• Deepak K Kapur
As long as they don't push away they'll stay in the same orbit as the station indefinitely. If they do push away or otherwise apply force to themselves(e.g., with rockets) they'll change orbit to a different one, which will most likely take them farther and farther from the station.f

#### Deepak K Kapur

When astronauts go into space (considerably away from Earth) they feel weightlessness. They just move aimlessly in space.

Why doesn't moon move aimlessly in space?

Just like the Moon, astronauts don't move aimlessly but orbit the Earth.

You are somewhat confused about "the experience of weightlessness", relative to how we should say whether a person is subject to the force of gravity, or not.

Now, first off:
If we look into general relativity, the conception of "force", in particular gravity, is radically different from that within classical mechanics, but YOUR confusion can as easily be explained in terms of classical mechanics, so that is what I'll do:

When we "feel" our own weight, what is the ACTUAL force we are sensing?
If you simply stand on the ground, it is the NORMAL FORCE acting from the ground on you experience, that you think of as your "weight" (it is oppositely directed to gravity, but of the same magnitude).

Note that if you are in an elevator accelerating upwards, you will FEEL heavier (you feel a stronger push on your feet), although gravity hasn't changed a bit, but the normal force acting upon you has increased.

Are you in FREE FALL, only gravity acting on you, you will feel weightless.

Astronauts and the moon is in FREE FALL around the Earth (the moon keeps missing its target, fortunately!)

But, free fall is a situation in which you, as emphasized are under the influence of gravity, which in the classical mechanics point of view means you are subject to an external force, making your motion deviate from that of following a straight line of motion. You are following a determinate orbit, not floating "aimlessly" around.

They just move aimlessly in space.
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You are somewhat confused about "the experience of weightlessness", relative to how we should say whether a person is subject to the force of gravity, or not.

Now, first off:
If we look into general relativity, the conception of "force", in particular gravity, is radically different from that within classical mechanics, but YOUR confusion can as easily be explained in terms of classical mechanics, so that is what I'll do:

When we "feel" our own weight, what is the ACTUAL force we are sensing?
If you simply stand on the ground, it is the NORMAL FORCE acting from the ground on you experience, that you think of as your "weight" (it is oppositely directed to gravity, but of the same magnitude).

Note that if you are in an elevator accelerating upwards, you will FEEL heavier (you feel a stronger push on your feet), although gravity hasn't changed a bit, but the normal force acting upon you has increased.

Are you in FREE FALL, only gravity acting on you, you will feel weightless.

Astronauts and the moon is in FREE FALL around the Earth (the moon keeps missing its target, fortunately!)

But, free fall is a situation in which you, as emphasized are under the influence of gravity, which in the classical mechanics point of view means you are subject to an external force, making your motion deviate from that of following a straight line of motion. You are following a determinate orbit, not floating "aimlessly" around.

So, why the astronauts who are to repair the space station tied with a rope to the space station?

If they are not tied, they would just drift away and may even reach the those regions of deep space from where they may never return back to earth. Isn't it so?

So, why the astronauts who are to repair the space station tied with a rope to the space station?

If they are not tied, they would just drift away and may even reach the those regions of deep space from where they may never return back to earth. Isn't it so?
As long as they don't push away they'll stay in the same orbit as the station indefinitely. If they do push away or otherwise apply force to themselves(e.g., with rockets) they'll change orbit to a different one, which will most likely take them farther and farther from the station.

This is also true for the Moon. It's much bigger and more massive than an astronaut, so it'd require more force to do it, but if you were to push it somehow it'd change orbit as well.

It's just Newton's laws of motion. You need forces to change motion, and the more inertia a body has got, the more force you need for the same result.

So, why the astronauts who are to repair the space station tied with a rope to the space station?

If they are not tied, they would just drift away and may even reach the those regions of deep space from where they may never return back to earth. Isn't it so?

They are tied for safety reasons. This is real life, not a cartoon. You never rely on just ONE safety precaution, especially when a life can be in danger. What if the astronaut accidentally pushed on something too hard? He/she would be propelled away from the space craft! Tethering is a safety precaution.

Zz.

So, why the astronauts who are to repair the space station tied with a rope to the space station?

If they are not tied, they would just drift away and may even reach the those regions of deep space from where they may never return back to earth. Isn't it so?

May I ask if you are a student and if so what grade?

For one thing, even if they drift out of the way of the ISS they will still be held in the same orbit until collisions with individual molecules at that altitude begins to slow you down you would not drift off into space, you would eventually become a meteor or meteorite if you happen to hit the Earth.

Note that in free space, the TINIEST collision type between astronaut and the ship will generate oppositely directed momenta (measured relative to the frame in which they gain the same velocity from the Earth). The (unrocketed/unattached) astronaut has NO way to exert upon himself a force to reduce this induced momentum difference between himself and the ship, and he will NECESSARILY slip away from the ship if such a mere bump occurs, and he is unable to catch something solidly attached to the ship.

Thus, the danger of the astronaut slipping away from the ship is a REAL one, but based on the astronaut's inability to induce a force to act upon him (or the ship) to close the gap, rather than having anything to do with gravity.

The equlibrium state between his own and his ship's orbit about the Earth due to commonly experienced force of gravity is UNSTABLE, since any induced imbalance between them will gradually develop into different orbits

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Well, why not? The rest of government moves aimlessly!

As long as they don't push away they'll stay in the same orbit as the station indefinitely.
One reason astronauts are tethered is that the astronaut and space station are *not* in the same orbit. Very similar orbits, yes. The same orbit? No.

Suppose the astronaut is below the station's center of mass and is moving at the same velocity as the station. For simplicity, assume the station is in a circular orbit. A circular orbit at the astronaut's altitude has a slightly greater velocity than that of the station (and hence the astronaut). Since the astronaut's velocity vector is (instantaneously) normal to the radial vector, the astronaut is at apoapsis of an elliptical orbit. If the tether broke, the astronaut's motion relative to the station would take the astronaut down and then ahead of the station.

Another issue is that the astronaut and station have very different coefficients of friction. Even if the astronaut was on the same orbit as the station (i.e., directly in front or behind the station's center of mass), those very different coefficients of friction means the station's orbit degrades much faster than does the astronaut.

A very similar issue happens with vehicles about to rendezvous with the International Space Station. Suppose the third worst thing happens1 to such a visiting vehicle: The vehicle goes completely dead while on final approach. The "big red button" solution won't work on this problem because the vehicle is completely dead. The solution is to carefully design the approach sequence so that the dead vehicle migrates away from the station purely due to orbital mechanics, and then keeps away from the station for at least 24 hours.

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1 Aside: The two worst things that can happen are the vehicle blowing up and a thruster failing on. The first is addressed by looking very closely at structural integrity issues, including micrometeoroid penetration. The second is addressed by designing thrusters so that they fail off rather than on, and then adding all kinds of failure protection to ensure that a failed on thruster won't stay failed on for long.

Thank you all for your replies.

Does all this mean:

1. The astronaut will be able to walk on an iron ball say 2 metre wide in all the directions (assuming astronaut and a ball only are in orbit).

2. If you take the spaceship to a place between Venus and Earth where the effect of gravitation of both the planets is nil (or negligible), would the spaceship start orbiting the sun?

3. Assuming there is nothing else in the universe except our Earth, would a spaceship orbit the Earth even if the spaceship is, say, a million light years away?

4. Does the moon also experience friction?

Does all this mean:

1. The astronaut will be able to walk on an iron ball say 2 metre wide in all the directions (assuming astronaut and a ball only are in orbit).
No. The gravitational force exerted by a 2 meter diameter iron ball on an astronaut 2 meters from the center of the ball is tiny, much smaller than the gravitational tidal force exerted by the Earth that acts to pull the astronaut away from the ball. For more info, google the term "Hill sphere."

2. If you take the spaceship to a place between Venus and Earth where the effect of gravitation of both the planets is nil (or negligible), would the spaceship start orbiting the sun?
A qualified yes. In a sense, the spaceship is *always* orbiting the Sun. You are implicitly treating "orbit" as a mutually exclusive term. For example, does the Moon orbit the Earth or the Sun? The answer is "yes". The Moon orbits both the Earth *and* the Sun.

3. Assuming there is nothing else in the universe except our Earth, would a spaceship orbit the Earth even if the spaceship is, say, a million light years away?
Another qualified yes. I'm not a fan of these kinds of questions. We don't live in a universe in which there is nothing but the Earth and the spaceship. However, the answer is yes with the assumption that the laws of physics in this nearly empty universe are the same as the laws of physics in our universe filled with lots of stuff. The spaceship needs to be moving at a ridiculously slow speed, however. Escape velocity at a million light years is 2.9×10-4 meters per second.

4. Does the moon also experience friction?
Not really. Atmospheric density falls off more or less exponentially, and the Moon is fairly massive. Atmospheric drag on geosynchronous satellites is tiny, tiny, tiny, and by the time you get to the Moon, the Earth's atmosphere is pretty much non-existent.

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Note that in free space, the TINIEST collision type between astronaut and the ship will generate oppositely directed momenta (measured relative to the frame in which they gain the same velocity from the Earth).

A friend of mine lost her toolkit in orbit when a grease gun didn't shut off properly. Propelled it like a rocket. A very slow rocket, but a rocket nonetheless. It wasn't until the following year until the toolkit reentered.

Well, moon does not move aimlessly in space because it is under the effect of the Earth gravitation and it doesn't fall upon Earth because of the reaction of the move regarding the gravitation of Earth as the third low of Newton said:
" For every action, there's an equal and opposite reaction"
And you can deduce and conclude that's why Moon can't stray off its orbit

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Any idea of how much force is involved of the gravitational attraction of said human to the ISS? The ISS does have some tiny gravity, would it be enough to draw back our hapless astronaut?

The Hill sphere of the ISS is about 5.5 meters in diameter. So no.

What is the hill sphere? New on on me.

The Hill sphere of the ISS is about 5.5 meters in diameter. So no.

What does that mean, hill sphere? Does that mean the dude won't be pulled back if he is more than 5 meters away?

The "Hill sphere" is named after 19th century astronomer George W. Hill. Google the term "Hill sphere."

I was reading about 'Hill Sphere', when a thought came to my mind as follows:

I can easily lift a small ball, say of 10 gm, with my hand. If I go to the top of a high tower and try to lift this ball with a super-light, super-strong thread I would also be able to do it with ease. Now suppose a tower ( or pole or whatever of some super-light and super-strong material) is made with a height of say 500 km or 50000 km. Again if I suspend this ball with a super-super-super light and super-super-super strong thread, I think I would still be able to pull the ball towards me by pulling at it slowly and slowly (ignore force due to air etc.).

If this is true (at least in principle), why do we need an escape velocity of 11.2 km/s.

conversely

I also thought of suspending a ball from a satellite right upto the surface of the Earth and then pulling it up slowly.

Thanks for the info about the 'hill sphere', hadn't heard of that before. Had no idea Earth had a reach of 1.5 million Km. So the moon will be held in Earth's orbit long after the sun bloats out to burn them up, assuming they survive that particular ordeal.

A friend of mine lost her toolkit in orbit when a grease gun didn't shut off properly. Propelled it like a rocket. A very slow rocket, but a rocket nonetheless. It wasn't until the following year until the toolkit reentered.
QED, in a very illustrative way!

Another qualified yes. I'm not a fan of these kinds of questions. We don't live in a universe in which there is nothing but the Earth and the spaceship. However, the answer is yes with the assumption that the laws of physics in this nearly empty universe are the same as the laws of physics in our universe filled with lots of stuff. The spaceship needs to be moving at a ridiculously slow speed, however. Escape velocity at a million light years is 2.9×10-4 meters per second.

Suppose the spaceship (that is a million light years away from Earth) stops firing its rockets. It will start moving towards earth.

In my view the information (happening, action) that the spaceship has started moving will travel in space starting from the spaceship and then moving towards Earth.

Suppose the spaceship (that is a million light years away from Earth) stops firing its rockets. It will start moving towards earth.
Stopping the engines doesn’t necessarily make it move towards Earth immediately. Especially if it was already moving faster than escape velocity at that distance.

A million years.

A friend of mine lost her toolkit in orbit when a grease gun didn't shut off properly. Propelled it like a rocket. A very slow rocket, but a rocket nonetheless. It wasn't until the following year until the toolkit reentered.

You have an astronaut friend? Awesome. The best I could do was get to hold a moon rock in my hand from the vault at Goddard when I was working Apollo, Tracking and Timing. Atomic clocks and the little transponder onboard Apollo that gave the distance to the craft within 50 feet even if it was a half million miles out, which of course it never got that far but the electronics was good for that distance. Sigh. Back when we were sending men to the moon. A distant memory now.

The fun part is, it doesn't matter. The Earth would be approximately equally attracted toward the spaceship and its fuel, no matter if they both fall toward the Earth together, or they split up, fuel hurling towards Earth so that the ship can move further away...

And if "approximately" is not good enough for you, the answer would depend on who you ask...
Newton would say the Earth instantly knows how to react. Einstein would say the Earth instantly reacts as if it assumed the fuel/rocket fell gravitationally, and if they didn't, the information about that would spread at light speed...

The fun part is, it doesn't matter. The Earth would be approximately equally attracted toward the spaceship and its fuel, no matter if they both fall toward the Earth together, or they split up, fuel hurling towards Earth so that the ship can move further away...

And if "approximately" is not good enough for you, the answer would depend on who you ask...
Newton would say the Earth instantly knows how to react. Einstein would say the Earth instantly reacts as if it assumed the fuel/rocket fell gravitationally, and if they didn't, the information about that would spread at light speed...

Let us divide the space between the very-very distant satellite and Earth into small parts, say 1 light second apart, each.

Unless each part of space communicates with each other part simultaneously, the effect of gravitation cannot take place. This communication, to my mind, has to be instantaneous.

Let us divide the space between the very-very distant satellite and Earth into small parts, say 1 light second apart, each.

Unless each part of space communicates with each other part simultaneously, the effect of gravitation cannot take place. This communication, to my mind, has to be instantaneous.
Your intuition is wrong. That's not how it works.

To understand how it works you have to learn Newtonian mechanics and simple calculus before you can even begin to dive off the deep end into general relativity and differential geometry. You apparently haven't even taken that first step.