On the noton of reference frames force and acceleration

[MeJennifer]

If you fell straight down from space towards the surface of the Earth a passing satellite will appear to be moving a straight line relative to you. This is because when you are falling you are a true inertial observer.

Really?

 

[yuiop]

Really?

I think it is true in a small enough region such as within a small falling elevator. It is not true if the elevator is large as the curvature of spacetime that is present around a sperical gravitational body becomes noticeable. This is where the equivalence principle breaks down, because a free falling elevator should be the same as a elevator far away from any gravitational sources and you would not expect to see any curved trajectories with no gravity present.

To be honest, it bothers me a lot that it seems impossible to find a situation where the equivalence principle holds exactly. If we define the principle as not being able to perform any experiments in an accelerating elevator/rocket that would detect whether the acceleration was due to a rocket or gravity, then I have not been able to find a single example where that is exactly true and it is only justified by making the elevator very small. Basically, the tidal effects always give the game away.

 

[yuiop]

If you fell straight down from space towards the surface of the Earth a passing satellite will appear to be moving a straight line relative to you. This is because when you are falling you are a true inertial observer.

Really?

Hi Jennifer,

I have found an example where my statement is exactly true, even over quite a large area and the apparent straight line motion of the orbiting particle to a free falling observer is shown in the attached gif. The box represents a falling elevator that is dropped from just above the Earth's surface and falls through a tunnel drilled right through the Earth. Such an elavator would fall to the other side of the Earth and then come back again following simple harmonic oscillation and would continue bobbing up and down indefinitely if there was no atmsosphere present creating friction. The period of the oscillating elevator in free fall would be the same as the period of a satellite in very low Earth orbit (again assuming no atmosphere). In the animated gif the apogee of the elavator is designed to coincide with the satellite passing the elevator. You can see from the gif that in this particular example it would not matter how wide the elevator is or even if the observer in the elevator looks out the windows, the satellite always seems to follow a stright path from his point of view. In a more realistic example of a satellite in high orbit and with a large elevator, some slight curvature of the satellites path would probably be noticed by the free falling observer in the elavator.

 

[yuiop]

Hi Jennifer,

I have found an example where my statement is exactly true, even over quite a large area and the apparent straight line motion of the orbiting particle to a free falling observer is shown in the attached gif. The box represents a falling elevator that is dropped from just above the Earth's surface and falls through a tunnel drilled right through the Earth. Such an elavator would fall to the other side of the Earth and then come back again following simple harmonic oscillation and would continue bobbing up and down indefinitely if there was no atmsosphere present creating friction. The period of the oscillating elevator in free fall would be the same as the period of a satellite in very low Earth orbit (again assuming no atmosphere). In the animated gif the apogee of the elavator is designed to coincide with the satellite passing the elevator. You can see from the gif that in this particular example it would not matter how wide the elevator is or even if the observer in the elevator looks out the windows, the satellite always seems to follow a stright path from his point of view. In a more realistic example of a satellite in high orbit and with a large elevator, some slight curvature of the satellites path would probably be noticed by the free falling observer in the elavator.

Ummm..here is the gif that should have been attached to my last post..not sure how it came unattached...it was there in there in the preview..

In case it is not obvious, the left part of the animated gif is the point of view of a non inertial observer watching the satellite follow a circular path while the right side of the gif is the point of view of the inertial observer in the free falling elevator who considers the elevator to be stationary. m

 

[Al68]

i think i understand, so they define a frame which is far away from all body as inertial frame, and an accelerometer will determine where is accelerate relative to the defined inertial frame, then you can tell whether the forces on a body is fictiticious or not, generally you cannot conclude whether you are accelerating or a body is accelerating if you do not define a first inertial frame!? correct, if correct then i completely get the fundamental idea of relativity

How about a homemade accelerometer? If you hold a bowling ball three feet in front of you and release it, measure its (coordinate) acceleration. If you're at rest in an inertial frame, the bowling ball will float in front of your face. If the bowling ball accelerates (coordinate) relative to you, then you're in an accelerated frame.

Seriously, Wikipedia has info: http://en.wikipedia.org/wiki/Inertial_frame_of_reference.
They also have articles on acceleration (proper and coordinate), fictional forces, and almost anything else you can think of.

Al