- #1

ntrand

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- TL;DR Summary
- I want to calculate length contraction from Earth to Proxima Centauri in the reference frame of a spaceship that is moving with acceleration between those two points.

Let's assume a spaceship traveling from the

The ship is accelerating the first half of the trajectory and decelerating the second half.

I calculated the velocity profile from the Earth reference:

The travel time on the spaceship is calculated to be

In order to calculate the length contraction from Earth to Proxima Centauri, I started with the formula:

where l

Then I insert the velocity formula:

but I am not able to calculate the integral since the independent variable is length l instead of time t.

**Earth**to the**Proxima Centauri**with constant acceleration**g = 9.81 m/s**.^{2}The ship is accelerating the first half of the trajectory and decelerating the second half.

I calculated the velocity profile from the Earth reference:

The travel time on the spaceship is calculated to be

**3.54 years**due to the time dilation.In order to calculate the length contraction from Earth to Proxima Centauri, I started with the formula:

where l

_{0}is length from the Earth reference.Then I insert the velocity formula:

but I am not able to calculate the integral since the independent variable is length l instead of time t.

**How can I calculate length contraction for such accelerated motion? I want to calculate the length from Earth to Proxima in the ship frame.**