladder, you would have most of the weight you do on Earth’s surface. You would, however, notice the weight measured by your scale decreasing all along the ladder’s length.
“Weightlessness” doesn’t start anywhere, and astronauts are not weightless – Earth’s gravity still exerts a force on them. They can float around inside their shuttle or other spacecraft because they and the spacecraft are both in orbit – that is, they are both in freefall. If you rode an elevator to the top of a very tall building and then the cable snapped, you would experience the same sensation. Relative to the elevator, you would be floating, and would seem weightless, for a very short time at least. 
The reason the astronauts and the space shuttle don’t come crashing back down to earth is because they’re also moving moving around the earth fast enough to constantly “miss the ground,” so to speak.
Incidentally, just to do the numbers:
The gravitational force between two objects decreases with the square of the distance between them. At the surface, if you stood on the equator, you would be about 6,378 kilometers from Earth’s center. 130 miles up your ladder is about 209 kilometers above that. Your mass will not change as you ascend the ladder (except negligibly due to sweating and maybe breathing), so we can determine what fraction of your Earth-bound weight you will retain by taking the ratio of the square of the two distances from Earth’s center:
(6378km)[sup]2[/sup] / (6378km + 209km)[sup]2[/sup] ~= 0.9375
In other words, at the top of your 130-mile high ladder, you will still have about 93.75% of your Earthly weight.
And if you stepped off that ladder, you would instantly feel weightless during your free-fall back to the Earth. 
That is, until you reached terminal velocity due to air resistance.
Note that you would not go into orbit, because at the top of a 130-mile ladder, you would not have enough sideways velocity. Therefore, you would just fall straight down.
Also note, that because you do not have that tremendous sideways orbital velocity, you will probably not burn up during your free-fall back to Earth. Indeed, you would likely just free-fall most of the way back down to the surface, continually slowing due to air resistance as your terminal velocity decreased due to the thicker air, then just open your parachute at the appropriate point. (You did pack a parachute, right?)
In 1960, during Project Excelsior, Capt. Joseph Kittinger, a U.S. Air Force officer, did a free fall from a balloon from 102,800 feet (19.5 miles). Free-falling from 130 miles would not be dramatically different, though you would hit a much higher re-entry speed.
It would be interesting to calculate the top speed for a human-sized object free-falling from a stationary point 130 miles up.
Or until you reached even-more-terminal velocity due to earth resistance.
And technically, a person falling straight down is in an orbit, just a very trivial one which happens to intersect the surface of the Earth.