How long does it take to get to the nearest star?

  • Thread starter frostedpoptar
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In summary, the time it would take to reach the nearest star to earth using a spacecraft that could accelerate at 1.5g for half a year would be 5.9 years.
  • #1
frostedpoptar
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Homework Statement



People hoping to travel to other worlds are faced with huge challenges. One of the biggest is the time required for a journey. The nearest star is 4.1 x 10^16 m away. Suppose you had a spacecraft that could accelerate at 1.5g for half a year, then continue at a constant speed. (This is far beyond what can be achieved with any known technology.)
How long would it take you to reach the nearest star to earth?

Homework Equations



Kinematic Equations, primarily:
Delta(x) = v(i)t + 1/2(a(x))t^2

The Attempt at a Solution



Never got that far after a long time of attempting to work it out.
Try not to provide me with the answer but just some hint or way to go about it if that's possible.
Thanks so much.
 
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  • #2
Try solving the problem in two steps:

1.How far do you travel while accelerating?

2. How much distance is left to cover? How long does this take going at that constant speed?
 
  • #3
Hi frostedpoptar. Welcome to Physics Forums.

You should try to write out what you think might be the relevant equations, and show an example of a calculation that you attempted.

Your problem statement seems to be missing some information (numerical value for distance, units for acceleration) that could make a big difference in how the problem is to be solved.
 
  • #4
G01, I was attempting to do that yesterday and it didn't work out. I erased it from my whiteboard but I will attempt to do it again and post my results.

gneill, You're completely write, I left some things out in the main post, I just edited it. Thanks for noticing. I'll attempt to work it out again and reply as soon as I do.
 
  • #5
frostedpoptar said:
G01, I was attempting to do that yesterday and it didn't work out. I erased it from my whiteboard but I will attempt to do it again and post my results.

gneill, You're completely write, I left some things out in the main post, I just edited it. Thanks for noticing. I'll attempt to work it out again and reply as soon as I do.

The value for the distance is still not there. Neither are the units on the acceleration. As gneill pointed out, we need these things in order to help you. EDIT: Okay I see I posted while you were editing.
 
  • #6
I just tried to work it out partially.

I used v(f) = v(i) + a*t

As v(f) = 14.7(1314000)
so I got v(f) as 19,315,800 m/s
 
  • #7
I also plugged that into
v(f)^2 = v(i)^2 + 2a(delta x)

and got delta x as 1.26904806 x 10^13 meters.
 
  • #8
frostedpoptar said:
I just tried to work it out partially.

I used v(f) = v(i) + a*t

As v(f) = 14.7(1314000)
so I got v(f) as 19,315,800 m/s

Your number of seconds in half a year seems wrong.
 
  • #9
frostedpoptar said:
I also plugged that into
v(f)^2 = v(i)^2 + 2a(delta x)

and got delta x as 1.26904806 x 10^13 meters.

That works, minus the error above. You could also just use

Δx = vit + (1/2)at2

Since you already know a, you already computed t, and you know that vi = 0. Either way, when you substitute in quantities like vf or t that were computed in intermediate steps, be sure to carry over a lot of digits in order to avoid accumulation of error. You can round off to the correct number of sig figs when you get your final answer at the end.
 
  • #10
Gotcha.

I plugged in the new value (15,768,000 s) and got these values for v(f) and delta x:
v(f) = 231,789,600 m/s
delta x = 1.827429206 x 10^15
 
  • #11
I got 5.3589 years as the time it takes from the moment the spacecraft stops accelerating to the moment it reaches the star..
 
  • #12
I got it! its 5.9 when you factor in the .5 year of acceleration.

Thanks so much guys.
 
  • #13
What about stopping?
 

1. How far away is the nearest star?

The nearest star to Earth is Proxima Centauri, located about 4.24 light years away. This means that it takes light, traveling at 186,282 miles per second, approximately 4.24 years to reach Earth from Proxima Centauri.

2. How long would it take to travel to the nearest star?

The answer to this question depends on the method of travel. With our current technology, it would take thousands of years to reach the nearest star. However, with future advancements in technology, it may be possible to travel to Proxima Centauri in a matter of decades.

3. Can humans survive the journey to the nearest star?

As mentioned before, it would take thousands of years to travel to the nearest star with our current technology. This makes it nearly impossible for humans to survive the journey. However, with advancements in technology and advancements in space travel, it may be possible for humans to survive the journey in the future.

4. What is the fastest spacecraft ever launched and how long would it take to reach the nearest star?

The fastest spacecraft ever launched is the Parker Solar Probe, which can reach speeds of up to 430,000 miles per hour. If the probe were to travel to the nearest star, it would take approximately 6,300 years to reach Proxima Centauri.

5. How do scientists measure the distance to the nearest star?

Scientists use a method called parallax to measure the distance to the nearest star. This involves measuring the apparent shift in position of a star when viewed from different points in Earth's orbit around the sun. By using trigonometry and precise measurements, scientists can calculate the distance to the nearest star.

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