Jump to content

constant acceleration


losfomot

Recommended Posts

Ok, two scenarios:

 

Getting there and stopping there.

 

Getting there I will take to mean you accelerate toward vega till you pass it.

 

Stopping there I will take to mean you accelerate toward vega, then decelerate and land on vega. If you are stopping there you have to start decelerating halfway there at the same acceleration amount.

 

d = v*t + 1/2at^2

 

Getting there: 9256 days (25ish years)

 

Stopping there: 12588 days (35ish years)

 

All of these calculations are absurd though because the energy required to accelerate at 20m/s^2 for that length of time would be IMMENSE and the velocities reached would surpass that of the speed of light hence breaking laws of physics and requiring even more energy to accelerate the accumulating mass.

 

Anyway, there are the two completely useless numbers:)

Link to comment
Share on other sites

Ok, two scenarios:

 

Getting there and stopping there.

 

Getting there I will take to mean you accelerate toward vega till you pass it.

 

Stopping there I will take to mean you accelerate toward vega, then decelerate and land on vega. If you are stopping there you have to start decelerating halfway there at the same acceleration amount.

 

d = v*t + 1/2at^2

 

Getting there: 9256 days (25ish years)

 

Stopping there: 12588 days (35ish years)

 

All of these calculations are absurd though because the energy required to accelerate at 20m/s^2 for that length of time would be IMMENSE and the velocities reached would surpass that of the speed of light hence breaking laws of physics and requiring even more energy to accelerate the accumulating mass.

 

Anyway, there are the two completely useless numbers:)

 

You can't actually work it out like this, because you will get to some very large speeds and it's accelerations we need to consider general relativity, unfortunately I can't do this because I'm not good enough at it.

Link to comment
Share on other sites

Yes, taking relativity into account... how long would it take 'ship time' to get there? I thought there was some (relatively) simple equation that you could use to figure it out.

 

Because your accelerating, I don't think there is. But I'm not good at this kind of thing....

Link to comment
Share on other sites

No one is good at this thing because the scenario is based on fantasy as the physical properties of matter and energy would be violated. One would need more energy than there is in the universe.

 

Back to reality. TheCPE points out an often forgotten variable is space travel...deceleration. It is one thing to propel an object to a thousandth the speed of light but quite another to slow it down again. Acceleration might be done with systems or fuels in orbit around the sun, or planets in the solar system but what is the energy source for deceleration? An interstellar spacecraft might weigh a millionth the weight of the fuel sources and infrastructure used to accelerate it to a thousandth the speed of light ....but to decelerate it needs to take all that with it....increasing the weight a million times...and the absurdity continues because then you need to increase the amout to accelerate it by a million times....then to decelerate...the numbers become absurd.

 

One can't used gravity at the other end to stop the craft because of the enormous speed. One could ricochet using the gravity of various stars along the way to slow down but that could add tens of thousands of years to a one way trip to a star. The irony is that the faster a craft goes, the more 'breaking power' it would need from stars along the way and increased speed might not be much help to reduce the time of the journey.

Link to comment
Share on other sites

You can't actually work it out like this, because you will get to some very large speeds and it's accelerations we need to consider general relativity, unfortunately I can't do this because I'm not good enough at it.

 

Yeh, thats why I included the last paragraph, especially the last sentence...:)

All of these calculations are absurd though because the energy required to accelerate at 20m/s^2 for that length of time would be IMMENSE and the velocities reached would surpass that of the speed of light hence breaking laws of physics and requiring even more energy to accelerate the accumulating mass.

 

Anyway, there are the two completely useless numbers:)

Link to comment
Share on other sites

Yes, taking relativity into account... how long would it take 'ship time' to get there? I thought there was some (relatively) simple equation that you could use to figure it out.

 

Taking Relativity into account:

 

[math]t_{ship time} = \frac{c}{a} \cosh^{-1}\left ( \frac{ad}{c^2}+1 \right ) = 2.24 yr[/math]

 

Earth time would be 26.39 yr

Link to comment
Share on other sites

No one is good at this thing because the scenario is based on fantasy as the physical properties of matter and energy would be violated. One would need more energy than there is in the universe.

 

Sort of but not really... I guess I could be more technically specific... how about this...

 

If I were in a ship and I left Earth (toward Vega) with a thrust that allowed me to move away from Earth at an acceleration of 20 m/s/s... and then I continued that same thrust for the entire trip to Vega... how long would it take me to get there?

 

This scenario is NOT fantasy. You can accelerate forever and still never reach the speed of light relative to any point in space. (actually I am not sure that this statement is completely true, in fact I think I will have to ask another question related to this statement)

 

Taking Relativity into account:

 

[math]t_{ship time} = \frac{c}{a} \cosh^{-1}\left ( \frac{ad}{c^2}+1 \right ) = 2.24 yr[/math]

 

Earth time would be 26.39 yr

 

Thank you, that sounds about right.

Link to comment
Share on other sites

If I were in a ship and I left Earth (toward Vega) with a thrust that allowed me to move away from Earth at an acceleration of 20 m/s/s... and then I continued that same thrust for the entire trip to Vega... how long would it take me to get there?

 

Thanks Janus, but taking the above paragraph into account changes things again I think as in this case the acceleration decreases with time?

Link to comment
Share on other sites

Thanks Janus, but taking the above paragraph into account changes things again I think as in this case the acceleration decreases with time?

 

Not for the occupants of the ship, they feel a constant 20m/sec² acceleration the whole time.

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.