Gravity and the Story of Weightlessness

The following is a summary of a talk I like to give to physics classes about gravity and "weightlessness". It all starts with a question.

Why do astronauts float around in space?

The most common response to this question is that they float around because there is no gravity in space. Some people take this a small step further and say that there is no gravity in space because there is no air in space. This is why they claim there is no gravity on the moon (even though there is - more on this later).

I like to start off with the concept of gravity. Gravity is an attractive force between any two objects with mass. Your pencil and your dog both have mass so there is a force pulling your dog and your pencil (that is if you have a pencil) together. This force turns out to be extremely small. So small that you would never notice it. However, if one of the masses is very large, it is noticeable. An expression for the gravitational force was first determined by Newton. He came up with the following (turning off vector notation for simplicity).
Where G is the universal gravitational constant, m₁ and m₂ are the two masses in the interaction and r is the distance between their centers. This force (as are all forces) is really a vector that points from one mass to the other.


Here is an astronaut in the International Space Station. Let me use the above expression and calculate the gravitational force on him both on the surface and in orbit. Suppose he is 70 kg. On the Earth, the gravitational force would be:

Now, in orbit (typically 360 km above the surface of the Earth, the same calculation (with a different r):

Well, that is odd. The picture clearly shows the guy "floating around" but the gravitational force is not that much less. How can this be? It turns out it is possible to be "weightless" without even going into space. Here is a picture:

These guys also look like they are floating around, but they are not in space. They are in an airplane commonly called "The Vomit Comet" - I didn't make that up, that is really what they call it (its even in wikipedia - so it must be true).

So how does this work? Let me start by pretending a person is in an elevator. Here is a force diagram for the person if the elevator is stationary and not accelerating:
Here, there are two forces acting on the person: the gravitational force from the Earth and the contact force of the floor pushing on the person. Since the person is not changing motion, these two forces must add up to zero (from Newton's second law) in the vertical direction this would be:
Everything looks ok, everything would feel normal in this case.

Now, suppose the elevator is accelerating upwards. This would happen if you got in an elevator and pressed the "up" button. In order to move in the upward direction, you would need to accelerate upwards at first. Here is the force diagram:
Comparing this diagram to the previous, you should notice that the gravitational force is the same as before. This is because your mass did not change nor did the mass of the Earth. However, the floor must push harder. This is because:
In order to accelerate upwards, the total force must be up. The only way this can happen is for the floor to be exerting a force greater than gravity (how does the floor know how to do this? See this article). I assume you have been in an elevator before. This effect can be more easily felt if you have a very tall building that has a fast elevator. If the elevator is only going up one floor, it really doesn't need to go too fast and thus does not have a large acceleration. How do you feel when you push the up button on an elevator? You should feel a little heavier - yes? But did your weight change? No. (extra credit: under what other circumstances would you feel heavier in an elevator?)
KEY POINT: You feeling heavier is not due to your weight changing (because your weight did not change).

Now suppose you accelerate down in an elevator. This would happen if you press the "down" button. Here is the force diagram for that case:
Now the force of the floor is LESS than gravity for the following:
And here you FEEL lighter (but you are not). So, when the force the floor pushes on you is large, you feel heavy. When the force the floor pushes on you is small, you feel light. What would you feel like if the floor didn't push on you at all? How would you make this happen? If the force of the floor is zero, the above equation becomes:
I could plug in the entire formula for the gravitational force (from above) but the radius of the Earth and the mass of the Earth are essentially unchanging. This gives an expression for the gravitational force on the surface of the Earth of
(Note: I already stated that the gravitational force was down, so here I am just declaring the magnitude of the gravitational force). So the force the floor exerts on you will be zero if the elevator accelerates downward at 9.8 m/s². What would this diagram look like?
If this happened, you would feel weightless. Maybe you have been in this situation. Hopefully it was not in an elevator but maybe something like this
This ride has the riders "falling" down the track. Instead of crashing into the ground, the track curves away. This is called the "Tower of Terror".

Key Point: How you feel depends on the force a floor (or something supporting you) and not the gravitational force. Some call this your apparent weight. For the elevator accelerating down at 9.8 m/s², your apparent weight would be zero. For the Vomit Comet, your apparent weight is zero. For the astronaut in orbit, his apparent weight is also zero. Why is the apparent weight what you feel? This is really a whole different conversation - but I have it here.

Back to the vomit comet, how does it work? Here is a good image showing something:
Pasted Graphic 3Basically, the vomit comet flies such that its acceleration is the same as 9.8 m/s². In this case, it doesn't crash because it "pulls up" before getting too low. This gives about 20 seconds of "weightlessness" or apparent weightlessness. Notice that the acceleration is down even during the time the plane is moving up. Again, this is another story - but I have it for you.

An interesting side note, the movie Apollo 13 had realistic looking "space shots". The reason for this is that those shots were filmed in a studio of the apollo capsule inside a vomit comet. (I tried to find a good image of the set inside the plane, but my internet searching skills failed me).

You could do this same thing in you own plane - here is an example:


My Own Vomit Comet.
I can make my own "vomit comet". The basic idea is to put a video camera inside a box and throw it. After several versions, here is what I came up with:

This is three plastic cups. The top cup hold the CVS "disposable" video camera. The next cup (with the lines drawn on the inside) is where the "astronaut" will go. Below that cup is a third cup with a 2 lb weight. This gives the capsule enough mass so that air resistance does not play a significant role. Here is much more information on my quest for a "zero-g-box".
I am still not completely pleased with these videos (I know I can do better) - but these give you an idea of what I am trying to do.


Back to Astronauts.
Why do they float around? They must be accelerating the same as the space station. In fact, they are. They are accelerating because they are moving in a circle. Should they be called weightless? Maybe. You can call them apparent weightless - that would work. NASA calls it microgravity (which doesn't make much sense to me). Some will argue that indeed astronauts ARE weightless because in their frame of reference, there is no gravity - OK, if that makes you happy.

Currently, my video camera is undergoing some repairs. If I get better video, I will post it.