Will KSP 2 simulate the affects of special relativity on ships moving near the speed of light?

[Gaming Kraken]

The question is in the title, I imagine not, as that seems quite daunting to implement, but it would be really interesting to see the MET clock on board a spacecraft to reflect to time elapsed on board the ship, or to run into the exponential decrease in acceleration as you approach c. Even accounting for the 0.1x scaling of the Kerbolar system, distances to the nearest stars will still likely be measured in light years I imagine, so these long range crafts will likely want to reach these speeds, which is why I wonder if KSP 2 plans to tackle it. Interested to hear what you guys think!

Edited April 9, 2022 by Gaming Kraken

[Catto]

Probably. I hope so.

[Axelord FTW]

It COULD work as a simple % modifier for hab-resource utilization. It kinda breaks down the moment you realize comms are still instantaneous, and that once the ship has slowed down the game-elapsed time still match.

I'm a big proponent of light-lag for probe control, so I can imagine it would be funky to implement.

[CFYL]

Well IMO special relativity isn't only about differences in the coordinates of time&space...

For example, in the static frame (say, Kerbol frame), the ΔV generated will differ from the ΔV generated by the same amount of fuel in a moving frame (say, ship frame). 

For the sake of Physics...

KSP1 (and possibly real space missions) depends "immensely" on Tsiolkovsky rocket equation,

ΔV=μln(m₀/m_k),

where μ is the speed that the engine pushes exhaust fume backwards relative to the spacecraft (a.k.a. specific impulse, I_sp), m_o is the mass at start and m_k is the mass at end. 

(If I_sp is in "seconds", then it means "how long can the engine provide thrust equal to the gravity of something which weighs 1kg, while using only 1kg of fuel". So I_sp in seconds and μ in m/s can be related by μ/g=I_sp)

In the classic model, this is correct. If you have an upper stage which moves in space without gravity and accelerates in a straight line, its engine I_sp is 380s, it has 3t fuel and 1t dry mass, let g=9.8m/s², then its ΔV=380×9.8×ln(4/1)=5162.56m/s.

However in the case where special relativity is taken into concern, Tsiolkovsky rocket equation needs some "correction" to be Physically correct.

I'll leave the process behind, but with Lorentz transformation, conservation of momentum and some calculus, you get:

m₀/m_k=[(1+ΔV/c)/(1-ΔV/c)]^c/2μ=exp{ln[(1+ΔV/c)/(1-ΔV/c)]×c/2μ}

as a correct result. (This equation is correct given that μ<<c, which appears to be true for most modern thrusters) (Aclé equation, but I don't know whether that's the correct spelling or not. Also the ship has to start the acceleration from a static position, so for acceleration from a moving position, some Lorentz transformation for speed may be useful.)

Taylor expansion of "ln[...]" and we get:

m₀/m_k=exp(ΔV/μ)×{1+[(ΔV/μ)×(ΔV/c)²]¹×(1/3)+[(ΔV/μ)×(ΔV/c)²]²×[(1/18)+(μ/5ΔV)]+[(ΔV/μ)×(ΔV/c)²]³×[(1/162)+(μ/15ΔV)+(μ²/7ΔV²)]+...}

If we do some math and extract m₀/m_k out of the Tsiolkovsky rocket equation, we get:

m₀/m_k=exp(ΔV/μ)

So yes, when ΔV<<c that {...}≈1, nice and neat. But when ΔV gets closer to c, it will take some more fuel to achieve each little amount of acceleration as m₀/m_k increases. When ΔV reaches some 0.1c, special relativity kicks into action and makes a small difference. When ΔV reaches "interstellar worthy" speeds of some 0.5c or 0.8c, special relativity makes a HUGE difference. When ΔV goes really close to c, special relativity makes an ABSURD difference, not only about being "slower" in time and "shorter" in length, but also an ABSURD amount of fuel is required to go to that speed. (Interstellar travel can be seen as moving on a straight line without much interation with gravity, when you reach 0.x times the speed of LIGHT)

Let's calculate the fuel needed to propell 1t payload to 0.8c (AND to slow it down to 0c or it will fly forever!) with different engines.

Chemical: I_sp=450s, a somehow ideal engine already. slowing down from 0.8c to 0 requires [1.8/0.2]^{299792458/(2×450×9.8)}= exceeds the memory of my poor little CASIO-991. That's far more than 10¹⁰⁰t fuel required for braking. Which means faaaaar more than 10²⁰⁰t for acceleration. Tip: the mass of our Milkyway galaxy is somewhere around 1.7×10⁴²kg. Completely impossible.

Nuclear: I_sp=1.5×10⁷m/s, which is the theoretical upper limit of a 6D --> 2He(7.1MeV) + 2protons(17.1MeV) + 2neutrons(16.55MeV) + 1.8MeV engine. Slowing down from 0.8c to 0 requires [1.8/0.2]^{299792458/(2×1.5E7)}=3.4342×10⁹t, or 3.4342 billion tons. To accelerate such a mass to 0.8c requires a 1.1794×10¹⁹t ship on a parking orbit. Don't bother to think how to get that thing into orbit from ground though...

Photon/Antimatter: a concept that I had discussed in a topic earlier. 

It uses a different equation. Braking to 0 from 0.8c requires (5/3)t mass (1.6667t), and to get that mass from 0 to 0.8c requires (25/9)t mass (2.7778t). It may seem possible but it needs 100% efficient photon engines (putting matter and antimatter together, convert 100% of energy released to photons and shoot them exactly backwards). I don't know if KSP2 will have that.

All data about mass refer to static mass, measured from a inertial frame where the object is static.

Also, When the we enter the flying mode, we are in the "ship" frame. Keep in mind that special relativity tells you that "all inertial frames of reference are equal by nature". The ship moves at 0.8c. A clock on the ship ticks 5 times. But we see the clock at base only ticks 3 times in the meanwhile. (say, we are smart enough to correct deviations caused by the limited speed of light and the Doppler Effect). When we switch on our magical engine, we experience acceleration in ship frame, where acceleration a=TWR×g

In the ship inertial frame(which moves at 0.8c, reaches the same place at the same time as the ship, but not accelerating), the ship experiences another acceleration a₁, a₁=aγ³=a×(5/3)³=125a/27≈4.630a. 

In the static frame(Kerbol frame), the ship experiences yet another acceleration a₂, a₂=a/γ³=a÷(5/3)³=27a/125=0.216a.

Special relativity just makes it too complex to code&play, I suppose...

To achieve a speed where special relativity is worthy of concern, we need either very advanced engines, or use entire celestial bodies to send a small probe/spaceship. (Pluto weighs 1.303E19t, and all of that has to be fuel to put into the reaction chamber...). Advanced engines may work well, and special relativity needs to be taken into consideration in that case. But with conventional propulsion methods there seems to be little need for simple relativity bucause the ship never reaches 0.xc (0.01c is great for conventional engines...). Given that KSP2 HAS Antimatter, I suppose it is possible to implement special relativity, but I don't see a very high probability.

Edited May 6, 2022 by AllenLi
I hope it's ok to link to a Chinese website about science. There're some details about this thing. https://www.zhihu.com/question/337919697/answer/787275901

[CFYL]

41 minutes ago, AllenLi said:

The ship moves at 0.8c. A clock on the ship ticks 5 times. But we see the clock at base only ticks 3 times in the meanwhile.

This refers to the famous “twin paradox”. I'm giving a brief explanation here.

A pair of twins are both astronauts. One(elder) stays on the Earth as control group, while the other(younger) goes on a spaceship to travel at 0.6c. 

Earth frame(pretend it's inertial lol)

For the elder twin, the younger travels for 50 years at 0.6c to 30lys away, and then back at the same speed. The younger returns. For the elder 100 years have passed since the younger left. For the younger it's just 2×50×sqrt(1-0.6²)=80 years. So the younger is now 20 years younger then the elder.(really)

Moving frame

For the younger, the travel length is 30×sqrt(1-0.6²)=24ly. Total travel time is 2×24÷0.6=80 years. The elder experiences a total time of 80×sqrt(1-0.6^2)=64 years.(In the frame of the younger, the elder moves at 0.6c so time gets slower for the elder) The younger returns, and the younger is now 16 years older than the elder(emm... try to understand what i mean lol)

So will the younger be 20 years younger than the elder or 16 years older than the elder?

The answer is: 20 years younger. So what's wrong with our theory with the moving frame?

Actually,it is true that, in the moving frame, the younger sees that time gets slower for the elder. But special relativity only applies to inertial frame. The younger has to, somehow, change the trajectory, from (0.6c leaving the Earth) to (0.6c approaching the Earth). Suppose that this is completed in a tiny "moment" in the moving frame. The younger will see a sum of 100-64=36 years passing on the elder (and the Earth) in that "moment" which is used to deccelerate and then accelerate again.

So IF special relativity will be applied... the playerbase may find it hard to adjust to it, not to mention the difficulty to "find a way" to code it into the game. (Oh come on, I learned this when preparing for (China's) National Physics Olympiad)

Edited May 6, 2022 by AllenLi

[Dhruv]

From your question.

I guess no! Because it is absolutely un realistic and impossible to achieve speed of light in KSP (1 or 2) as it is a game which realistic physics and other things cannot be replicated (It can be by mods but let's not talk about it)

 

Say if you've reached speed of light in game the chances are either the game gets crashed or as you've mentioned above it will be hard to adjust course after that speed is attained. Moreover once that speed is achieved you will require same amount of reverse speed to slow it down and then change the course and then again repeat the same process which is useless and not fun.

 

The better way to solve this issue is to use time lapse to see the effect of ships moving fast along with time and there is no time delay which will cause the effects of special relativity and there will be difference in the in game clock.

It will be an immense hard work and extremely difficult to code to add the effects of special relativity in game like KSP where they focus in making players learn about space travel and stuff....

So I in conclusion no is the answer 

[Fletch4]

On 5/6/2022 at 12:35 AM, AllenLi said:

So IF special relativity will be applied... the playerbase may find it hard to adjust to it, not to mention the difficulty to "find a way" to code it into the game. (Oh come on, I learned this when preparing for (China's) National Physics Olympiad)

what they could do is scale down the size of kerbin as you move faster and slow down the relative velocity of the ships that aren't the one that you control. then, mask a new clock on top of the old one and slow down the old one as the controlled ship moves faster. then, everything else will have a slower relative velocity, but not crash into the planet, while you retain you current acceleration.

for that amount of time, everything else will move slower, except for you, at least until you come out of speeds where special relativity is applied.

[Bej Kerman]

On 5/6/2022 at 6:59 AM, Dhruv said:

I guess no! Because it is absolutely un realistic and impossible to achieve speed of light in KSP (1 or 2) as it is a game which realistic physics and other things cannot be replicated (It can be by mods but let's not talk about it)

 

A bit quick to say that, no? Even if the engines in the game aren't optimised for 0.2+c, there's no doubt in my mind players will design rockets specifically built to push 0.999c.

[LHACK4142]

Wow. You're a good explainer.