How is weight zero in interplanetary space? The Moon is orbiting the Earth because of the gravitational pull of earth. Then gravity must exist in interplanetary space too. So any body in space must also have an acceleration due to gravity ($g$) but $g$ must actually be 0 for weight to be zero. Can anyone please help me with this?
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1$\begingroup$ See also physics.stackexchange.com/q/109636 $\endgroup$– PhotonCommented Oct 23, 2022 at 15:28
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$\begingroup$ If you have astronauts in artificial satellites in mind, that's in cislunar space. $\endgroup$– J.G.Commented Oct 24, 2022 at 13:20
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3 Answers
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Weight depends on the reference frame.
In the reference frame of the Earth, the gravitational acceleration onboard the International Space Station is about 8.5 m/s$^2$ (about 90% of $g$).
In the reference frame of the ISS, the gravitational acceleration onboard the ISS is between -0.0001 and +0.0001 m/s$^2$, depending on whether you are closer to the floor or to the ceiling.
So the weight of an astronaut depends on which reference frame you want to express it in.
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$\begingroup$ What is weight for you? Usually, it is defined as gravitational force acting on you. On board of ISS it is however compensated by centrifugally force because ISS is orbiting. Therefore, the astronauts are weightless there. The weight depends on the mass and the place where you measure it and not on the chosen reference frame. $\endgroup$– JanGCommented Oct 23, 2022 at 18:11
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$\begingroup$ @JanGogolin Yes, I am including the inertial force into the weight. I think it's reasonable to do so, and even to include the inertial force into gravity. This is consistent with how we talk about "microgravity", "weightlessness" and "zero g" in the context of space travel. It also makes sense in the context of the "equivalence principle" -- inertial forces are equivalent to a gravitational field. $\endgroup$ Commented Oct 23, 2022 at 18:20
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It's not that gravity doesn't exist in interplanetary space - gravity has no "maximum range", it exists everywhere - but that you don't feel it. Imagine a weighing machine attached to the floor of the spacecraft and you standing on it. If the reading is $0$, then you are weightless, although you are still being acted on by gravitational forces.
If you stand on a weighing machine and jump off a building with the weighing machine, then you feel weightless because you and the machine are both falling at the same speed. Something similar applies to astronauts in the International Space Station.
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Depends how you define weight. Operational weight, (which you measure with weight scales) is zero, of course because body doesn't exert any force on scales/support operating in Earth orbit or space.
However, gravitational weight defined as $$ W = G \frac {Mm}{r^2} $$ is not zero, because body $m$ is attracted gravitationally to the bigger body $M$.
Besides if to be technically correct, even in orbit body and scales will be attracted towards each other due to acting microgravity force between them, so even operational weight may be not plain zero, but on the order of $μN$ or so.
answered Oct 24, 2022 at 9:06