if there is no direction in space
Sorry, I'm new here, but who has claimed there is "no direction in space?"
"There is no "up" in space. Earth has nowhere to fall to." this comment was made by "RocksEverywhere" on my post "I thought perpetual motion didn't exist"
Note for those watching, this is the comment in question:
But weight is a force and the Earth is very heavy.
There is no "up" in space. Earth has nowhere to fall to.
The issue is that "up" in space is ambiguous.
I think what he meant was that there is no universal "up" direction where everything should be falling "down".
But yes, he was technically wrong.
Also, in that thread other people, including myself, answered you.
I pointed out 2 of your questions were related, effectively having the same answer.
That was your question about what is propelling Earth/keeping it in motion, and why Earth doesn't fall.
The answer was that Earth does "fall". That falling is what is propelling (and steering) Earth, keeping it in motion and keeping it orbiting the sun.
As it falls it also moves sideways. And as it moves sideways, the direction of "down" will change as well, as it will point to the barycenter of the Earth-Sun system (approximately).
Okay then what about when they are on space walks, they have to be tethered or they will just float out into space? Wouldn't the gravity hold them to the ISS? So gravity behaves differently in space? It seems gravity behaves like a selective tractor beam.
The gravitational attraction of the ISS is pretty much nothing.
Gravity is fairly predictable with a possible exception of very large distances (galactic scales).
The force due to gravity is given by the formula:
F=GMm/r^2, which G is a constant 6.67E-11 N m^2/kg^2=m^3/ s^2 kg, M is the mass of one object, m is the mass of the other object and r is the distance between them.
The acceleration due to gravity for the object with mass m is GM/r^2.
For someone just outside the ISS:
Earth has a mass of 5.97E+24 kg. The distance to the centre of Earth is roughly 6800 km (6400 km radius, 400 km orbital height) or 6 800 000 m (6.8E+6 m).
This means their acceleration due to Earth's gravity is 8.62 m/s^2. (On Earth, it is a lot higher).
For the ISS it is a lot less.
The ISS's mass is ~420 000 kg (4.2E+5 kg). So if you treat it as a point particle, with the astronaut 1m away from the centre (which would still be inside it), then the acceleration would be 2.8 E-5 m/s^2.
If you assume this magically stays constant (which it doesn't, it will drop as the astronaut drifts away), and an astronaut pushes themselves away at a staggering rate of 1 cm /s (which is VERY slow), then it would take them over 350 seconds just to stop, which is quite some time.
In those 350 seconds, the person would have moved an extra 178 cm, or 1.78 m. This will increase their distance from the centre to 2.78 m and thus their acceleration drops to 3.6E-6 m/s^2.
You can also calculate the escape velocity of an object. This is the velocity at which gravity (so ignoring with resistance) will slow the object down continually without stopping it. So it will lose speed as it goes away and the rate it will lose speed will also drop and it will forever be approaching a speed of 0, but never quite getting there. If you are below that velocity, then gravity alone is enough to stop you moving away from the object and bring you back to it. If you are above it, instead of approaching 0, you will approach some other speed with you continuing to move away from the object.
This is similar to the formula for acceleration, it is:
v=sqrt(2GM/r)
So for Earth (with an enlarged radius of 6400 km), the escape velocity is 11160.7 m/s or over 11 km/s. That is very fast. You would need some pretty decent rockets to achieve that.
For Earth, at ISS' orbit, it is lower, but not by much. It is still over 10.8 km/s.
For our hypothetical person location 1m away from the hypothetical point particle ISS, it is only ~0.0075 m/s or 7.5 mm/s.
What this means is that if an astronaut on the ISS, even in this best case hypothetical situation, manages to push themselves away at a speed of 7.5 mm/s, they will never be coming back unless they manage to intersect the orbit or are otherwise rescued.
That is why they are tethered.
Perhaps one thing to note is that the mass of an object (assuming the density stays the same) scales as r^3, which means the escape velocity scales as a function of sqrt(r^3/r), or r, and the acceleration will scale as a function of (r^3/r^2) or r. This means for something tiny like the ISS, it will have basically no gravity detectable by man. It is too small for us to feel it.
But for something massive like Earth, it will be very easy for us to notice it unless we are in free fall.