# I Best Way to measure Relativistic Rocket Acceleration?

1. Oct 31, 2016

Someday, mankind will be able to construct rockets that can move at relativistic speeds.

The acceleration is given by $a=\frac{F_0}{γ^3m_0}$

$F_0$ can be easily measured by placing a force gauge on the rocket itself.

The acceleration is much harder to measure, is has to be measured in a frame in which the rocket is zipping past at relativistic speeds.

What efficient methods to measure the acceleration can you think of?

My idea is placing a camera far away from the rocket's path and taking snapshots of it to see how its position evolves over time.

But we also have to consider tricky relativistic optics.

2. Oct 31, 2016

### BvU

The ?

And what would $\gamma$ be in this expression ?

I expect it's a lot easier to measure a Doppler shift and differentiate. Leaving cameras all over the place doesn't sound efficient.

3. Oct 31, 2016

The Lorentz factor? based on the speed of the rocket

4. Oct 31, 2016

### BvU

I know. But it's relative to something...

5. Oct 31, 2016

relative to the frame which you are in, making the measurements.

6. Oct 31, 2016

### BvU

Yeah, I looked it up . It's the expression for transformation of acceleration between two inertial frames. Have to let it sink in to understand whether it's necessarily between two inertial frames or can be applied within a non-inertial frame as well. Somewhat above my pay grade (experimentalist). @Orodruin ?

7. Oct 31, 2016

### Orodruin

Staff Emeritus
Force in the conventional sense is not very well defined in SR. From your post, it would seem that you are using $F_0$ to be the force in the instantaneous rest frame, which would make $F_0/m_0$ equal to the proper acceleration. Your formula will then generally depend on whether or not you are accelerating in the direction of motion or not.

It is unclear to me what you want to use this for. Acceleration is easily accessible in any frame. As you say, just observe the position as a function of time an account for the travel time of light.

8. Oct 31, 2016

Yup, all the vectors are pointing in the same direction. Just linear acceleration.

Yes, that's what I said, now I need a good way to practically and experimentally carry it out. Ideas for the near future perhaps.

Engineers will have to test the relativistic performances of rockets and spaceships in the future.

9. Oct 31, 2016

### Orodruin

Staff Emeritus
It is still unclear what you wish to accomplish. This has already been well tested in particle accelerators.

Relativistic space ships of macroscopic size are not a near future thing.

Furthermore, you cannot neglect mass losses if you use a rocket to generate thrust and wish to reach relativistic velocities.

10. Oct 31, 2016

Yes, but the rockets still have to be tested after they have been built. I'm just wondering what methods future engineers might use to accomplish the task of tracking a relativistic rocket's position. Something efficient and as cheap as possible.

Ok, maybe the far future then. Does near-future mean in about 50 years time to you?

Certainly we can take into account the rocket's changing mass.

11. Oct 31, 2016

### Orodruin

Staff Emeritus
Barring unexpected giant advancements you will not see macroscopic relativistic rockets in the next 200 years. Have you taken the time to compute what portion of a rocket's mass must be converted into thrust in order for it to reach relativistic velocity? It is humongous.

12. Oct 31, 2016

Do you have any link regarding that? Not that I don't believe you.

13. Oct 31, 2016

### Orodruin

Staff Emeritus
The 200 years is a personal lower estimate. I would be surprised if it happened at all unless special relativity is fundamentally misguided for macroscopic objects - which we have no reason to believe.

The computation of the mass fraction needed to be ejected in order to reach relativistic velocities is a typical textbook exercise.

14. Oct 31, 2016

ok. but why do you think that it is impossible? someday we might find a way to harness enough energy.

and anyway for this thread I want to focus on tracking a rocket.

15. Oct 31, 2016

### Orodruin

Staff Emeritus
Because the energy required is essentially the entire starting mass of the rocket. It is not a matter of finding the energy, it is the ratio between total rocket mass and useful payload that will kill you. Never mind the useful payload if you ever want to decelerate to return to the original state of motion.

You have much more pressing problems than relativistic optics then. For example, where does the illumination of the rocket come from and what frequency it will be observed at.