How can I calculate the speed needed for a 30-year journey to Alpha Centauri?

[texasman1979]

related to my other thread: https://www.physicsforums.com/showthread.php?t=732462

Here's the hypothetical scenario:

A trip from Earth to alpha centauri in 30 years. Steadily accelerating to half way then turning around and steadily decelerating.

Trying to figure out a way to figure speeds along the time line.

I don't want the answer, but the math formula to figure it out.

Thx.

30 years -- time line
4.2 lightyears -- relative distance to stars

 

[texasman1979]

calc thrust non rocket engine

related to my other thread: https://www.physicsforums.com/showthread.php?t=732459

Writing a fiction scifi book.

The spacecraft will have a magnetic based propulsion system. In the book the spacecraft weighs 130 metric tons.

I would like some educated numbers to go by for figuring thrust and speed from 0 thrust to 1g.

Obviously, with a non rocket type propulsion there would be no mass loss as fuel is burned cause there wouldn't be any fuel. So i don't divulge too much of the story line pretend it is solar based energy making electricity making a magnetic field.

This is a book I'm writing, but there is some real science behind it and I'm wanting it to be as real as it can be.

Thx.

 

[mfb]

I merged your threads, as the questions are closely related. This is not really astrophysics, so the thread could get moved.

For a uniform acceleration "a", starting at rest, and neglecting relativistic effects, the distance traveled after time t is given by $s=\frac{1}{2} a t^2$. You know t and s (half the distance and time), so you can calculate a. With that, the velocity is just acceleration*time.
The deceleration part works the same way, just backwards.

I would like some educated numbers to go by for figuring thrust and speed from 0 thrust to 1g.

F=m*a
Calculate a, and you can get F.
What is a "magnetic based propulsion system"? You have to accelerate something backwards. Mass from the rocket, mass or light incoming from some external source, or interstellar medium. You do need fuel to power your ship - even if you have a system that does not need reaction mass.

 

[texasman1979]

two parts to this.

In space, once you are going 1,000,000 miles per hour you are going to continue going 1,000,000 miles per hour till some force acts to modify that.

In my story and inventor makes a new type of ship set in the next few decades. As far as the details to that, you'll have to read the book. :)

So, a 30 year trip to Alpha Centauri, binary star system. The character and his craft will begin in Earth's orbit and sling shot around a couple planets to achieve system exit velocity. Then he will continue to accelerate toward Alpha Centauri for 15 years and then turn around and decelerate the next 15 years.

At the same time the ship weighs 130 metric tons. That's 286600.6 pounds. How many pounds of thrust would be needed to gain 1 gforce from the acceleration?

I am having a bit of trouble relating your math with the principles I have stated. I would help me a great deal if you related the math to my particular problem so i can relate the two better.

thx.

 

[Bandersnatch]

I am having a bit of trouble relating your math with the principles I have stated. I would help me a great deal if you related the math to my particular problem so i can relate the two better.

the ship weighs 130 metric tons

That's the m in F=ma. Convert to kilograms.

1 gforce from the acceleration?

that's the acceleration a(use the value in m/s^2)
Plug these in and you get the force(thrust) in Newtons.

Same with s=at^2. s is half the distance to αCen in metres; a is the acceleration you're looking for; t is the time to get half way there, in seconds. Just plug the values in.

By the way, at 1g constant acceleration, you'll get there in 3.5 years on-board time, and 5.8 Earth time, as relativistic effects start to play a role at that speeds.
To get there in 30 years, you need about 0.02 g acceleration(here, relativistic effects are negligible).

You may find these resourses useful:
http://www.projectrho.com/rocket/calculators.php
in particular this one:
http://mysite.verizon.net/res148h4j/javascript/script_starship.html

 

[texasman1979]

how did you come up with those times and g forces? that web page?

how do i figure that manually?

 

[mfb]

So, a 30 year trip to Alpha Centauri, binary star system. The character and his craft will begin in Earth's orbit and sling shot around a couple planets to achieve system exit velocity.

That is not necessary, your ship is so powerful it would be a waste of time (several years) to use gravitational slingshots within our solar system for a tiny velocity gain.

I am having a bit of trouble relating your math with the principles I have stated. I would help me a great deal if you related the math to my particular problem so i can relate the two better.

I considered all those principles for the formulas and explanations I posted.Metric units are much more convenient.