I'm familiar with $F_{g} = G\frac{m_{1}m_{2}}{r^{2}}$ and I was wondering if that means anyone orbiting the Earth actually experiences greater perceived weightlessness due to orbit itself compared to someone located the same distance from Earth but not in orbit? It seems likely, since we can simulate weightlessness without actually leaving Earth, but is there a way to work out how much "more" weightlessness people in orbit may perceive? Additionally, does someone on the way to the moon then perceive less weightlessness once they're out of Earth's orbit and in transit to the moon? And would someone in geosynchronous orbit around Earth perceive any added weightlessness at all due to their orbit?
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5$\begingroup$ What is "greater perceived weightlessness" exactly? $\endgroup$– Organic MarbleCommented Jul 4 at 12:29
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6$\begingroup$ I'm very much puzzled by how you could have some zeros being bigger than other zeros. $\endgroup$– user53400Commented Jul 4 at 13:30
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$\begingroup$ Bear in mind that $r$ is measured between the centres of the bodies, so (for example) the $F$ isn't much lower in the ISS than what it is at sea level. $\endgroup$– PM 2RingCommented Jul 5 at 6:23
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2 Answers
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"Weightlessness" simply means you're following a natural trajectory through whatever gravity field is present. There's gravity everywhere in the Universe. We don't "simulate" weightlessness with aircraft: we achieve the real thing. But an aircraft can't follow a weightless trajectory for very long without crashing. Trajectories that don't intersect Earth's surface need more speed than an aircraft can achieve. We call such trajectories "orbits". So, for long exposure to weightlessness, you need a spacecraft.
In a practical spacecraft, there are deviations from weightlessness. In the ISS, there are small tidal forces, and the ISS rotates. It also moves a bit when people move themselves and equipment around in it. These deviations are too small for people to perceive, but they affect some sensitive science experiments.
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I was wondering if that means anyone orbiting the Earth actually experiences greater perceived weightlessness due to orbit itself compared to someone located the same distance from Earth but not in orbit?
This is an answerable question.
If you are in free fall in space (you're in a suit or a capsule, but have no propulsion) you will have the experience of weightlessness because you and your container move and accelerate the same.
If you are moving sideways fast enough, you trajectory can be circular, and you can avoid the unpleasantness of burning up. Instead, you can freeze or dehydrate or starve or go crazy.
But if you're not going quite fast enough sideways, then you're simply on a different orbit, one that intersects the Earth's atmosphere and then the Earth. You'll probably die in five minutes.
And if you start from motionlessness, just "pop" into space above the Earth, your orbit will be a straight line down. You'll have a few minutes to consider that you will have an orbital eccentricity of exactly 1.0, which makes sense - anyone who does this on purpose can be considered "perfectly eccentric".
All of these will give you exactly the same "weightless" experience at first, but they will end differently.
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2$\begingroup$ I rather like this answer because it reminds me of some of Douglas Adams' word usage. $\endgroup$– Rory Alsop ♦Commented Jul 6 at 8:34
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$\begingroup$ @RoryAlsop ya, his writing leaves quite a lasting influence. Once you read some Adams, the ideas of space and people in it can never the same again $\endgroup$– uhohCommented Jul 6 at 16:11