Physics Biology Education

While we're on the subject of space travel, let's talk about free fall and something that is misleadingly called "weightlessness" As you are reading this, you can probably feel your chair pushing upwards on you with a force of several hundred newtons. If your feet are not touching the ground, this is an upwards force equal in magnitude to your weight (a downwards force). My weight is 680 N downwards, so I know that the force from the chair is about this much, upwards. You can also feel your abdominal muscles holding your abdominal organs in place. These forces and some others give you the sensation of having weight. You do not really sense your weight directly very much, because it is applied homogeneously over your whole body. When the forces from the chair or on your abdominal wall are reduced or zero, you may feel 'weightless'--the feeling you get when a lift starts to accelerated rapidly downwards, or when you go quickly over a peak on a roller coaster. I have put 'weightless' in inverted commas because in these situations, and in an orbiting spacecraft, your weight is virtually normal. Since the moon flights stopped, no human has been far enough from the Earth for his/her weight to be substantially reduced.
The three diagrams below show two situations that produce free fall. In an orbiting spacecraft, the spacecraft and the cosmonaut are both accelerating towards the centre of the earth at the same rate (their centripital acceleration is a_c = v²/r, where v is the orbital speed and r the radius). Their weight is what keeps them in orbit: W = ma_c. Because they are *both* accelerating towards the centre of the earth at the same rate, there is on average no force between the cosmonaut and the spacecraft. This absence of forces from seat, floor, abdominal wall etc is what is commonly but misleadingly called 'weightlessness': the cosmonauts in the space station are not without weight, in fact the have (almost) their usual weight. It's just that they don't feel the force of chairs on their bums and they don't feel their abdomens holding in their organs.

feel their abdomens holding in their organs.

                                  

In the figure in the middle, the cable of a lift (elevator) has broken. Both the lift and its passenger are in free fall, accelerating downwards at g. The passenger no longer feels the force on his abdominal muscles, and so, like the cosmonaut, he might say that he feels 'weightless'. He is not, of course, without weight. His weight is still W = mg. Indeed it is his weight that will probably lead to his death, because his unopposed weight is continuously accelerating him. In figure at right, a NASA airplane (nicknamed the 'vomit comet') cuts the power in its engines and, for about 25 seconds, travels in a trajectory that is nearly parabolic. Both the plane and its occupants accelerate towards the Earth at g: all are in free fall. Astronauts are thus exposed to free fall and obtain brief periods of experience in working in this condition.
Physicists tend to use the word 'weightless' in scare quotes (as I have done here), to make it clear that they are not talking about a situation in which there is no weight. Many physicists prefer to avoid the word altogether and talk instead about free fall.
There are some similiarities between the passenger (mass m) in the lift (let's put it at the equator) and a cosmonaut (mass m) in low Earth orbit. The weight of each is about mg. Both accelerate towards the centre of the Earth at approximately g. The difference is that the spacecraft makes a circle around the Earth in about 90 minutes, whereas the lift makes a circle around the Earth in about 24 hours. The acceleration g is just enough to keep an object in low Earth orbit with a period of 90 minutes. It is far too great for the 'orbit' of the hapless passenger in the lift. If a satellite loses speed, it gradually spirals in towards the Earth. The horizontal speed of the passenger in the lift is so low that his 'spiral' towards the center of the Earth is almost a straight line. (There have been a few approximately's and almosts in the above. If you are interested in the analysis of motion in the rotating frame of the Earth, have a look at the formal analysis of the motion of a pendulum at the Earth's surface.)


from : http://www.phys.unsw.edu.au/