Understanding Results from a Relativistic Star Ship Calculator

In summary, the conversation discusses the use of a "Relativistic Star Ship Calculator" to determine the time and speed it would take for a hypothetical star ship to travel a certain distance at a constant acceleration of 1G. The poster's initial understanding was that the ship would reach a high fraction of the speed of light in approximately 2 years, but the calculator results showed a longer time and slower speed. The explanation given is that this is due to Special relativity, where velocities do not add in the same way as under Galilean relativity. The conversation ends with the poster expressing their surprise at not understanding this concept before.
  • #1
danielgoodman
2
0
Hello, first time poster here!

I am trying to understand some results I am getting from this "Relativistic Star Ship Calculator". This site sets up the question I'm trying to answer exactly like I imagined it should (thanks to The Forever War). From the description:

The star ship accelerates continuously from the origin to the midpoint of the mission.
At the midpoint, the ship turns its thrusters to face the destination.
The ship decelerates continuously from the midpoint to the destination.

The way I understood it, if you are accelerating at 1G and hope to come arbitrarily close to the speed of light, it should take (3*10^8 m/s)/(9.8 m/s^2)= ~354 days. Similarly, if you hope to decelerate from such a speed, it will require the same amount of time. So say about 2 years of combined acceleration/deceleration.

Further, I thought that at a velocity which is arbitrarily close to c, your Lorentz Factor becomes arbitrarily high, meaning that light years can be traveled in seconds (or less). So the conclusion I reached is that you can travel virtually any distance in ~2 years if you had a ship that accelerates at 1G and can reach a very high fraction of c.

When inputting large distances in the calculator linked above, I get results that don't fit with my rationale. Example:

Input: Distance: 10 LY
Acceleration: 1G
Output: Time: 4.9 Y
Max Speed: 0.987 c

So this calculator assumes your trip takes 4.9 Y (not 2) and you only reach 0.987 c (not .99999...c)

Can someone explain the fault in my reasoning?

Thanks so much!
 
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  • #2
danielgoodman said:
The way I understood it, if you are accelerating at 1G and hope to come arbitrarily close to the speed of light, it should take (3*10^8 m/s)/(9.8 m/s^2)= ~354 days.
Velocities do not add that way. That would be true under Galilean relativity, but not Special relativity. (See: How Do You Add Velocities in Special Relativity?)

The longer the acceleration is applied, the less affect it has on the speed with respect to the original frame. (Note that the acceleration is measured from an inertial frame co-moving with the rocket at any moment--not with respect to the original frame.)

After one year (in rocket time) of accelerating at g, your speed would be only about .77c. (See: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html)

Further, I thought that at a velocity which is arbitrarily close to c, your Lorentz Factor becomes arbitrarily high, meaning that light years can be traveled in seconds (or less).
That's true.
So the conclusion I reached is that you can travel virtually any distance in ~2 years if you had a ship that accelerates at 1G and can reach a very high fraction of c.
The problem is that you are not going as fast as you think. It takes a while to reach a really high speed at that acceleration.
 
  • #3


Thanks Doc Al, I'll read those links. I'm kind of miffed that I made it out of my Physics course (which covered special relativity) without understanding that bit. Anyway, good to know!
 

1. What is a relativistic star ship calculator?

A relativistic star ship calculator is a tool used to calculate and understand the effects of special relativity on a spacecraft traveling at near-light speeds.

2. How does the calculator work?

The calculator uses the principles of special relativity, including time dilation and length contraction, to determine the effects on a spacecraft traveling at high speeds. It takes into account the velocity and distance traveled to provide accurate results.

3. What can I learn from using a relativistic star ship calculator?

By using the calculator, you can gain a better understanding of how special relativity affects the perception of time and distance for objects traveling at near-light speeds. You can also learn about the potential challenges and limitations of interstellar travel.

4. Are the results from the calculator accurate?

Yes, the results from the calculator are based on well-established principles of special relativity and have been verified through various experiments and observations. However, it is important to note that the calculator may not account for all variables and factors, and should be used as a guide rather than an absolute measure.

5. How can I use the results from the calculator in my research or work?

The results from the calculator can be used to inform and guide the design and planning of future interstellar missions. They can also be used to explore the possibilities and limitations of space travel at near-light speeds, and to make informed decisions about the feasibility of such endeavors.

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