Inertia/acceleration question

[Bushranger]

Consider a space ship in near/far Earth orbit.  Suddenly accelerates to thousands of mile an hour instantly.  Would the astronauts be slammed to the rear of the vehicle or would the fact that they were only subject to micro gravity (mass but little/no gravity to act upon the mass) they would not be so effected?  In short, in the absence of gravity (I understand that there is "microgravity" in Earth orbit) is law of inertia (bodies at rest remain at rest), in effect?  Please explain it to me like I was a six-year old.

[swansont]

The presence or absence of gravity has no effect here. In a Newtonian view these are forces, and forces add as vectors. Whatever acceleration that's exerted on them via rockets (or whatever) is something they will experience.

In any event, a body in orbit isn't at rest. The astronauts are perpetually in freefall, but if one analyzes their motion one would deduce that there is a net force on them, because they are not in uniform motion. Therefore, they are undergoing acceleration.

[Bufofrog]

4 hours ago, Bushranger said:

Suddenly accelerates to thousands of mile an hour instantly.  Would the astronauts be slammed to the rear of the vehicle

Yes.  I am assuming that you don't actually mean instantly, you mean really quickly.

[beecee]

We are forgetting about "star trek" inspired inertial dampers. 😉

[MigL]

Even for GR where gravity is not actually considered a force, the Equivalence Principle suggests that acceleration is equivalent to gravity ( without tidal effects ).
That is why we can expess acceleration in g , or multiples of 9.8 m/s/s.
IOW, an acceleration of 2g is equal to 19.6 m/s/s , and you would be 'pushed back' as if you weighed twice your normal weight, or the Earth's gravitational force was doubled.

[Bushranger]

I am trying hard to understand.  Consider a rocket in space that suddenly accelerates (thousands of miles per hour).  The rocket cabin (a cylinder) is filled with air.  Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

[Curious layman]

31 minutes ago, Bushranger said:

The rocket cabin (a cylinder) is filled with air.  Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

Just a thought, but If this were true, wouldn't the same thing happen on planes?

I know you said thousands of miles per hour, but wouldn't the same effect happen at slower speeds.

Edited February 19, 2021 by Curious layman

[Markus Hanke]

1 hour ago, Bushranger said:

Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

If the acceleration was large enough, and the rocket able to withstand the forces involved, then you could make this happen in principle, since the air in the cabin is not rigidly connected to the rocket. In practice though it is unlikely that any kind of real-world rocket would survive this kind of acceleration. 
But regardless, your understanding of the basic principle is correct.

1 hour ago, Curious layman said:

Just a thought, but If this were true, wouldn't the same thing happen on planes?

I know you said thousands of miles per hour, but wouldn't the same effect happen at slower speeds.

No, because acceleration isn’t the same as velocity. A plane may go reasonably fast at cruising altitude, but it takes time to reach that maximum velocity, so the rate of acceleration involved is comparatively small - which is fortunate for the passengers, since otherwise they’d get crushed into bloody puddles during takeoff  

[Halc]

On 2/17/2021 at 5:41 PM, MigL said:

Even for GR where gravity is not actually considered a force, the Equivalence Principle suggests that acceleration is equivalent to gravity ( without tidal effects ).

There are still tidal effects with acceleration.  An accelerometer at the front of a rockets reads less than one at the rear. The difference is negligible for the tiny acceleration of our rockets, but if you really jacked the g forces and made the rocket long (and strong) enough, the figures would be very different.

8 hours ago, Bushranger said:

I am trying hard to understand.  Consider a rocket in space that suddenly accelerates (thousands of miles per hour).  The rocket cabin (a cylinder) is filled with air.  Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

Yes, the air moves to the rear, just like helium balloons tend to move to the front of a car when it is accelerating.

If the accleration acts on all particles of the ship (say due to a large mass passing in front of it), then the passengers will feel no acceleration at all, only tidal effects at best. Alternatively one could put the people in a weighless situation like under water. That makes you weightless on Earth despite the 1g acceleration, and thus you'd be fairly weightless under this insane acceleration as well. The danger then would be from the bends, and not so much from being bent.

[swansont]

9 hours ago, Bushranger said:

I am trying hard to understand.  Consider a rocket in space that suddenly accelerates (thousands of miles per hour).  The rocket cabin (a cylinder) is filled with air.  Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

Not all the air; there will be a gradient of density. Similar to how air pressure (and density) near the earth’s surface is higher than it is at some distance above the surface, owing to the affect of gravity.

 

[Janus]

10 hours ago, Bushranger said:

I am trying hard to understand.  Consider a rocket in space that suddenly accelerates (thousands of miles per hour).  The rocket cabin (a cylinder) is filled with air.  Is all the air then suddenly "pushed" to the rear of the rocket due to "bodies that are at rest tend to remain at rest", and a vacuum formed at the front of the rocket because all the air is not in the rear?  This all seems counter-intuitive to me.

As swansot has already mentioned, it isn't quite that simple.   There will be a gradient.  Not only that, but there is the fact that the air in your ship will already be under pressure.   If it is at 1 atm, this pressure is the same as caused by the weight of a column of air at constant sea level density which is 8.5 km tall.( at 1 g of gravity).

So let's say your spaceship is 10 meters long and full of air at 1 atm.   If you were to accelerate at 850 g, that air would be "pushed back" towards the rear of the ship. That 10 m column at 850g would act like a 8.5 km tall column at 1g.   The air pressure at the rear of the ship will double. (but not increase by 100's of times.)

The pressure would decrease as you moved towards the nose of the craft, but in this scenario would not decrease to zero.

And of course, this would only occur during the acceleration phase

So, if the ship accelerates up to 10,000 mph, that is the same as 4444 meters/sec.

850g is 8330 m/s/s, so it would take just a bit over 1/2 sec for your ship to go from 0 to 10000 mph at that acceleration.  It would be during this time that the air would be compressed towards the back of the ship. Once the ship attains it's target velocity and stops acceleration, it will return to its previous uncompressed state.

And while the air would start to compress towards the back the instant the ship begins acceleration, there would be some lag before it could come to its new state, and then some lag before it can return to its previous state once the acceleration ceases. 

 

 

[MigL]

I don't think you'd be breathing anyway, at anything over 10 g, never mind 850 g.

5 hours ago, Halc said:

There are still tidal effects with acceleration.

Sorry Halc.
I meant only that subset of tidal effects which originate from the fact that field lines are not parallel in a gravitational field, but spread out from the CoM.
( but I didn't know how to put that in a few words )

[Halc]

Indeed.  A pair of plumb bobs will not be parallel on Earth, but will be in an accelerating ship.

In the inertial case, a plumb-bob in the no-gravity case will not point anywhere, but off-center in an orbiting space station, they will.  So there are very much differences.

The most basic test: Create a 3D arrangement with 4 balls (stationary relative to our small orbiting lab) arranged in a tetrahedron (in a vacuum so air currents don't move them around).  The movement of the balls will show the direction of the source of gravity, or at least the axis of it.

Edited February 19, 2021 by Halc