Tiny rocket in Galileo’s ship to detect motion

[vibhuav]

Let’s consider Galileo’s description of relativity of motion using the example of a moving ship. The ship is at rest and made to accelerate extremely slowly for a few minutes, and then moves at a constant velocity. When the ship is moving at some constant velocity, the contents of the ship will also move with the ship and we will not be able to tell if the ship is moving or not.

1. A box on the floor of the ship will obviously move with the ship and so can’t help us.
2. The smoke emitted from a cigarette lying on a table in the ship will also follow the ship. This can be explained because as the particles of the smoke are emitted from the cigarette, these particles attain the velocity of the cigarette which is that of the ship. So the smoke continues to move forward with the ship. Same explanation for dropping water drops…
3. A butterfly flying around in the ship has the ship’s interior as its local reference, and so follows the ship
4. How about a mechanical “fly” hovering in midair inside the cabin? Will it also follow the ship? How to explain this phenomenon? Is it the air in the ship, which the mechanical fly is using to stay put, making the fly to move with the ship?
5. What about a tiny rocket, burning rocket fuel, hovering midair in the ship and the cabin is a vacuum? Will it move with the ship? How? Would the tiny rocket be considered as another inertial reference frame which we are using to detect motion?

The tiny rocket is a very simple one, burning the fuel just at the correct rate to stay put. There is no electronics or any such fancy stuff to control its location.

Maybe I am missing something?

 

[ghwellsjr]

Are you talking about a spaceship in zero gravity or a ship on the water where there is [STRIKE]no[/STRIKE] gravity?

 

[TSny]

[*]What about a tiny rocket, burning rocket fuel, hovering midair in the ship and the cabin is a vacuum? Will it move with the ship? How? Would the tiny rocket be considered as another inertial reference frame which we are using to detect motion?

Please specify if the little rocket is already hovering before the ship is accelerated up to its final speed, or if the rocket is placed in hovering mode after the ship reaches final speed.

 

[Nugatory]

Are you talking about a spaceship in zero gravity or a ship on the water where there is no gravity?

Considering that OP mentioned Galileo's ship, I'd expect that he means a ship traveling at constant speed on the surface of a calm sea - that's a thought experiment generally attributed to Galileo.

If that's what OP meant, the answer to all five questions is the same. The object, whether it is a particle of smoke, a drop of water, a box on the deck, a live insect or a robotic insect beating its wings against the air to hold itself up from the deck, or a rocket using its motor to exactly counterbalance the downwards pull of gravity... all will move with the ship, and none will provide a way of detecting the motion of the ship through the water.

And in all cases the reason is the same. The object started out moving at exactly the same speed as the ship and in exactly, and pushing it up (insect wings, rocket motor) or down (raindrops falling under the influence of gravity) doesn't do anything to change this sideways motion.

The presence or absence of air in the cabin has nothing to do with this. If there is air in the cabin, then it and the cabin and the object are all moving at the same speed, so the air exerts no force on the object; or equivalently, the object feels no wind.

The air matters only because if it's not there, the things that are using the air for support (the live and robotic insect and the particles of smoke) won't stay up - they'll fall straight down towards the floor in a vacuum, just as the raindrops do.

 

[vibhuav]

I was referring to the a real ship on water with gravity which Galileo uses to explain relativity (please see http://en.wikipedia.org/wiki/Galileo's_ship). Of course, this is an ideal ship in that it moves smoothly, etc.

The tiny rocket is already hovering inside the cabin before the ship is accelerated up to its final speed. Assume that the ship is very long and is accelerated only along the length of the ship. I don't want to do the observational experiment during the accelaration phase because acceleration can be determined; it is just the uniform velocity that can't be.

After the final, uniform velocity is reached, I think a person inside the cabin can determine that the ship is actually moving because the tiny rocket would have moved towards the back of the ship and will continue to do so until it hits the rear of the ship. If not, ie the rocket also moved with the ship just like the fish and the butterflies, how could it have moved?

 

[vibhuav]

I am really sorry; I assumed that Galileo's ship would be understood by all. I meant this Salviati's experiment: http://en.wikipedia.org/wiki/Galileo's_ship

Quoting parts of it relavant for my expt:

"...With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like...[but the ship's motion cannot be determined]..."

My comments within [ and ]

 

[Nugatory]

The tiny rocket is already hovering inside the cabin before the ship is accelerated up to its final speed. Assume that the ship is very long and is accelerated only along the length of the ship. I don't want to do the observational experiment during the acceleration phase because acceleration can be determined; it is just the uniform velocity that can't be.

Ah - starting the rocket hovering before the ship is accelerated, and not observing the rocket until after the acceleration is complete is an interestingly different twist.

In that case, the rocket will be moving relative to the ship - they both started at the same speed, but when the ship accelerated it changed its speed and the rocket didn't so now they're at different speeds. However, you still can't tell whether it is the ship that is moving or the rocket. It could be that the ship was accelerated... or it could be that someone walked into the cabin and gave the hovering rocket a shove that started it drifting towards the stern of the ship. We'd know which if we were allowed to observe the acceleration, of course, but we've agreed not to do that because it spoils the experiment.

 

[ghwellsjr]

I was referring to the a real ship on water with gravity which Galileo uses to explain relativity (please see http://en.wikipedia.org/wiki/Galileo's_ship). Of course, this is an ideal ship in that it moves smoothly, etc.

Your comment about the cabin being a vacuum made me wonder. Thanks for explaining.

The tiny rocket is already hovering inside the cabin before the ship is accelerated up to its final speed. Assume that the ship is very long and is accelerated only along the length of the ship. I don't want to do the observational experiment during the accelaration phase because acceleration can be determined; it is just the uniform velocity that can't be.

After the final, uniform velocity is reached, I think a person inside the cabin can determine that the ship is actually moving because the tiny rocket would have moved towards the back of the ship and will continue to do so until it hits the rear of the ship. If not, ie the rocket also moved with the ship just like the fish and the butterflies, how could it have moved?

You are correct in your first assessment, the rocket will move to the back of the ship and so will all the other objects that aren't restrained by friction to some degree. Any object that experiences acceleration can calculate its change in velocity before and after acceleration, that's what acceleration is. All the objects in the ship can know they have experienced a change in velocity except the hovering rocket in vacuum, that is, until it smacks up against the rear of the cabin when it will experience a great deal of acceleration all at once.

 

[vibhuav]

Ah - starting the rocket hovering before the ship is accelerated, and not observing the rocket until after the acceleration is complete is an interestingly different twist.

...However, you still can't tell whether it is the ship that is moving or the rocket. It could be that the ship was accelerated...or it could be that someone walked into the cabin and gave the hovering rocket a shove that started it drifting towards the stern of the ship...

Good answer! I am happy; thanks! ( I should have though about it... )