The Eternal Fall

Here is a video of some astronauts on the International Space Station (ISS).  It depicts some common (and uncommon) activities that they do aboard it.  It has background music – so turn down your volume if you are at work.

As you can see, astronauts in space operate in a ‘zero-gravity’ environment.  They float around effortlessly and don’t fall toward the ‘floor’ of the space station.  Water, in a space station such as the ISS, automatically assumes the shape of a ball and floats around.  This is indeed, quite a strange environment.  But have you ever stopped and wondered – why are the astronauts actually floating?  Is it because there is no gravity in outer space?  Is it because the earth’s pull is so weak that it no longer affects them?  Is it because they are constantly being pushed away from the earth by rockets?  Or is it something more subtle?  In this post, we shall explore the phenomenon of micro-gravity.

Newton’s Universal Law Of Gravity

Newton's Law of Gravity between two bodies of mass m1 and m2 separated by a distance r

Newton's Law of Gravity

The gravitational attraction of any two bodies is (mostly) governed by Newton’s law of gravitation.  This law states that the gravitational attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:

F = G\frac{m_1m_2}{r^2}

F is the gravitational force of attraction between two bodies of mass m1 and m2 separated by a distance rG is known as the gravitational constant.  G \approx 6.67 \times 10^{-11} \text{Nm}^2\text{kg}^{-2}.  Ignore the units on that constant for a second.  Notice that it is a really small number.  This implies that gravity is a very weak force.  So how come we feel the gravitational force of the Earth so strongly?  It is because of the enormous mass of the Earth, coming close to 6 \times 10^{24}\text{kg}.  For a spherical body, Newton proved that we can calculate its gravitational attraction by assuming that all the mass was concentrated at its center (a point mass).  Can we use this to calculate the gravitational force felt by a person standing on the surface of the earth?  Sure.  The radius of earth is about 6400 km.  Hence, a person standing on the surface is roughly 6400 km from the center of the Earth.  Lets assume a hefty human of mass 100kg.  We can now put all the values into our equation – plug and chug:

F = \frac{6.67 \times 10^{-11} \text{Nm}^2\text{kg}^{-2} \times 6 \times 10^{24} \text{kg}\times 100 \text{kg}}{(6.4 \times 10^6 \text{m})^2} = 977 \text{N}

How much force would be acting on the human if he were in orbit in a space station around Earth?  The ISS orbits the Earth at an altitude of about 400 km (making the total distance from the center of the earth about 6800km).  Plug and chug again:

F = \frac{6.67 \times 10^{-11} \text{Nm}^2\text{kg}^{-2} \times 6 \times  10^{24} \text{kg}\times 100 \text{kg}}{(6.8 \times 10^6 \text{m})^2} = 865 \text{N}

Notice that the gravitational force on the person would have decreased by only about 10%.  This is not enough to account for the total weightlessness felt by astronauts.  Something else more subtle must be in play.

Free Fall

A Drop Tower Amusement Ride

A Drop Tower Amusement Ride

Imagine us waiting at the top of one of those amusement park rides that drop you vertically and cause you to puke.  These rides are called drop towers.  Do we feel Earth’s gravity?  Yes we do.  We feel heavy.  We are sitting in our seats.  We don’t float.  We feel every day forces that keep our body pinned to the ride.  Now, without warning, the capsule with all the riders plunges towards the earth in free fall with no brakes on.  What do you feel (besides possibly fear and nausea)?  You may feel a queasiness as you realize that your body is no longer attached to your seat.  The capsule and you are both accelerating towards the earth in free fall.  Hence, the seat you are in does not push back against you.  You are now in a ‘zero-gravity’ environment.  You feel no downward force.  There clearly is a downward force – you are accelerating towards the earth.  But there is no reactive normal force.  No force to hold you up.  No force to keep you from accelerating.  It is this balancing force that we feel everyday.  If we eliminate the balancing force, then we feel weightless and refer to this as a ‘zero-gravity’ environment.  The word is a misnomer because the force of gravity is not zero.  It is the force that is holding you up against gravity that is zero.  We now know how to recreate a weightless environment.  How do we do it for long periods of time (or indefinitely)?  After all, the ride quickly comes to an end once you hit the bottom.

Sling Shots and Orbits

International Space Station on 20 August 2001

The ISS in orbit

A stone that is thrown into the air comes back down to earth pretty quickly.  A pebble fired from a sling shot travels a lot farther but yet, it does come back to hit the ground.  An artillery round shot out of a cannon travels quite far before hitting the ground.  In fact, naval artillery rounds travel far enough that firing tables usually account for the curvature of the Earth.  In other words, they need to account for the fact that the earth has curved away underneath it and can no longer be considered a flat surface.  The farther a round travels, the further the earth has curved away underneath it.  Now, imagine this – imagine a projectile traveling so fast, that as it tries to fall towards the earth, the earth just curves away just as quickly.  In other words, the projectile simply never hits the earth.  It just keeps rotating forever.  Such a projectile is now in free fall and will remain so.  This is the principle behind a space station.  Such a long-lasting free fall is known as an orbit.  Stable orbits allow the projectile to remain in free fall forever.  The ISS is in an orbit about 350-400km above the earth.  Due to atmospheric drag, it still slows down and its altitude decreases.  Hence, at regular intervals of time, the ISS fires its built in rockets to boost it back up to orbit.  The astronauts aboard the ISS feel no weight as long as the rockets are not firing.  During the orbit maintenance rocket burn, the crew members will feel a force similar to what they would feel on earth.


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4 responses to “The Eternal Fall”

  1. gramani says :

    Wow wow..

    (1) I am in the midst of my own work and so haven’t read this in complete. But whatever I read, leaves me a doubt. I believe, the weight of the person is relevant to the location. If he is on surface, you assumed 100Kg. But you applied the same when he is in space, which is not correct. He will be weighing almost negligible. So the weightlessness has an answer, but I do not know, further to explain this.

    (2) Is the mass and weight same ?. Relative to universe, is the mass of earth same as weight of earth ?
    (3) What we feel as weight of earth, is it not measured reference to the pull it makes towards the centre of earth ?

    (4) Relative to the universe, is not earth having zero weight and floats in the space ? So does all celestial bodies.

    (5) How does earth gets its pulling power? (this can cover yet another topic).


  2. Simple Scientist says :

    @gramani Mass is a property of matter that is independent of things like altitude or pressure or temperature or gravity (in the non-relativistic realm). Hence, when I say someone has 100kg, that person has 100kg regardless of where he is.

    “Weight” (on earth) colloquially refers to two things which are usually equivalent —
    a) the force acting on a body due to earth’s gravity at the current altitude.
    b) the reactive/normal force acting on the body to keep it from accelerating. This is usually from the floor the body is standing, the buoyant forces from the liquid in which the body is floating or, in the case of airplane, the reactive force from airflow being redirected.

    The above two forces are equivalent *only* when the body in question is not accelerating. When it is, the question of “weight” is a vague question because we are no longer under the conditions under which our original definition was made. We can redefine weight to be the one or the other (with different results). To complicate matters, we can define weight in yet another manner based not on acceleration due to gravity but based on proper acceleration (as opposed to co-ordinate acceleration). Proper acceleration is acceleration that can be measured from an inertial frame or locally measured from a free-fall reference frame (and now I have plunged this discussion into Einstein’s General Relativity). Needless to say, there is a reason why I tried to avoid using the word “weight” throughout the article.

    This should answer your (1), (2) and (3). (4), as per the above discussion is meaningless because weight is very undefined for celestial bodies. Mass is the only intuitive meaningful measurement. And as for (5), depends on how you define ‘how’. The observed effects can be modeled using Newtonian Gravity (and more accurately using Einstein’s General Theory of Relativity). Gravitational force is one of the 4 intrinsic forces in our current model of physics (along with E/M, Weak and Strong nuclear forces).

  3. fake gucci bags on sale says :

    Hello, your articles here The Eternal Fall | Simple Scientist to write well, thanks for sharing!

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