Velocity of a spacecraft at relativistic speed

In summary, the conversation discusses a physics problem given as a challenge by a teacher. The problem involves using the relativistic position update equation to determine the maximum speed attained and the time it takes for a cargo ship to travel to the nearest star system, which is 4.3 light years away. The use of kinematic equations is not applicable due to the effects of relativity. The conversation also mentions the need for a stationary observer to measure all values for a simpler solution. The participant in the conversation is directed towards the concept of the "relativistic rocket" for further understanding.
  • #1
Huston
3
0

Homework Statement


The closest star system is about 4.3 light years away from Earth. A spacetug is able to move a cargo ship at a constant force of g=9.8N/kg times the mass of the cargo ship for many years. Starting from rest, speed up the cargo ship until you're halfway to the nearest stars, then pull back with the same force to slow the ship down to rest. Determine the maximum speed attained and how many Earth years the trip there takes.

Homework Equations


I'm not sure. I really just need help starting it. We haven't really gone over relativity, and my teacher is giving this project as a challenge. I'm not sure if it's easier than I'm making it, but our book doesn't really have much pertinent information on the subject except that we need to use the relativistic position update equation to solve it. We haven't done any relativity problems in class and I'd just love a push in the right direction!

The Attempt at a Solution


Normally, I'd start with the kinematic equations, but here they end up with wrong answers because they don't account for relativity. Please help me get started! Thanks!
 
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  • #2
:welcome:
You got yourself a tough teacher if he isn't going to teach you relativity before giving you relativity problems. Ever hear of the relativistic rocket? There should be many threads about it here on PF.

Btw, it's not easier than you are making it to be, unless I'm missing something myself ?:)
 
  • #3
It may depend on who is doing all the measurements of time, mass, force, distance and velocity. If they are all done by the stationary observer, there may not be a problem. It does specify Earth years and is careful to define the force so that mass does not matter. If some of the values are as measured by the traveler, it is more complicated.
 
  • #4
FactChecker said:
It may depend on who is doing all the measurements of time, mass, force, distance and velocity. If they are all done by the stationary observer, there may not be a problem. It does specify Earth years and is careful to define the force so that mass does not matter. If some of the values are as measured by the traveler, it is more complicated.
It is looking for measurements from a stationary observer I believe.
 
  • #5
Comeback City said:
:welcome:
You got yourself a tough teacher if he isn't going to teach you relativity before giving you relativity problems. Ever hear of the relativistic rocket? There should be many threads about it here on PF.

Btw, it's not easier than you are making it to be, unless I'm missing something myself ?:)
I'll go look at the relativistic rocket! I appreciate the help! It's definitely not the easiest class I've ever taken. There's a lot of learning on my own. I had some physics in high school, but this is my intro to physics as a major in University. It seems like this program is going to be intense. It'll be good for me in the long run though.
 
  • #6

1. What is the difference between the velocity of a spacecraft at relativistic speed and regular speed?

At relativistic speeds, which are speeds close to the speed of light, the laws of physics are different than at regular speeds. This means that the velocity of a spacecraft at relativistic speed can have a much greater impact on its surroundings and can cause effects such as time dilation and length contraction.

2. Can a spacecraft reach the speed of light?

According to the theory of relativity, it is impossible for any object to reach the speed of light. As an object approaches the speed of light, its mass increases infinitely, making it impossible to accelerate any further. Therefore, a spacecraft cannot reach the speed of light, but it can get closer to it.

3. How does the velocity of a spacecraft at relativistic speed affect its fuel consumption?

At relativistic speeds, the energy and fuel required to accelerate a spacecraft increase exponentially. This means that the faster a spacecraft travels, the more fuel it will consume to maintain that speed. As a result, spacecrafts must carefully manage their fuel consumption when traveling at relativistic speeds.

4. What are the potential dangers of traveling at relativistic speeds?

One of the main dangers of traveling at relativistic speeds is the intense radiation that is present in space. As a spacecraft approaches the speed of light, it may encounter high-energy particles that can damage its systems and harm the crew. Additionally, the high speed can also cause collisions with interstellar objects, which can be dangerous for the spacecraft.

5. How is the velocity of a spacecraft at relativistic speed measured?

The velocity of a spacecraft at relativistic speed can be measured using various methods, such as Doppler shift, time dilation, and length contraction. These methods use the effects of relativistic speed on time and space to determine the velocity of the spacecraft. Other methods, such as radar and laser ranging, can also be used to measure the spacecraft's velocity relative to a known reference point.

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