From Earth to Pandora

Last week, I created a simulator to better understand what the experience of interstellar travel feels like. As I discovered before, the experience is very interesting.

However, because of the difficultly with the Math around relativistic travel, I was very worried that my math might be incorrect. If I really want to gain confidence in my simulations, I need to replicate on a known interstellar trajectory.

Today, I’d like to try and replicate the award winning movie Avatar by James Cameron.

Journey to Pandora

If you’ve seen the movies, you probably have noticed the ISV (interstellar vehicle). Above, from the second movie Way of Water, we are introduced to the return of humans by the flotilla of ISVs arriving in orbit around Pandora.

From Avatar Fan Wiki

In a industry filled with warp drives and worm-holes, the ISV stands out as a reasonably realistic rendition of what a future interstellar vehicle might look like. Although most argue it’s still far beyond our current technology¹. Like a weight hanging from the string, the ISV is built much the same. On one end, the crew and cargo modules are suspended in tension beneath the propulsion section².

Additionally, when the ship departs from Earth, the ISV saves on fuel by deploying a solar sail to reflect light from a Massive earth-based laser array⁶. The basic outline of the journey thus becomes:

1. Laser arrays on Earth push off the ISV’s solar sail
2. ISV coasts
3. ISV uses anti-matter engines to decelerate
4. The ISV spends time in orbit of Pandora
5. ISV uses engines to accelerate and leave Pandora
6. Again, ISV coasts
7. Earth Laser arrays are deployed to decelerate ISV as it returns

Setting up simulation

When I first looked into replicating the ISV’s journey, I only had a few numbers to go off of.

According to the Fan Wiki, the ISV has the following journey²:

• Limited to 1.5 G
• Travels to Alpha Centauri A (4.37 lightyears away)
• Top speed 0.7 c
• Acceleration and deceleration last five and a half months each
• Cruises for 5.83 years
• Total Journey takes 6.75 years

Using my (code on GitHub), we can change out the model of the ship (along with some other rendering changes) and then specify the trajectory from above:

1.5, 5.5 months
0, 5.83 years
-1.5, 5.5 months

Easy! All we need to do is run the simulation:

Oof, our spaceship just flew pass Pandora. What happened?

Remember Time Dilation

The simulation I created for interstellar travel is meant to help a ship captain to plan their voyage to the galaxy’s hottest destinations³. Thus, the sequence of maneuvers above is actually based on ship time. However, as the ship accelerates, the clock aboard will also tick slower.

In short, the five and a half month duration you find online is for the Earth based observer, not the ship. So, how do we figure out when to stop firing the engines?

Binary Search Baby!

Yes, you could use all the math I detailed in my previous blog post to figure out the exact sequence³. However, that requires a lot of work. All the calculators I found online, only appear to use brachistichrone trajectories and do not support coasting⁴⁵. Instead, let’s try and search for the correct numbers using my existing code.

1.5, 5.5 months
0, 5.83 years
-1.5, 5.5 months

Produces the following output from my code

Like before, we overshoot the destination. I then try a slightly modified trajectory:

1.5, 6 months
0, 4 years
-1.5, 6 months

This time, we undershoot the target:

By optimizing both the distance remaining and the time elapsed on earth (Coordinate time), I was able to find the correct sequence!

1.5, 6.7208 months
0, 3.93085 years
-1.5, 6.7208 months

Well, this isn’t exactly correct. The journey takes about a week longer and about an astronomical unit away. However, for my purposes, I find this acceptable.

Animation

Like last time, we can see how an observer on Earth and the ISV will perceive the ship’s journey.

At the start, the ISV deploys a solar sail. Earth uses a large laser array to propel the ISV away². Flipping around, the ISV then coasts until it is time for deceleration. As described, the entire journey takes about 5 years ship time, and 6.75 years earth time.

Analysis

Like before, spatial contraction causes the apparent distance to contract for the ship-based observer.

Unlike the coasting brachistochrone trajectory I previously analyzed, travelers on the ISV do not reach a high enough speed to observe the strange reversing affect that sometimes occur when decelerating from relativistic speeds:

Regardless, we find the same interesting disparity between the acceleration felt onboard the ship vs what is measured by observing the universe around the ship:

Because of the spatial contraction and time dilation, neither observer will measure their acceleration relative to the destination to match with the acceleration ordered to the engines. Instead, from earth’s perspective, the ship appears to take its foot off the gas and star reducing acceleration. From the ship, it appears as though the the ship’s engines are becoming more efficient over time.

Conclusion

I have always been fascinated by interstellar travel and the peculiar experience that Einstein describes. However, over the years, I have felt a bit underwhelmed by the few online calculators⁴⁵. Although they are sufficient for exploring the concept, I really wanted more control and data then they could provide.

Although we are far far away from making anything like the ISV, we can at least find solace in our ability to explore the math that illuminates the way.

As always, the code is available on GitHub