Will I float about 100 km above earth surface?

[bhanugarimella]

I want to know whether a person can float in the space just 100 km above the Earth's surface. If we would float, what are the factors that make us float? And if we don't, what are the factors that keep us from floating in the space? Those object need to orbit around Earth at high speed like international space station to keep us floating or is it enough to move along Earth's speed of rotation?
I would like to give you an example to tell what I actually want to know about. It is like this that I have taken a big air-tight box that has enough air for a rat to survive for 10 days, tied some Helium balloons to it and tied a rope of length 105 km to the box. Now I left the box up and allowed it go as high as 105 km (the length of the rope) while anchoring the other end of the rope on the earth. Now the question is will the Rat in the box float? If yes, why will it float?? If no, why won't it float??

 

[phinds]

The rat won't "float". Do the math. take the radius of the Earth and calculate the gravitational attraction (you already know the answer is 32f/s*2) and then add 100 km and do the calculation again. you won't see a lot of difference. The rat is WAY far from being weightless.

 

[bhanugarimella]

How far should the box be from the Earth to make the rat float?

 

[Mark44]

How far should the box be from the Earth to make the rat float?

There is a point between the Earth and the moon where the effects of gravity from each object cancels the effects from the other (not including whatever gravitational effects there are from the sun).

 

[Bandersnatch]

35786 km

As to why, it goes like this:
To float, the box must be in free-fall. That is, it must stay in orbit purely by the virtue of its orbital velocity. This is achieveable in any orbit. But you want the box to remain exactly above a single point on the surface. This limits the orbits to a single orbit called "geostationary". It means that the orbital velocity and the length of the orbit is such that it takes exactly one day to complete one orbit.
To calculate where such an orbit should be, you need to compare the gravitational force with the centripetal force for the angular velocity satisfying the above mentioned requirement($ω=2∏R/T$ where R is the orbital radius and T is one day), and solve for R. Try doing that and see if you get the same number.

Do note, that (obviously)you can't send a balloon that high, and if you were to have a rope attached to the box connecting it to Earth, the weight of the rope would be entirely below the geostationary orbit, and as such not in free fall. That is, it'd pull the box down.
If you want to have a rope, you'd need to add another length dangling beyond the geostationary orbit so that it's inertia(centrifugal force) would counteract the weigth of the other part.

What I've just described is pretty much one of the designs for a space elevator. You may want to read up on those:
http://www.mill-creek-systems.com/HighLift/contents.html

Another thing to consider is that geostationary orbits can be only coplanar to the equator. I.e., you can't have one at any other lattitude. Maybe you can figure out why.

Googling "geostationary orbit" will net you more information.


@Mark44: L1 doesn't satisfy the requirement of remaining above the launch point.

 

[sophiecentaur]

I should point out that the rat (ignoring the effects of vacuum and cold!) would 'feel it was floating' - even if it were plunging towards the Earth. At 100km altitude, the atmosphere is pretty rarified so it would only be when the rat reached a speed of many m/s that the drag of the atmosphere would make itself felt (to the rat).

100km altitude is too low to establish a long lasting orbit, because the drag is significant. Go out to several 100km and an orbit will last for years and years before it degenerates appreciably.

The feeling of 'floating' (or weightlessness) occurs when there are no other objects (e.g. the ground or a fixed rope) preventing you from falling by providing a force on your body against your weight force. In a space station, everything is is the same orbit and there are (virtually) no such forces to be felt. So you feel you are floating.

 

[CWatters]

How far should the box be from the Earth to make the rat float?

If you want the rat in a box to float above the same point on the Earth then google "geostationary orbit".

If the rat in a box can orbit faster or slower than the Earth so that he doesn't stay above the same point on the ground then you have options. Suppose there was no atmosphere ... You could in theory put the rat in a super cannon and fire him horizontally from the top of a building. If you fire him at the right speed he will orbit the Earth at the launch height (eg the height of the building). He will feel like he's "floating" even though the ground will rush past beneath him rather quickly.