This is one of the commonest misconceptions among otherwise intelligent people. Almost everyone knows that astronauts experience “weightlessness”; today, we see TV broadcasts from the International Space Station, showing the crew effortlessly “floating” along its corridors, and those of my generation and older will remember seeing broadcasts from the Apollo spacecraft on their way to the Moon. But a great many people don’t understand why, and believe that astronauts are weightless, “because there’s no gravity in space”.
Well, if there is “no gravity in space”, then what do they imagine holds the Moon in its orbit around the Earth, and the Earth in its orbit around the Sun? Nothing could be further from the truth! Gravity affects everything in the Universe; in fact, it’s what holds the entire Universe together!
While NASA itself uses such terms as “weightlessness” and “zero-gravity”, these terms are in fact extremely misleading; astronauts in orbit are very much under the influence of gravity, and have nearly as much weight as they do on the surface of the Earth. Understanding why they appear to be “weightless” requires just a little elementary physics, which I’ll explain in this essay.
6.1. “The cruellest hoax”
In recent years, there has been a disturbing worldwide trend for TV programmes in which members of the public are ridiculed and humiliated for other people’s “entertainment”. This trend plumbed entire new depths in 2005, with a series on British TV entitled Space Cadets. This was described by critics as “the cruellest hoax in the history of television”; frankly, those who were stupid enough to fall for it and take part deserved all they got! I didn’t waste my time watching it, but couldn’t avoid hearing about it.
The idea was that two “winners”, from a group of ten contestants, would supposedly be sent into space aboard “the Russian space shuttle”. Ahem. Apart from the sheer absurdity of the notion that anyone could be sent into space for a TV show, anyone with any slightest knowledge of spaceflight knows that no such spacecraft exists! In the late 1980s, the Russians did build an experimental space shuttle; it flew a single and successful unmanned test flight, but the programme was then cancelled after the collapse of the Soviet Union. It never flew carrying humans. To this day, Russia ferries crews to and from the International Space Station using Soyuz spacecraft, versions of which have been in use since 1967!
The viewers were told all along what was really going on; only the contestants didn’t know. Two of the “contestants” were in fact actors, whose job was to pretend to believe that everything was real, and convince the others if they had doubts. The contestants were, they believed, taken to a training base in Russia – which was in fact a disused airfield in England; the plane which supposedly took them to Russia had simply flown in circles over the North Sea for a few hours. There, they were subjected to a programme of “training” for their “mission”; while one was voted off each week, Big Brother style.
When the time came, the two “lucky winners” actually believed that they were going into space. They were taken aboard a mock-up of the mythical “Russian space shuttle”, whose “launch” was simulated with a lot of noise and vibration. ( How did they imagine it took off – were they really so stupid as to not even realise that to launch anything into space requires a rocket? Had they never even seen the launch of a real space shuttle on TV? ) For a couple of days, they “performed experiments”, apparently genuinely believing that they were in space! Only when they “landed” did they learn the humiliating truth, that they had never left the ground.
So now we come to a rather obvious question. How was it possible for anyone, however gullible, to believe that they were in space, when they were still on the ground? Specifically, how could they believe that they were in space, when they were not weightless? The answer, believe it or not, is that they were told that they were “not going high enough to be weightless”!!!!!
Think about that. The “success” of the whole enterprise – getting the contestants to fall for it – depended on them not having any remotest comprehension of what “weightlessness”, or being in orbit, actually means! It all depended on them believing the “there’s no gravity in space” misconception – either believing that gravity somehow magically “disappears” at some particular height above the Earth, or more likely, that it becomes rapidly weaker with height, such that it drops off to zero by the height of the International Space Station.
In fact, such misunderstanding was the primary selection criterion for the contestants. All applicants were initially given a test of knowledge – but unknown to them, those with the worst scores were selected to take part! Anyone who demonstrated any slightest knowledge of spaceflight, or any slightest comprehension of the most basic physics, was rejected.
Of course, gravity does become weaker with distance from the Earth – but nowhere near as rapidly as many people apparently think. In fact, astronauts aboard the ISS still have 89% of the weight which they have on the ground! To understand why they don’t feel it, we need to consider the basic physics of motion. Don’t worry; it’s nothing more difficult than a couple of very simple equations!
6.2. “Weightlessness” on Earth
As I said earlier, the term “weightless” is inaccurate and misleading; that’s why I’m using it in quotes throughout this essay. It’s far more accurate to say that astronauts in orbit are in free fall. There are a couple of ways in which it’s possible to experience free fall on Earth – though the first is definitely not desirable.
Imagine you’re in a lift ( elevator, for American readers ) near the top of a tall skyscraper, and the cables break, and the lift falls freely down the shaft. For those last few seconds of your life, you would experience “weightlessness”, just as astronauts do! I’ll explain exactly why in Section 6.5.
Another way to experience free fall - and live to tell the tale – is aboard an aircraft which makes a steep dive. This is exactly how NASA trains astronauts to cope with “weightlessness”, before they go into space for the first time. They are flown aboard a modified aircraft, which has a large empty hold space, whose walls, floor and ceiling are padded to prevent injury. On each flight, the plane alternately climbs steeply, then goes into a steep dive; during the latter, the trainees are “weightless” for about half a minute. This is done several times in succession. As you might imagine, this is not for the weak of stomach – not for nothing is the plane nicknamed the Vomit Comet!
In the excellent film Apollo 13, most of the scenes inside the spacecraft have the astronauts strapped into their seats – but there are several scenes in which they are “weightless”, and float through the hatch between Command Module and Lunar Module. This was not done by camera trickery; it was done for real! A replica of the spacecraft set was built in the hold of the Vomit Comet; in those scenes, the actors really were in free fall. ( If you watch the film closely, and know what you’re looking for, you’ll see that none of the “weightless” scenes last longer than about 30 seconds – the longest they could shoot in one go, during each of the plane’s dives. )
To understand free fall, we need to consider a little elementary physics.
6.3. Velocity, acceleration and force
In everyday language, the words “speed” and “velocity” are often used interchangeably, and assumed to mean the same thing – but in physics, they have distinctly different meanings. Speed is a scalar quantity, meaning it has only size; velocity is a vector quantity, meaning it has both size and direction. Speed is simply the rate of motion, measured in metres per second ( denoted by ms-1 ), or in kilometres or miles per hour. Velocity is the rate of motion in a particular direction.
Acceleration is the rate of change of velocity, measured in “metres per second squared”, or “metres per second per second” ( denoted by ms-2 ); if we say an object has an acceleration of 10 ms-2, that means its velocity increases by 10 metres per second, every second.
Again, in everyday language – especially that of driving – “acceleration” is normally taken to mean an increase of speed. In fact, it means a change of velocity, either up or down; a decrease of velocity is simply a negative acceleration. Note again the difference between speed and velocity; acceleration is a change of velocity, not necessarily of speed – it can mean a change of speed or direction, or both. When a car goes around a bend without changing its speed, it is in fact accelerating – though you wouldn’t think of it as such when driving – because it’s changing its direction of motion.
To cause an object to accelerate requires a force to be applied to it. If the force acts in the direction of the object’s motion, or the opposite direction, then it will change its speed, but not its direction; if the force acts at an angle to the direction of motion, then the direction will also change. In the example of a car rounding a bend, turning its front wheels at an angle to its direction of motion creates a sideways friction between the tyres and the road; this is the force which causes it to change direction.
6.4. Newton’s Three Laws
The simple physics of velocity, acceleration and force, as described above, is summarised by Sir Isaac Newton’s famous Three Laws of Motion. These are actually quite simple, though it took the genius of Newton to formulate them. So here they are.
First Law: “A body will remain at rest, or move with a constant velocity in a straight line, until that state is changed by the action of a force on the body.”
Second Law: “The rate of change of linear momentum is proportional to the applied force, and occurs in the same direction as that of the force.”
Third Law: “For every action, there is an equal and opposite reaction.”
A body’s linear momentum is its mass multiplied by its velocity, so in the Second Law, the rate of change of momentum is the rate of change of ( mass x velocity ). But the rate of change of velocity is acceleration – so we can say that the force applied to a body is equal to its mass times its acceleration. This is stated mathematically as
F = ma
where F is the force, m the body’s mass and a the acceleration it experiences.
The significance of the Third Law will become clear a little later.
6.5. Mass, weight and gravity
Next, we need to consider Sir Isaac’s most famous law, the Law of Gravity – or to give it its correct name, the Law of Universal Gravitation. This states that:
“Every object attracts every other object, with a force which is directly proportional to the product of their masses, and inversely proportional to the square of their distance apart.”
It can be expressed mathematically as follows. The force F, mutually exerted between two bodies of masses m1 and m2, separated by a distance r, is given by
F = G m1 m2 / r2
where G is a constant, called the Universal Constant of Gravitation. If the masses are expressed in kilograms, the distance in metres and the force in newtons, the value of G is 6.67 x 10-11 Nm2kg-2.
The r2 on the bottom of the equation shows us that gravity obeys the inverse square law. If the distance apart is doubled, the force is reduced by a factor of four; if the distance is multiplied by ten, the force is reduced by a factor of 100, and so on.
The fact that G is such a tiny number shows us that gravity is actually a very weak force! You might not think so if you fell off a cliff – but that’s because the Earth is an extremely big mass. Think about it – when you pick up a nail with a tiny magnet, the attraction of that magnet is overcoming the gravitational attraction of the entire Earth!
Now let’s consider gravity on or near the surface of the Earth. In the physics of motion, any object can be considered as a point mass located at its centre of mass, or centre of gravity. So for an object on the surface of the Earth, to calculate the force between it and the Earth, we can say that the “distance apart” in the above equation is the radius of the Earth. If we call that radius R, and the mass of the Earth M, then the force exerted on a body of mass m is
F = GMm / R2
But remember that force is equal to mass times acceleration; so if we divide this by m, we see that the body experiences an acceleration of
g = GM / R2
This is what we call the acceleration due to gravity, denoted by g. The mass of the Earth is 5.98 x 1024 kg ( 1024 means a one followed by 24 zeroes ), and its radius is 6380 km, or 6380000 metres. So the value of g at its surface is
g = ( 6.67 x 10-11 ) x ( 5.98 x 1024 ) / 63800002
If you do the maths, this comes to 9.8 ms-2. So near the surface of the Earth, any object which falls under gravity accelerates at a rate of 9.8 ms-2 – that is, its velocity increases by 9.8 ms-1 every second.
Every falling object, regardless of its mass, falls at the same rate, with that same acceleration. Galileo first realised that in the 17th Century; legend has it that he demonstrated it by dropping objects from the top of the Leaning Tower of Pisa. It doesn’t always appear to be the case; very lightweight objects, such as a feather, fall much more slowly, but only because they are carried by air currents. In a vacuum, a feather would fall at the same rate as a stone or a hammer. In 1971, astronaut Dave Scott demonstrated this by dropping a hammer and a feather together on the surface of the Moon.
In everyday language, the words “weight” and “mass” are often used interchangeably – but again, in physics, they are not the same thing. The mass of any object is always the same, whether it’s on Earth, on the Moon or in a spacecraft in orbit. But its weight depends on where it is; an object’s weight is the gravitational force acting on it – more correctly, the mutual gravitational force between it and the planet on which it’s standing – which is equal to its mass multiplied by the acceleration due to gravity. So an astronaut on the Moon has the same mass as he does on Earth, but one sixth of the weight.
In everyday language, we usually express weight in the same units as mass, such as pounds or kilograms – but in physics, this isn’t correct. As stated above, weight is in fact a force, so it’s measured in the units of force, newtons. A mass m, at the surface of the Earth, has a weight of m times g, so a mass of one kilogram has a weight of 9.8 newtons. It’s also valid to say it has a weight of “one kilogram force”.
Obviously, the value of g does decrease with distance from the Earth – but nowhere near as rapidly as those Space Cadets contestants thought! For a spacecraft at a height of h above the ground, its distance from the centre of the Earth is ( R + h ), so we can substitute that for R in the above equation, and we see that
g = GM / ( R + h )2
The International Space Station ( ISS ) orbits at a height of about 400 km, or 400000 m. So at that height, the value of g is
g = ( 6.67 x 10-11 ) x ( 5.98 x 1024 ) / ( 6380000 + 400000 )2 = 8.68 ms-1
This is 89% of the value of g on the surface – so we see that the astronauts aboard the ISS still have 89% of the weight which they have on the ground!
When a spacecraft takes off, it obviously needs to accelerate at a rate greater than g. The Saturn V rocket, which launched the Apollo spacecraft, accelerated at a rate of about four times g, and the Space Shuttle at about three times g. So during their ascent, shuttle crews had three times their normal weight; it’s said that they experienced an acceleration of “3G”, or “three gravities”. This is where the misleading term “zero-G”, or “zero-gravity” comes from – because when a spacecraft reaches orbit and its engines shut down, the crew go from feeling three times their normal weight to not feeling any. But that doesn’t mean they don’t have any! ( Fighter pilots and racing drivers also experience significant “G forces”. )
Now we return to the concept of free fall. To understand it, consider Newton’s Third Law – “For every action, there is an equal and opposite reaction.” On the Earth, as we have seen, your weight is the gravitational force between yourself and the Earth. That force is always trying to pull you towards the centre of the Earth; what prevents it doing so is the resistance of the ground or floor on which you’re standing. So what you feel as your weight is in fact the reaction of the ground to your weight!
Now think again about the example of the falling lift ( Fig. 7 ).
