Quote
TeleMad: If the occupants were being pulled by a DIFFERENT STRENGTH of the Earth' gravity then they would. But the spacestation and everything in it experiences the same downward graviational pull, because they are all the same distance from the Earth's center of mass, so they are all effected to the same degree. They all fall towards the Earth is the same arc, so the occupants don't get pushed to one side or the other.
Quote
Smokinjoe9: Got it, more studying....
Let's look at Newtons equation for universal gravitation.
F = G(mM / r^2)
F is the force of attraction between two objects.
G is the universal gravitation constant
m and M are the masses of the two objects
r is the radius: that is, the distance separating the two objects' centers of mass
We simplify this a bit by getting rid of G: we just have to change the equation to being only a proportionality. I'll use the ~ to indicate "is proportional to"
F ~ mM / r^2
What this says is that the force of attraction between two objects is (1) directly proportional to the product of their masses, and (2) inversely proportional to the square of the distance separating the two objects' centers of mass.
If we get less technical we can simplify that too.
F ~ mM / r^2
What this says is that the force of attraction between two objects is determined by two factors: their masses and the distance between them: (1) the more massive the objects the stronger the force, and (2) the greater the distance between them the weaker the force.
So for objects at the same distance from the center of the Earth, r and r^2 is the same. Since this is the case for the spaceship in orbit, we can simlify this even more by eliminated r^2.
F ~ mM
What this says is that for any object that is a given distance away from the center of the Earth, the force of attraction between the object and the Earth is proportional to the mass of the object.
But since the Earth is always being used here, we can eliminate it too.
Here's the final, fully simplified 'equation':
F ~ m
What this says is that for any object that is a certain distance away from the center of the Earth, the force of attraction it experiences is proportional to its mass
That makes it sound like an astronaut in the orbiting spaceship would experience a greater force of attraction towards the Earth's center of mass than would a basketball in the spaceship. AND IT WOULD!
But remember Newton's second law: a = f / m
If you have two objects A and B (astronaut and ball) where the mass of A is 100 times that of B, then A will experience 100 times stronger force pulling him towards the Earth. HOWEVER, having 100 time the mass, it will also take 100 times the force to produce the same acceleration!
So mass cancels out. Thus, all objects in the orbiting spaceship experience the same acceleration. They arell pulled out of straight line motion to the very same degree. Consequently, they all follow the same arched trajectory across the sky, and an astronaut it not flung up against a wall.
Napoleon Bonaparte: “You have written this huge book on the system of the world without once mentioning the author of the universe.”
Pierre-Simon Laplace: “Sire, I have no need for that hypothesis.”