4 spaceships are pulling a membrane through an asteroid belt

[eaglechief]

TL;DR Summary

I'd like to understand if a constant moving inertial system could simulate gravitational effects

Given 4 spaceships are pulling an elastic rubber membrane with constant speed and slow velocity into an asteroid belt.

- In that way, that they all start in empty space and have a constant low speed of say 50km/h as they reach the belt.
- The four edges of the membrane are tied to one of the four spaceships.
- the spaceships do not slow down and pass the asteroid belt with constant speed
- the rubber membrane is made that way, that on Earth a rock weighting 10kg is curving the membrane visibly
- the asteroid belt constains different kind of rocks from 10kg to 100kg in random distribution
- the rocks of the belt have no speed and are resting with v = 0 in the belt

will the following happen or not ?

(a) as the brane passes the the belt, single rocks will have contact to the brane and are beeing accelerated in the direction the spaceships are heading until they move with the same velocity of 50 km/h as the brane and the 4 spaceships (Yes/No)
(b) due to the inertia of the rocks the rocks will curve the brane and different dents occur depending on the mass of the different rocks (Yes/No)
(c) 100kg rocks will cause bigger dents with larger radius. Smaller rocks which are klinging to the membrane in the very neighbourhood will begin to accelerate towards the bigger dents (Yes/No)
(d) "bulk dents" appear, where several rocks have been collected by the heaviest rocks (Yes/No)
(e) distributed along the membrane will occur more and more bulk dents which are curving the membrane locally in a strong way and are collecting further single rocks as well as other smaller bulk dents (Yes/No)

Thanks in advance
Carlo

 

[jbriggs444]

You speak in passing about rocks "klinging to the membrane". But you have not spoken about the energy absorbing or dissipating capabilities of the membrane directly at all. [We also do not know its areal density or lateral tension. So the speed of transverse and compressional rubber sheet waves is unknown]

Why do you expect the rocks to end up moving at 50 km/h rather than 100 km/h?

If this is supposed to be related to relativity, it sounds like you are trying to motivate a rubber sheet model. But it's best to ignore the rubber sheet model and actually learn general relativity instead.

 

[Halc]

- the asteroid belt constains different kind of rocks from 10kg to 100kg in random distribution
- the rocks of the belt have no speed and are resting with v = 0 in the belt

Can't be. You're describing hitting a bunch of asteroids with a giant badminton racquet. The asteroids pressing into the rubber sheet are not going to stay there, but instead will be accelerated with the motion of the setup and bounce ahead of the motion of the sheet. They will for a finite time press into the sheet, yes.

will the following happen or not ?

(a) as the brane passes the the belt, single rocks will have contact to the brane and are beeing accelerated in the direction the spaceships are heading until they move with the same velocity of 50 km/h as the brane and the 4 spaceships (Yes/No)

No. They'll continue to accelerate to faster than the sheet.

(b) due to the inertia of the rocks the rocks will curve the brane and different dents occur depending on the mass of the different rocks (Yes/No)

And also depending on how far from the supported edges the force is applied. A rock near a ship attachment point will cause a smaller dent and be in contact with the brane for less time than a similar mass rock near the center. The rock near the ship will be correspondingly defected to the side, not straight forward.

(c) 100kg rocks will cause bigger dents with larger radius.

Even the small rocks deflect the entire sheet, so there's not a radius to it, just like there's not a radius to the reach of gravity, which seems to be the analogy you're suggesting. Big rocks deflect it more, all else being equal, yes.

Smaller rocks which are klinging to the membrane in the very neighbourhood will begin to accelerate towards the bigger dents (Yes/No)

Depending on when they hit, but yes. The dents are temporary.
You made no mention of clinging except for this. If the sheet has glue, the dents will osculate both ways and no 'collection' or other lateral movement will take place. It then becomes a giant vibrating fly strip.

(d) "bulk dents" appear, where several rocks have been collected by the heaviest rocks (Yes/No)

There's little chance that they'll hit each other, so no.

(e) distributed along the membrane will occur more and more bulk dents which are curving the membrane locally in a strong way and are collecting further single rocks as well as other smaller bulk dents (Yes/No)

No collection takes place. Everything bounces away after brief contact, so no.

 

[PeterDonis]

I'd like to understand if a constant moving inertial system could simulate gravitational effects

What "gravitational effects" do you think your setup is trying to simulate?

 

[Dale]

I agree with @Halc’s analysis in post 3

 

[MikeeMiracle]

This reminds me of the Flat Earth theory that we are accelerating "upwards" at 7.2m/s which is why we "experience" gravity...

 

[eaglechief]

Thanks for your replies. I learned from your answers that the setup will not "collect" any rocks from the meteorite belt but causes some kind of space-tennis

I tried to understand if the "rubber-membrane" analogy explaining gravity by showing stars and planets curving the membrane could be amended in that way, that (a) the membrane itself is moving and (b) not accelerated but with a constant speed, instead.

In addition to that, i was thinking about the experimental set-up, where circular motion with constant speed is causing gravitational effects, as well, and if that could be transformed in a set-up where a constant linear velocity is used ...

 

[Ibix]

You seem to be trying for a "rubber sheet" model of gravity. It's an absolutely terrible model, because it only talks about the spatial curvature and completely misses the "time curvature" (scare quotes, because that's not really a clear concept, but it'll do for this point). All gravitational effects in every day life can be traced to that bit of curvature that is left out of the rubber sheet model - spatial curvature is a very tiny correction.

This post has a much better diagram. Also this post, and also this video. All thanks to @A.T.

 

[PeterDonis]

the membrane itself is moving

This won't work because the whole point of the rubber sheet analogy is that it only shows "space" at an instant of time, and that "space" stays the same at every instant of time. So nothing changes about "space" in this analogy; but "motion" implies that something is changing.

the experimental set-up, where circular motion with constant speed is causing gravitational effects, as well, and if that could be transformed in a set-up where a constant linear velocity is used

What kind of "gravitational effects" due to circular motion are you talking about? If you mean things like seeing "centrifugal force" if you are inside a spinning space station, say, then the linear analogue is being in a linearly accelerating rocket and watching a dropped rock "fall" towards the bottom of the rocket due to a "pseudo-gravitational force". In both cases the source of the "force" is the fact that your motion has nonzero proper acceleration: you feel a force (in the spinning space station, a force pushing you against the outside wall; in the linearly accelerating rocket, a force pushing you upward as you "stand" on the bottom of the rocket). But if you are moving with constant linear velocity, you feel zero proper acceleration, and you will observe no such "forces".