Voyager can get home in 1.38 years!

[Anticitizen]

I was thinking about Voyager's plight of being 70,000 light years from home.

Not being a mathematician myself, I posed the following question over at physicsforums.com:

My question: what if the crew forgot about the prospect of getting back in a timely fashion as far as Earth is concerned, and just wanted to get back home in their OWN lifetimes... and thus switched off the warp drive and accelerated normally, in order to rely on time dilation to make the trip?

Since the starship has magical gizmos called 'inertial dampeners,' let's assume they can accelerate at a solid 10 G's without the crew being pancaked. Let's ignore deceleration time by saying that can use their warp drive to stop suddenly without killing everyone aboard.

So my question is, how long would a journey of 70,000 light years take with a constant acceleration of 10 G-units for the entire journey, relative to the crew's POV? Secondarily, what sort of acceleration would get the crew back home in their own lifetime, if any?

Oh, and what sort of time would pass on Earth in the meantime?

The thread is here: http://physicsforums.com/showthread.php?t=317655

Plugging in x=70 000 ly, a=10*1.032 ly/y^2 and c=1 yields:



Realize that this means you're accelerating with 10g all the way to earth and then instantly decelerating to zero once you reach earth so I hope those inertial dampeners work properly.

Using equation 17 we can calculate the time that has expired on earth.

So Voyager can get back to Earth in only 1.38 years of their own time by NOT using warp drive, assuming they can keep a constant acceleration of 10 g's using impulse! Unfortunately, 70,695 years will pass on Earth. But hey, slingshot around the sun or a black hole a few times before you make the trip, and problem solved!

I guess there wouldn't have been a series though.

 

[TigerOfDarkness]

Most interesting!

 

[JB2005]

...well that'd have been easier...

 

[Guy Gardener]

Could they navigate through relativistic perspective?

there was an episode of Andromeda which covered this. Andromeda was broke down between star systems when it bumped into a ship from earth travelling at relativistic speed under the command of Tony Todd. They all wore uniforms that looked trek. I think they were taking the piss.

 

[thedude]

Yabbut...

Then they wouldn't have had 7 years of TV show... DUH!

As a very famous man once said... "MERCHANDISING!"

 

[Akiraprise]

How fast do the impulse engines go though? I thought that full impulse was like 1/4 the speed of light.

 

[Zameaze]

So Voyager can get back to Earth in only 1.38 years of their own time by NOT using warp drive, assuming they can keep a constant acceleration of 10 g's using impulse! Unfortunately, 70,695 years will pass on Earth. But hey, slingshot around the sun or a black hole a few times before you make the trip, and problem solved!

I guess there wouldn't have been a series though.

Am I missing something here? Wouldn’t a constant acceleration of 10 g's, or 322 ft/sec^2, take us past the speed of light and make any results obtained from such an equation meaningless?

 

[Bosch571]

So Voyager can get back to Earth in only 1.38 years of their own time by NOT using warp drive, assuming they can keep a constant acceleration of 10 g's using impulse! Unfortunately, 70,695 years will pass on Earth. But hey, slingshot around the sun or a black hole a few times before you make the trip, and problem solved!

I guess there wouldn't have been a series though.

Am I missing something here? Wouldn’t a constant acceleration of 10 g's, or 322 ft/sec^2, take us past the speed of light and make any results obtained from such an equation meaningless?

No it won't 10 g's = 322 ft/sec^2 only works on low velocities.
You can accelerate indefinitely (assuming an unending fuel supply) and still never reach the speed of light.

 

[Bill Morris]

Thrusters, not impulse engines, which are basically a sublight version of warp drive, using driver coils instead of true warp coils.

But Janeway had the chance to get Voyager home early on, just by agreeing to explore with Q, just as Vash did. And since Q had the ability to let her be in two places at the same time, she could have stayed with the ship and explored strange, new worlds simultaneously, not to mention do as she pleased with the Borg, the Dominion, etc. just by nagging Q whenever she wanted something.

 

[Jaespol]

wut

 

[TheGodBen]

Unfortunately, 70,695 years will pass on Earth.

So by the time they got back to Earth the human race would have evolved into orange lizards? Ironic.

 

[Anticitizen]

So Voyager can get back to Earth in only 1.38 years of their own time by NOT using warp drive, assuming they can keep a constant acceleration of 10 g's using impulse! Unfortunately, 70,695 years will pass on Earth. But hey, slingshot around the sun or a black hole a few times before you make the trip, and problem solved!

I guess there wouldn't have been a series though.

Am I missing something here? Wouldn’t a constant acceleration of 10 g's, or 322 ft/sec^2, take us past the speed of light and make any results obtained from such an equation meaningless?

Nah, you'll get within 99.9% of the speed of light... and then 99.99%... then 99.999%.... and so on. Time will dialate more and more, but the 'light barrier' will never be crossed.

 

[Zameaze]

So Voyager can get back to Earth in only 1.38 years of their own time by NOT using warp drive, assuming they can keep a constant acceleration of 10 g's using impulse! Unfortunately, 70,695 years will pass on Earth. But hey, slingshot around the sun or a black hole a few times before you make the trip, and problem solved!

I guess there wouldn't have been a series though.

Am I missing something here? Wouldn’t a constant acceleration of 10 g's, or 322 ft/sec^2, take us past the speed of light and make any results obtained from such an equation meaningless?

Nah, you'll get within 99.9% of the speed of light... and then 99.99%... then 99.999%.... and so on. Time will dialate more and more, but the 'light barrier' will never be crossed.

Thanks for the answer, Anticitizen. However I’m still confused--if Voyager is accelerating in the direction of motion at 322 feet per second per second, the ship would never reach the speed of light because of time dilation?

At around 186,000 miles per second, would it seem to the crew that they were still constantly accelerating at 322 ft/sec/sec?

If they passed Earth while traveling at 99.9 per cent of the speed of light, how fast would they be traveling from the frame of reference of the people of Earth? I'm guessing not as fast since they would be very massive.

Now, this brings another question to mind--Voyager can’t reach the speed of light because she would obtain infinite mass--does this mean she would be infinitely large or just infinitely dense? And can she become infinitely dense without becoming infinitely large?

 

[shatastrophic]

This is the craziest cool shit I've read in a while!! Sorry for the slang.

 

[Jaespol]

This is the craziest cool shit I've read in a while!! Sorry for the slang.

That's really not slang...

 

[Nebusj]

Thanks for the answer, Anticitizen. However I’m still confused--if Voyager is accelerating in the direction of motion at 322 feet per second per second, the ship would never reach the speed of light because of time dilation?

Assuming endless acceleration and the universe obeying the rules of special and general relativity (which does look overwhelmingly like the way to bet, in the real world), yes. It'd keep accelerating but never reach the speed of light.

At around 186,000 miles per second, would it seem to the crew that they were still constantly accelerating at 322 ft/sec/sec?

Yes, that's so. Somebody on Voyager would measure their speed as increasing at 322 feet per second per second. Somebody off of Voyager would measure Voyager's speed as increasing a fewer number of feet per second per second. This is because --- and this is central to the wonder of relativity --- the person on Voyager and the person off of Voyager would have different lengths that each thought was ``a foot'' long, and have different intervals of time that each thought was ``a second'' long, and both would be right about those lengths.

If they passed Earth while traveling at 99.9 per cent of the speed of light, how fast would they be traveling from the frame of reference of the people of Earth? I'm guessing not as fast since they would be very massive.

Someone on Earth watching Voyager fly by would say the ship was travelling at 99.9 percent the speed of light, yes. Someone on Voyager watching the Earth would see the Earth as travelling at 99.9 percent the speed of light. The wondrous and strange things happen when you ask what someone on Enterprise, approaching Earth at half the speed of light but from another direction, measures Voyager's speed as being. As above, each observer has a different idea of how long a ``foot'' is, and how long a ``second'' takes, and each one is correct for themselves and is just as right for how they see things.

To be careful, you really shouldn't just say ``Voyager flying at 99.9 percent the speed of light''; you have to say what reference point is doing the measuring of that speed. Otherwise it's actually surprisingly like saying ``the bunny is to the left of Heather'', when if you don't say who's doing the looking that sentence is true, false, or meaningless.

Now, this brings another question to mind--Voyager can’t reach the speed of light because she would obtain infinite mass--does this mean she would be infinitely large or just infinitely dense? And can she become infinitely dense without becoming infinitely large?

An observer on Earth watching Voyager fly past would measure the ship as being shorter end-to-end --- contracted in length, they say --- compared to how they would measure the ship when it was at rest on Earth. (But Voyager would say the same thing about the Earth, from its point of view.) The observer on Earth would also conclude that Voyager's mass was effectively more than it would be at rest, in no small part because of how little its speed changes with a given force, going back to the whole force-as-mass-times-acceleration idea (which does get confusing and is a good reason to remember force is only mass-times-acceleration at low speeds where you can ignore relativity's complications; better to think of force as change-in-momentum-with-time).

Be very, very careful in talking about `infinitely dense' or `infinitely large' things, though. Human brains have almost no intuition about how these work and it's very easy to get wild ideas that may make for fun science fictional stories but which are not logically rigorous. (Case in point, the above stuff does not mean a fast enough Voyager becomes a black hole. Promise.)

 

[Zameaze]

Be very, very careful in talking about `infinitely dense' or `infinitely large' things, though. Human brains have almost no intuition about how these work and it's very easy to get wild ideas that may make for fun science fictional stories but which are not logically rigorous. (Case in point, the above stuff does not mean a fast enough Voyager becomes a black hole. Promise.)

Thank you, Nebusj. You have a way of making things simple by keeping a person’s mind on point.

One thing that I still don’t understand is this: If the mass of any particle that has a mass initially would be infinite at the speed of light, and this infinite mass doesn’t refer to infinite density nor infinite size, to what does it refer? Just that it would take an infinite force to move it?

 

[Nebusj]

Thank you, Nebusj. You have a way of making things simple by keeping a person’s mind on point.

You're quite kind. I'm afraid my real work is teaching, as opposed to what I do for pay, and that bleeds over into other things I do if I'm not careful.

One thing that I still don’t understand is this: If the mass of any particle that has a mass initially would be infinite at the speed of light, and this infinite mass doesn’t refer to infinite density nor infinite size, to what does it refer? Just that it would take an infinite force to move it?

The first thing is that something which has a nonzero rest mass --- that is, anything that doesn't always move at the speed of light (such as, er, light) --- is that you can't get it up to the speed of light. You could put all the energy there is in the universe together in one big burst to make the particle move as fast as you can, but you can't accelerate it up to the speed of light.

But if you are willing to pretend, what if you can just keep pulling more energy out of nowhere, then yeah, you do run into exactly what you describe there: if you put the same amount of force on an object when it's nowhere near the speed of light (in your reference frame), you get the same amount of acceleration the first second of doing this that you get the tenth second and the hundredth second, when the speed is so low that you can ignore relativistic effects.

When the thing is going fast enough that it's near the speed of light, the same amount of force will change the speed it travels less.

If you're still comfortable thinking of 'force' as 'mass times acceleration', then since the 'force' stayed the same and the acceleration drops towards zero, this concludes that the mass is growing infinitely large. So you can think of this as one of the other reasons that, as we presently understand the universe, you can't speed things up to be as fast as light (much less get faster).

 

[Zameaze]

Thank you, Nebusj. You have a way of making things simple by keeping a person’s mind on point.

You're quite kind. I'm afraid my real work is teaching, as opposed to what I do for pay, and that bleeds over into other things I do if I'm not careful.

One thing that I still don’t understand is this: If the mass of any particle that has a mass initially would be infinite at the speed of light, and this infinite mass doesn’t refer to infinite density nor infinite size, to what does it refer? Just that it would take an infinite force to move it?

The first thing is that something which has a nonzero rest mass --- that is, anything that doesn't always move at the speed of light (such as, er, light) --- is that you can't get it up to the speed of light. You could put all the energy there is in the universe together in one big burst to make the particle move as fast as you can, but you can't accelerate it up to the speed of light.

But if you are willing to pretend, what if you can just keep pulling more energy out of nowhere, then yeah, you do run into exactly what you describe there: if you put the same amount of force on an object when it's nowhere near the speed of light (in your reference frame), you get the same amount of acceleration the first second of doing this that you get the tenth second and the hundredth second, when the speed is so low that you can ignore relativistic effects.

When the thing is going fast enough that it's near the speed of light, the same amount of force will change the speed it travels less.

If you're still comfortable thinking of 'force' as 'mass times acceleration', then since the 'force' stayed the same and the acceleration drops towards zero, this concludes that the mass is growing infinitely large. So you can think of this as one of the other reasons that, as we presently understand the universe, you can't speed things up to be as fast as light (much less get faster).

You can tell that a person is an exceptional teacher when what he says is so obvious after he says it. Thanks again.