Why do astronauts float?
Everytime I have asked someone the question: Why do astronauts in orbit float? I nearly always get the same response, that there is no gravity in space.
F = G * (m1.m2)/r^2
This famous equation by Sir Isaac Newton says that the force of gravity between two objects with mass m1 and m2
is inversely proportional to the square of the distance between the two objects multiplied by the gravitational constant.
Earth's radius is approximately 6371.393 km. Let's say we have a box that weighs 1 kg sitting on the ground. What would be the
force acting on that box as a result of the Earth's gravity?
G (5.972e24)/(6371393^2) = 9.8
9.8 newtons is the amount of force exerted by gravity on the box. Now what if that box was 400 km above the surface of the Earth? How much less would the
force of gravity be at that altitude? Take a look at this messy expression and try to make sense of it:
G * (5.972e24) * (1/6371393^2 - 1/(6371393+400*1000)^2)
This expression gives us the difference between the force of gravity on the surface and 400 km up, and it turns out to be roughly 1.12 newtons. All we have done is factor out the gravitational constant and the mass of the Earth. We have to convert the 400 km to meters, the SI
unit for length. That's where the 400*1000 is coming from.
1 newton is not a lot of force. An average apple exerts around 1 newton of force. The key takeaway is:
400 km up, 90% of Earth's gravity is still there.
So why then did people float in the Space Shuttle and do float in the international space station? It has to do with the fact that
things in Orbit are moving extremely fast. More than 7 km per second fast. So fast, that they simply fall "over" the curvature of Earth,
and therefore never hit the ground.
Imagine taking a box and putting some items inside of it:
Imagine you drop the box from a 100 story skyscraper. What do you think will happen?
With respect to the box, all the items inside the box will appear to float! And this is exactly what is happening to objects in orbit. They are simply in free-fall. Except their tangential velocity is so high, they simply fall over the curvature of the Earth.
The same principle is used to train astronauts in planes that simulate micro-gravity. A plane flies a parabolic trejectory. During the descent phase, the plane is pitched down to maintain a downward acceleration of 9.8 m/s^2, which is the rate at which objects accelerate towards Earth. The plane is the box in this case (referring to the example above).