WHY DO ASTRONAUTS FEEL “WEIGHTLESS”?
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You have probably seen the pictures on TV or in a movie. Astronauts in orbit act as though they have no weight at all; they float around the cabin, let their tools and other objects float beside them, take a drink of water from a big spherical glob of water floating without a glass or a cup, and their hair stands on end. They also feel weightless.
If you think about it, this is a little hard to understand. Occasionally someone will say that astronauts in orbit are “beyond the earth’s gravitational field”. But, if you look back at the article on Newton’s Law of Gravitation, you will see that this cannot be true. It points out in that article that the force of gravity decreases smoothly as you go up from the earth’s surface. In fact, it decreases with the square of the distance from the center of the earth, and the law is called an inverse square law.
So if you stand on the surface of the earth, you are about 4000 miles from the center. Suppose that you weigh 200 pounds on the surface. Then you go straight up another 4000 miles so that you are twice as far away from the center. You will then weigh one fourth as much, or 50 pounds. Most of the time, the astronauts are in orbit only about 200 miles from the surface. The weight at that altitude is about 91 percent of the weight on the earth’s surface. Want the gory mathematical details? Then read what is in the box below. Otherwise, just accept the 91% figure and skip below the box.
This is Newton’s gravitational formula: F = GMm/R2, Where R is the distance from the center of the earth, M is the mass of the earth, G is the Gravitational constant
– always the same no matter what you are weighing. The weight of a person on the earth’s surface is FE,
where FE = GMm/RE2, where RE
is the radius of the earth. The weight of the same person, with the same mass, at a
higher altitude is FH, where FH = GMm/RH2, where RH
is the greater distance from the center of the earth. It is the same GMm both times, so GMm = FH times RH2 =
FE times RE2. Therefore FH = FE(RE/RH)2 If RH is 200 miles more than RE,
and RE is about 4000 miles, then FH = FE (4000/4200)2 =
FE (.9524)2
= FE x 0.907, or
approximately 0.91FE Since FE is the weight on the surface, then the
weight 200 miles up from the surface is about 91% of the surface weight.
m is the mass of the individual being weighed, and
If you weigh 100 pounds on the surface, then you weigh about 0.91 x 100 = 91 pounds when you are 200 miles up.
If you weigh 200 pounds on the surface, then you weigh about 0.91 x 200 = 182 pounds when you are 200 miles up.
And yet the astronauts look weightless and feel weightless. The reason for this could not be that they are “beyond” the earth’s gravity.
The weightless feeling is the same as a feeling of falling. It has been said in earlier articles that you can feel acceleration but not uniform motion. The acceleration feels like some extra weight against the direction of the acceleration. But there is an important exception to this: gravity.
In the earth’s gravitational field, you feel the weight not when you are accelerating but rather when you are just motionless on the ground. If you let yourself fall, you don’t feel the weight any more. The fact that acceleration feels like gravity and gravity feels like acceleration was an important starting point for Einstein when he was working on the Theory of Relativity. We will not worry about relativity now but just note this: When you are resisting gravity by, say, standing on the ground, then you feel like you are accelerating. So when you stop resisting gravity, say, by falling, then you don’t feel like you are accelerating any more.
So the feeling of no gravity is the feeling of falling, and sometimes your stomach seems to have moved up into your mouth. The astronauts say that they get used to this before long although a recently eaten meal might end up floating in the cabin.
It was pointed out in the article on Newton’s Second Law that the planets really are falling towards the sun. They do not crash because they have enough sideways motion to miss. The same thing is true of space ships and satellites in orbit around the earth. Here is how to put something into orbit:
First, you need to take it up to the desired
altitude. Then give it some
sideways velocity, and let it fall If you don’t give it enough sideways velocity, it falls
like this, but anyway it does fall.
If you could shrink the mass of the earth into a small
enough volume, then with the same starting velocity, it would miss the
earth and go into an elliptical orbit with the center of the earth at one
focus.
As it is, with an “unshrunken” earth, we are going to
need a larger sideways velocity. It
still falls, but it has enough sideways motion to miss. Then it will go into an elliptical orbit
with the center of the earth at one focus, and it will return to the
starting point. The exact nature of the ellipse will depend on the initial
velocity. It might be just right
for a circular orbit, or the farthest point from the earth might be higher
than the starting point. If the
initial velocity is escape velocity or greater, the satellite would never
come back.
So the spacecraft and the astronaut are falling just as surely as if they were falling straight down. Sideways motion that curves down toward the surface is a type of falling even if the path of the object actually misses the earth.
There is another important thing about falling: all objects fall at the same rate regardless of their masses as long as gravity is the only force that is present. You can demonstrate this to yourself just by dropping several things such as a baseball and a quarter. Let them go at the same time, and they will hit the ground together. You cannot let them fall too far in this experiment, because then air resistance will start to play an important role. As mentioned, they fall at the same rate provided the only force pulling on them is gravity, but air resistance can make them fall at different rates.
An extreme case of this is a rock and a piece of paper falling with the flat side parallel to the ground. You can do an interesting experiment if you hold the flat side of a piece of paper at right angles to the ground and drop it at the same time as a rock. The air resistance is very small on the thin edge of the paper, so that the paper can fall as fast as the rock. The air might catch the paper and sail it away from the rock in which case this experiment won’t work. You have to hold the paper very still before you drop it.
The reason for this behavior can be found in Newton’s Second Law. Say you drop two masses, one twice the other. The larger mass also has twice the weight, and if that were the only difference then its acceleration would be twice the acceleration of the smaller mass. But mass also hinders acceleration because mass is essentially the same thing as inertia. That would make the more massive object accelerate only have as much. So both effects cancel one another, and the acceleration is the same for both objects.
Actually, the argument in the preceding paragraph is much easier to follow if you use algebra to make the argument. That assumes, of course, that you are comfortable with the algebra. Here, in the box below, is an algebraic version of the argument. Skip to the text below the box, if you wish.
Newton’s Second Law is F = ma F is force, m is the mass of the moving object, and a is
its acceleration, which you may remember, is a number that tells how
rapidly its motion is changing. In this case, F is the gravitational force, so GMm/R2
= ma, or
GM which means that the acceleration depends of G, M (the
unchanging mass of the earth), and R (the unchanging radius of the
earth). Since a just depends on
numbers that never change, then it is the same for all objects. This means that, for objects that fall
from rest, all other aspects of the motion will be the same. It turns out, for example, that all
objects will fall 16 feet in the first second near the earth’s surface.
m/R2
= ma
where G is the gravitational constant, M is the mass of the earth, and R is
the radius of the earth. In the
second version of the equation above, notice that the mass of the moving
object, m, cancels out of the equation because it is on both sides. So
a = GM/R2,
If you hold two objects over the ground and drop them together, they will fall together as long as air resistance is not important. Compact, dense objects such as small rocks and pieces of metal will not be affected by air resistance too much in the first couple of seconds of falling. So this idea can be fairly easily demonstrated. Galileo is the one who first introduced this idea to the world, and there is a famous story that he demonstrated it by dropping objects from the leaning tower of Pisa. If the Pisa story is true, Galileo probably got himself into a somewhat embarrassing situation if he dropped the objects from too high a floor in the Leaning Tower. The path of the rocks would have been long enough for air resistance to affect them differently, and they would probably not have struck the ground at quite the same time. In fact, a recent book Galileo’s Daughter, reports on a situation in which Galileo had to explain himself out of this very situation.
The reason the astronauts look weightless is that they are falling right with the spacecraft they are in. If you could get one started in the first place, an astronaut would orbit the earth just fine without a spacecraft (except, of course, for little things like a supply of air etc.) Since they are falling together, they can seem to float around the cabin just as you would in an airplane if it was falling.
In summary, the astronauts feel weightless because this is the same feeling as the feeling of falling. They are, in fact, actually falling. They look weightless along with everything else in the spacecraft because everything is falling together, which keeps everything right together.