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Well, this question has been puzzling me for kinda long time, many people believe that orbiting astronauts feel weightless because they are "beyond the pull of Earth's gravity"...How far from the Earth would a spacecraft have to travel to be truly beyond the Earth's gravitational influence? If a spacecraft were really unaffected by Earth's gravity would it remain n orbit? If so, what is the real reason for weightlessness in orbit?

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astronauts feel weightless because they are "beyond the pull of earth's gravity"

This is a misunderstanding. Astronauts feel weightless because they are accelerating towards the earth at the same rate as the spaceship.

You've probably seen videos of the airplane used to produce weightlessness for astronaut training. The plane does this by flying in the same trajectory as a freely falling object so the freely falling astronauts are (approximately) stationary with respect to the plane. It can do this well within Earth's gravitational field. Astronauts in for example the ISS feel weightless for exactly the same reason.

You ask:

How far from the earth would a spacecraft have to travel to be truly beyond the earth's gravitational influence?

In principle the Earth's gravitational field extends to infinity (or at least to the age of the Earth times the speed of light). In practice at large distances the Earth's gravitational field becomes negligable compared to other sources of gravity. Where this happens is a matter of opinion. For example the Earth's gravitational acceleration at the distance of the Moon is 1/400 $g$, which seems pretty small but it's still enough to hold the Moon in orbit.

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  • $\begingroup$ Satellite's rotate around the earth only due to the earth's pull. then they also use power sources like battery,don't they? $\endgroup$ Mar 12, 2013 at 13:15
  • $\begingroup$ They use electricity to operate the instruments on board (antennas, sensors, etc). The only motor capability most of them have is to move the solar panels, and perhaps change their orientation; hardly ever to actually change position. $\endgroup$
    – Davidmh
    Apr 23, 2014 at 10:33
  • $\begingroup$ Not quite true. Some satellites which relay television signals need to stay in precisely the same position relative to the surface of the Earth, because - for example - all the tv satellite dishes in England are mounted with a fixed focus on that one spot in the sky. The tv satellite uses its reaction jets (from time to time, not continuously) to maintain that precise position in the sky, over a period of many years. So it carries a supply of fuel for its reaction jets, used to prevent it changing position (counteracting the prevailing gravitational effects). $\endgroup$
    – Ed999
    May 15, 2019 at 19:13
  • $\begingroup$ I would express it this way: the Moon, which was originally part of the Earth, was flung off into space in the distant past, and its mass and acceleration carried it up to a particular altitude; but because it was originally part of the Earth they both had a common rotation and velocity, so that (instead of separating) they began orbiting their common centre of mass. The Moon's orbital distance from the Earth represented that distance at which its momentum (mass x velocity) is in exact equilibrium with the Earth's gravity (which chanced to be the distance where the latter is 1/400th of g). $\endgroup$
    – Ed999
    May 15, 2019 at 19:28

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