Special Relativity math question, thanks in advance again

CapelDodger said:
I think there's a need to allow for us on Earth being in Earth's gravitational field (and the Sun's, and Jupiter's, and ...) when calculating the time-difference.
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The gravitational potential is far too low to matter here. You're not going to get more than a few parts per hundred million correction.

CapelDodger said:
You might want to check this out http://en.wikipedia.org/wiki/Tau_Zero, a Poul Anderson sci-fi story where the ship's accelerator gets jammed on or some such. I read it a long time ago, it's good fun.
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Neat.

Have a song about relativity by the astrophysicist Brian May:
 
Vorpal said:
The gravitational potential is far too low to matter here. You're not going to get more than a few parts per hundred million correction.
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Just trying to show off before sol invictus turns up ;).

Neat.
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At the Earth's centre its gravitational field is zero, so time moves quicker down there. I find that pretty neat. Of course I could be wrong, I've got a lot of my science knowledge from SciFi, particularly Larry Niven.

Have a song about relativity by the astrophysicist Brian May:
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What a lovely song, thanks muchly.
 
CapelDodger said:
If 40 years subjective time for people on the ship is what you meant then yes. If you meant 40 years subjective time for us on Earth then no. There is, of course, no objective time.

I think there's a need to allow for us on Earth being in Earth's gravitational field (and the Sun's, and Jupiter's, and ...) when calculating the time-difference. I'm no expert, though.
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I was thinking about aging body time. That's an objective measure. If you traveled for 40-80 years in space you'd be talking reproducing in a biosphere along the way if you didn't go for some kind of suspended animation.
 
When i go on a long drive, time seems to get bigger.
Its likely a subjective observation, but it can occur in as little as 12 hours, at 60 mph.
 
Skeptic Ginger said:
I was thinking about aging body time. That's an objective measure. If you traveled for 40-80 years in space you'd be talking reproducing in a biosphere along the way if you didn't go for some kind of suspended animation.
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All clocks, including aging, are affected. All are relative. High speed doesn't have a mechanical or optical effect; it changes what it means to measure distances and elapsed times.

(Well, technically, you don't want a grandfather clock on a spaceship, because how fast it ticks depends on a source of gravity or acceleration. But your body will age at the same rate as your wristwatch, as long as you don't get zapped by too much radiation.)

No offense intended if you already know this, but I think it's crucial to understanding relativity. There is no "objective" measurement of time that is consistent for all observers, which is why it's called "relativity." Every measurement is equally valid. Students often ask if time really slows down or if it just seems that way. There is no such distinction in relativity. The measurement is the reality.
 
epepke said:
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No offense intended if you already know this, but I think it's crucial to understanding relativity. There is no "objective" measurement of time that is consistent for all observers, which is why it's called "relativity." Every measurement is equally valid. Students often ask if time really slows down or if it just seems that way. There is no such distinction in relativity. The measurement is the reality.
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Not offended. We are just using "objective" to mean different things. What I mean is the objective measure, 'aging', of how time would be perceived to the people on the spaceship. I didn't mean aging was an objective measure of time elsewhere.
 
CapelDodger said:
At the Earth's centre its gravitational field is zero, so time moves quicker down there. I find that pretty neat. Of course I could be wrong, I've got a lot of my science knowledge from SciFi, particularly Larry Niven.
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Not quite. In a gravitational well (when you're standing, not falling), or under acceleration, clocks above you go faster, and clocks below you go slower. It's all about where the observer and the clock are relative to each other (and how they are moving, of course).

There's a really neat thing that surprises even some old-timers. You take a clock that you know ticks at a certain rate. Put it on top of a tower and look at it from the base of the tower. You will measure it as ticking faster, but by how much?

You can solve that by some arguments about light and conservation of energy, or solve GR for that case and really pull your hair out, but there's an easier way. Knock the clock off the tower. Ignoring air resistance, of course (do it on the moon or just pretend) and it picks up speed. Measure how fast it's ticking when it passes right by you. It will be ticking slower than it would be if you were holding it still. Work the numbers backward, and you can figure out how much faster it was ticking before you knocked it off.
 
Skeptic_Ginger -

If you're really going to try for manned interstellar travel via nuclear pulse propulsion, and you care about getting the numbers right, I suggest that you need to do some research. The numbers involved are pretty mind-boggling. For a start, try http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)#Economics.

A few basic principles:

1) These things are huge. One way to look at it is that you need nukes for fuel/energy efficiency, and nukes have big bangs. This in turn means you need big shock absorbers to keep the explosion impulse from crushing the passengers, and there are severe material limits to what you can do. Note that this means you can't do small ships, and what you can do (barring specifying von Neumann robots) will be fabulously expensive.

2) These things take an enormous number of nukes. Put it this way, to get to 0.1c at 4 g's takes about 750,000 seconds. If you get this by dropping one bomb per second, well, that's a whole lot of bombs. And having a stockpile of 3/4 of a million nukes in orbit around the earth would seem to suggest all sorts of plot twists.

3) If you want to specify unobtainium plated with handwavium, you can make all sorts of ameliorating suggestions, but you need to think them through.

Best of luck.
 
If you want to go into "reality" calculations, then a good one might be the rocket equation.
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

This page http://en.wikipedia.org/wiki/Nuclear_pulse_propulsion suggests that an advanced theoretical nuclear engine could get up to a specific impulse of 100000 seconds.

Plugging in:
ln(m0/m1) = dV /(Isp g0)
ln(m0/m1) = 0.1c / 100000s * 9.81m/s^2
ln(m0/m1) = 30
m0/m1 ~ 10^13

This states that to get to a ship to 0.1c with (excellent) nuclear propulsion, you have to start with 10^13 times that ship's mass in bombs/fuel.
 
Skeptic Ginger said:
Not offended. We are just using "objective" to mean different things. What I mean is the objective measure, 'aging', of how time would be perceived to the people on the spaceship. I didn't mean aging was an objective measure of time elsewhere.
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It has to give the same answers as another kind of (good) clock. Such as a light stick.

In any event, the people in the spaceship would not notice anything weird. Their clocks would work, just as they'd expect. It's only when looking outside that they'd notice anything weird, such as slowing clocks in other places moving relative to them, or in the contraction of the universe in the axis of their line of flight.
 
WhatRoughBeast said:
Skeptic_Ginger -

If you're really going to try for manned interstellar travel via nuclear pulse propulsion, and you care about getting the numbers right, I suggest that you need to do some research. The numbers involved are pretty mind-boggling. For a start, try http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)#Economics.

A few basic principles:

1) These things are huge. One way to look at it is that you need nukes for fuel/energy efficiency, and nukes have big bangs. This in turn means you need big shock absorbers to keep the explosion impulse from crushing the passengers, and there are severe material limits to what you can do. Note that this means you can't do small ships, and what you can do (barring specifying von Neumann robots) will be fabulously expensive.

2) These things take an enormous number of nukes. Put it this way, to get to 0.1c at 4 g's takes about 750,000 seconds. If you get this by dropping one bomb per second, well, that's a whole lot of bombs. And having a stockpile of 3/4 of a million nukes in orbit around the earth would seem to suggest all sorts of plot twists.

3) If you want to specify unobtainium plated with handwavium, you can make all sorts of ameliorating suggestions, but you need to think them through.

Best of luck.
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It's a very minor part of the story. I only need a suggestion of plausibility. It was better than saying warp drive was invented/discovered.

But the time frame is important because time needs to pass between certain events and that either happens on Earth or during transit. I have two ships with populations emigrating to Proxima Centauri and they arrive with ~ century between them give or take.

Thanks, though, that link might be very useful if I decide to describe the ships in more detail. The size of the ships will be fairly large so that is helpful.
 
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BowlOfRed said:
If you want to go into "reality" calculations, then a good one might be the rocket equation.
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

This page http://en.wikipedia.org/wiki/Nuclear_pulse_propulsion suggests that an advanced theoretical nuclear engine could get up to a specific impulse of 100000 seconds.

Plugging in:
ln(m0/m1) = dV /(Isp g0)
ln(m0/m1) = 0.1c / 100000s * 9.81m/s^2
ln(m0/m1) = 30
m0/m1 ~ 10^13

This states that to get to a ship to 0.1c with (excellent) nuclear propulsion, you have to start with 10^13 times that ship's mass in bombs/fuel.
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Well, I might just have to pretend I didn't read that. ;)

Or, perhaps I'll look more at the antimatter drives. That might work better anyway because if it's very difficult to isolate or collect the particles, that would limit more than the two ships being able to leave Earth.
 
Skeptic Ginger said:
Thanks, though, that link might be very useful if I decide to describe the ships in more detail. The size of the ships will be fairly large so that is helpful.
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If you go to the link provided by BowlofRed, http://en.wikipedia.org/wiki/Nuclear_pulse_propulsion, and push down the page to Project Longshot, you'll find a study of a system using He3/deuterium with an Isp of 10^6, which allows a mass fraction at 0.1c of about 35. Also, the thrust for this system can be much lower than with nukes, so you can consider a really big ship (like a hollowed out asteroid) which won't collapse under thrust. You're falmiliar with the phrase "generation ship", I hope.

Also, these numbers reflect what you need to get to 0.1 c, and make no provision for slowing down at the destination. When you do that, the mass ratio is squared, so even with the Longshot technology, useful payload is about 0.1%

And, if you find the concept useful, keep in mind that your ship will requre more He3 than exists on earth. The Longshot study recommends helium mining on Jupiter as one possible source.
 
Problems, always problems. :D

I'll take a look at Project Longshot too. Thanks.
 
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I should add, I only need to go ~4 light years and 40-80 Earth years to get there would be acceptable. I don't need to go close to light speed.
 
This is interesting:

A Workable Photon Drive?


Here's a note about the blog writer:
In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last five years, this site has coordinated its efforts with the Tau Zero Foundation, and now serves as the Foundation's news forum. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and surely a primary target for early interstellar probes.
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