Undergrad Predicting Local Arrival Time w/ Rocket Ship Clock & Accelerometer

[Bob Walance]

TL;DR

This is a discussion about predicting Earth-based time from within a traveling rocket ship.

First, create a rocket ship with:

* a clock
* a 3-axis accelerometer
* a computer
* a 3-axis external thruster

The rocketeer begins in Earth orbit and sets the clock to Earth time. Then the ship takes off on a random trip through our universe. The pilot will arbitrarily point and apply the thruster in various directions. The path of this rocket might also be influenced by various forms of external matter (e.g. planets and stars and black holes).

Miraculously, after a long trip, the disoriented spaceperson finds that their rocket is back in Earth orbit.

Is it possible for the Earth time at arrival to be accurately predicted by feeding ONLY the rocket ship's clock and accelerometer data into the computer?

 

[Ibix]

Is this a homework question? Either way, what do you think and why?

 

[Bob Walance]

Not homework (I'm a 63yo EE). I have no formal training in GR.

I hope that the answer is yes but I don't yet have an intuitive feel for relative time in GR. SR seems easier to grasp but its effects aren't covered by more complex scenarios.

 

[PeroK]

Not homework (I'm a 63yo EE). I have no formal training in GR.

I hope that the answer is yes but I don't yet have an intuitive feel for relative time in GR. SR seems easier to grasp but its effects aren't covered by more complex scenarios.

What has this problem got to do with GR?

And don't say because SR can't handle acceleration!

See, for example:

https://en.wikipedia.org/wiki/Acceleration_(special_relativity)

 

[Ibix]

What has this problem got to do with GR?

He allows the path to go near black holes.

I hope that the answer is yes

Unfortunately, no. What does your accelerometer not detect from your list of effects?

 

[Bob Walance]

"...Unfortunately, no. What does your accelerometer not detect from your list of effects?"

My understanding of GR is that when the ship's thruster is off then the accelerometer will read 0.000... in all directions. That is, the ship is inertial (zero external net forces) when the thruster is off.

 

[PeroK]

He allows the path to go near black holes.

Unfortunately, no. What does your accelerometer not detect from your list of effects?

I assumed the idea was that gravity is "equivalent" to acceleration. So, by measuring acceleration of the ship you could measure the gravitational effects.

 

[Ibix]

My understanding of GR is that when the ship's thruster is off then the accelerometer will read 0.000... in all directions. That is, the ship is inertial (zero external net forces) when the thruster is off.

Correct. So what might affect your elapsed time that you can't detect by this methodology?

 

[Bob Walance]

He allows the path to go near black holes.

Unfortunately, no. What does your accelerometer not detect from your list of effects?

Correct. So what might affect your elapsed time that you can't detect by this methodology?

That's a great point, Ibix. The only effect (that I can think of) is all of the previous non-zero values detected by the accelerometer.

 

[Ibix]

That's a great point, Ibix. The only effect (that I can think of) is all of the previous non-zero values detected by the accelerometer.

No. Clocks deeper in gravitational fields tick slower than those further away (look up the Pound-Rebka experiment, or gravitational time dilation more generally). You can't detect this with your accelerometer, and hence you can't tell what your Earthly return time would be. You could if you could guarantee you were never deep in a gravitational field, and hence that SR was a decent approximation.

 

[Ibix]

...or, to be fair, if you had a sufficiently precise map of the galaxy that you could deduce your route from your proper acceleration history, that would also work. You'd be able to calculate where you were and hence factor in the gravitational effects. I strongly suspect that the precision needed to do this is implausible, but it's possible in principle.

 

[pervect]

Summary: This is a discussion about predicting Earth-based time from within a traveling rocket ship.

First, create a rocket ship with:

* a clock
* a 3-axis accelerometer
* a computer
* a 3-axis external thruster

The rocketeer begins in Earth orbit and sets the clock to Earth time. Then the ship takes off on a random trip through our universe. The pilot will arbitrarily point and apply the thruster in various directions. The path of this rocket might also be influenced by various forms of external matter (e.g. planets and stars and black holes).

Miraculously, after a long trip, the disoriented spaceperson finds that their rocket is back in Earth orbit.

Is it possible for the Earth time at arrival to be accurately predicted by feeding ONLY the rocket ship's clock and accelerometer data into the computer?

As others have said, your accelerometer reading won't give you information on the external matter, planets, stars, and black holes. If you eliminate that external element, and assume you are in the flat space-time of special relativity (SR), I believe the answer is basically yes, subject to how much accuracy you want and how accurate your instruments are.

At one time I saw a paper on the inertial navigation problem in SR, though I don't recall the author of the paper. So I'm relying on my fallible memory when I say the answer is "yes", but that's what I recollect.