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Space Travel (a physics question)
El Cid at 6:51AM, Jan. 28, 2010
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Howdy folks. This is sort of an odd post and I didn't know where to put it so I guess by default that means I post it here.

I've been trying to lay the groundwork for a comic set in our solar system, and was trying to do some basic calculations about what likely travel times would be to the planets using advanced propulsion systems (but not “cheater” physics like warp drives, worm holes, etc.). And that was when I discovered something shocking: Astrophysics are f***ing complicated!

WARNING! NERD CONTENT
Okay, here's the dilemma: Ideally, you don't want your spacecraft to accelerate faster than 1g, because even though humans can survive greater accelerations than that in the short term, it would become unpleasant and eventually even harmful in the long term (at least this is my understanding of it). So we're not dealing with a constant velocity here; the craft is constantly accelerating at 9.8 meters per second^2, I'd guess about halfway or a little bit more to the destination, and then it has to start decelerating so that it doesn't slam into the planet or moon or asteroid it's traveling to. So… traveling like that… how long does it take to reach Mars? Or Jupiter?

That's where I'm at right now. I have no idea how to solve that problem, but I know there's lots of smart folks here on Drunkduck so anybody here wanna take a crack at it? Do you know any good web sites on space travel that might help me out? Or am I missing something completely obvious here?
last edited on July 14, 2011 12:20PM
Ironscarf at 8:16AM, Jan. 28, 2010
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El Cid
I have no idea how to solve that problem, but I know there's lots of smart folks here on Drunkduck so anybody here wanna take a crack at it? Do you know any good web sites on space travel that might help me out?

If you find out let us all know, so I can blow the dust of an old manuscript of mine too!
After trying to work this stuff out for a while it kind of fizzled out and I realised why most people write science fantasy instead of science fiction.

El Cid
Astrophysics are f***ing complicated!

Amen to that brother!
 
last edited on July 14, 2011 1:02PM
ozoneocean at 10:02AM, Jan. 28, 2010
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Isn't that pretty simple though? I mean that's just basic physics. We ALL did small scale versions of that in highschool!
If you look at it simply and not worry about calculating the gravitational pull of the planets you're flying to and things like orbiting around them to slow down or speed up, or even the effect that the loss off mass due to fuel usage has on your velocity , -then al you need to do is find out the distance to the intended destination, halve it and work out the time it take to travel at constant acceleration over that distance, from zero to your end speed… And that's all since if you're doing things simply it will take the same time for the rest of the trip because acceleration and deceleration are the same.

…but then I've forgotten my highschool physics -_-
We need some 16 year old students to enlighten us!

OK, Mars at its closest to us (theoretically) is 54.6 million km. Half of that is 27.3.
The equations of motion are (according to my old highschool physics book):

s = 1/2(u+v)t
s = ut + 1/2 at^2
s = vt -1/2 at^2
v = u + at
v^2 = u^2 +2as

Acceleration is:
a = (v - u) / t

v is end velocity
u is initial velocity
t is time
s is distance
^2= squared…

You know u = 0
You know a = 9.8 ms^2
You know s = 27,300,000,000 meters

Given that, it shouldn't be too tricky to work out… shouldn't it? :(

I came up with 82.97 days half way (rounded), which is 165.94 days for the full journey. But I am SHITE at algebra and physics, so I don't trust that figure for a second.
 
last edited on July 14, 2011 2:35PM
ramlama at 4:55PM, Jan. 28, 2010
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ozoneocean
Isn't that pretty simple though? I mean that's just basic physics. We ALL did small scale versions of that in highschool!
Would this be a good time to point out the flawless reputation of public high schools in the USA? Just sayin'
last edited on July 14, 2011 3:00PM
bongotezz at 5:40PM, Jan. 28, 2010
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i think i remember NASA saying that for a round trip to mars with a 2 month stay on mars would take 2 years with current technology.
last edited on July 14, 2011 11:32AM
r3v3rend at 5:51PM, Jan. 28, 2010
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Good page that takes into consideration the orbital movement and path of the planets.

http://www.astronomycafe.net/qadir/q2811.html

Quoted from the page:
“All in all, your trip to Mars would take about 21 months: 9 months to get there, 3 months there, and 9 months to get back. With our current rocket technology, there is no way around this. The long duration of trip has several implications.”
last edited on July 14, 2011 2:57PM
Product Placement at 6:08PM, Jan. 28, 2010
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bongotezz
i think i remember NASA saying that for a round trip to mars with a 2 month stay on mars would take 2 years with current technology.
Sounds about right. The problem with constant acceleration is that you need fuel for the entire trip. The more fuel you need, the more weight the ship is, which in turn demands even more fuel to accelerate the increased mass. It's a vicious cycle.
Modern day conventional space travel is all about fuel conservation which means that they'll stop pushing the pedal once they've reached an acceptable speed.

I remember reading about some far off idea about designing rockets that could superheat the hydrogen based fuel, turning it into plasma, in order to get “better millage” out of it. At best it could shave couple of months from the trip. That's the most advanced idea I've heard off that's actually on the drawing board. Other ideas like solar sails are still just speculations.
Those were my two cents.
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ozoneocean at 7:13PM, Jan. 28, 2010
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The question isn't about “current technology”, it was:
El Cid
the craft is constantly accelerating at 9.8 meters per second^2, I'd guess about halfway or a little bit more to the destination, and then it has to start decelerating

If he wants to be totally accurate with current technology, then he should consider things like using the gravity of the intended destination planet to slow his craft down, or at least enter into an orbit to preserve the momentum and use a shuttle lander to reach the surface. That way he can still use that initial speed, plus any gained from slingshotting away from that orbit as impetus for his next destination.

There are other equations to work out the changes in acceleration and velocity that would result.

Productplacement
he problem with constant acceleration is that you need fuel for the entire trip. The more fuel you need, the more weight the ship is, which in turn demands even more fuel to accelerate the increased mass. It's a vicious cycle.
Not necessarily. You can use an external fuel source such as the solar “wind” of supercharged particles heading away from the sun, or even energy “beamed” to the craft from an stationary source. There's solid theory behind both of those.
Besides, your cycle isn't entirely vicious- you only need enough fuel to accelerate for a set amount of time and no more. And as you consume that fuel you lose mass so you need progressively less as you go. :)
With El Cid's craft we don't know how big it can be or how much the fuel costs, what it is, or where it comes from.
 
last edited on July 14, 2011 2:35PM
El Cid at 7:37PM, Jan. 28, 2010
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Ozone seems to pretty much have it. It's basically a pretty simple calculation that I was overthinking because, duh, it's been years since I took physics and I've forgotten all my equations. Funnily enough, a friend of mine at another site is an actual astrophysicist (or I should say he got his degree in that, but went into geology)… and he was stumped too. But another poster who happened to be taking basic physics in college saw through it right away. :)

Ooh! And I did find a really cool reference site for sci-fi authors on space travel: http://www.projectrho.com/
last edited on July 14, 2011 12:20PM
El Cid at 7:41PM, Jan. 28, 2010
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ozoneocean
With El Cid's craft we don't know how big it can be or how much the fuel costs, what it is, or where it comes from.

I'm more or less ignoring those factors. My working assumption is that by this point in the future they've already worked it out to where the limiting factor is the human body and what it can withstand. Don't know how they'd actually pull that off, and it's probably best just not to be too specific about it.
last edited on July 14, 2011 12:20PM
lba at 8:08PM, Jan. 28, 2010
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Couldn't you just take the 9.2 meters a second and multiply it out to kilometers per hour/month/whatever and divide the distance by that number? It'd take like 3 minutes and a calculator.
last edited on July 14, 2011 1:30PM
El Cid at 8:23PM, Jan. 28, 2010
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It's a little more complicated than that because we're dealing with acceleration, not velocity. So it's not a uniform speed.

By the way, my calculations have me at Mars within about 49-and-a-half hours, but I doubt that's correct. Math is one of my many Achilles heels.
last edited on July 14, 2011 12:20PM
ozoneocean at 8:57PM, Jan. 28, 2010
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El Cid
By the way, my calculations have me at Mars within about 49-and-a-half hours, but I doubt that's correct. Math is one of my many Achilles heels.
Every time I calculated that's what I got too! T_T

So, I kept trying until I got something that sounded better :)
I am laughable at maths, so I'm probably WRONG.

I started with:

v^2 = u^2 +2as

V^2 = 0ms^2 + 2x(9.8ms^2 x 27300000000m)

Then I got the root of that:
V = 3238451.4818042279881162155572728ms

For time I used:

a = (v - u) / t

Which I reversed as:

t = a x (v-u)


Which was wrong.
It should have been:

t = (v-u) / a

lol!

t = (3238451.4818042279881162155572728ms - 0ms) / 9.8ms^2

t = 330454.23283716612123634852625224s

91.792842454768367010096812847868 hours???????????

or 3.8247017689486819587540338686602 days????????

Halfway…

And 7.6494035378973639175080677373194 days total one way.

lol! lol! lol!

I am shiz at maths.
 
last edited on July 14, 2011 2:35PM
LOOKIS at 8:59PM, Jan. 28, 2010
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Taking three months to get to Mars is too low tech. That makes it like back in the age of sailing ships when it took three months to reach America from Europe.

Are they just beginning to colonize Mars in your comic? Because if it's far enough in the future then you can just assume the trip only takes a few hours. There are daily flights to Mars from all the major cities of Earth. They use special cushioning chambers for the passengers and high-g fusion engines. Occasionally someone develops g-sickness, but it's very rare.
………………. LEAVE THIS SPACE BLANK …………………
last edited on July 14, 2011 1:39PM
El Cid at 9:35PM, Jan. 28, 2010
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Well, the premise of the comic (and I'm not even 100 percent sure about this) is that a group of misfits who can't stand each other are forced to share a spacecraft on a long voyage to some remote place in the solar system (as you can see, I still have a lot of blanks to fill in). So a grueling low-tech voyage is what I was aiming for.

Ugh. So right now it's looking like probably a week-long trip. I'll have to revisit my calculations tomorrow when my head's minus a few cobwebs.
last edited on July 14, 2011 12:20PM
ozoneocean at 9:54PM, Jan. 28, 2010
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El Cid
Ugh. So right now it's looking like probably a week-long trip. I'll have to revisit my calculations tomorrow when my head's minus a few cobwebs.
Yeah, and it's pretty likely that I'm still wrong there, but at least you can see my workings so that may help :)
 
last edited on July 14, 2011 2:35PM
Product Placement at 10:22PM, Jan. 28, 2010
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ozoneocean
Not necessarily. You can use an external fuel source such as the solar “wind” of supercharged particles heading away from the sun, or even energy “beamed” to the craft from an stationary source. There's solid theory behind both of those.
I
Other ideas like solar sails are still just speculations.
By that I meant, while the idea is solid, it's still just a theory. We still have no idea how to make a craft like that. Questions like how wast these sails need to be or what kind of materials are light and sturdy enough to work remain unanswered. Then you run into problems like how to decelerate once you're about to reach your destination. You're going to need a sun on the opposite side now for that. Works fine if you're planing to visit another solar system though but it's going to be a pain to use a craft like that to return to Earth from the outer ring planets. And we have no idea how to make those giant lasers either.
ozoneocean
Besides, your cycle isn't entirely vicious- you only need enough fuel to accelerate for a set amount of time and no more. And as you consume that fuel you lose mass so you need progressively less as you go. :)
Still is a big issue at the start. Breaking Earth's gravitational pull is a bitch like that. Unless we discover some sci-fi like technology that can deflect gravitation or get that space elevator (that's unfortunately at the same level of development as the solar sail ship) we're still gonna need to burn most of the fuel just to get a fraction of it into orbit. A lunar base will minimize the initial fuel burn, or we could simply refuel the ship and launch it from orbit but those ideas require us to build a lunar base or send several shiploads of fuel up into orbit, respectively.

Whatever idea the tech boys end up coming up with and using, I'll be waving my flag of support. I wanna go cruising through space like there's no tomorrow.
Those were my two cents.
If you have any other questions, please deposit a quarter.
This space for rent.
last edited on July 14, 2011 2:52PM
ozoneocean at 11:28PM, Jan. 28, 2010
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Product Placement
or we could simply refuel the ship and launch it from orbit but those ideas require us to build a lunar base or send several shiploads of fuel up into orbit, respectively
Of course, which was my assumption. But once in space, you don't need the same chemical fuel you used to get there. All you need is constant stable acceleration, and there are a number of ways to achieve that.

What about a nuclear reactor that heats material (gained from the asteroid belt or moon) into gaseous form that you can expel from behind your craft? There's ice of various sorts out there and you can even do that with metals…
 
last edited on July 14, 2011 2:35PM
DAJB at 4:21AM, Jan. 29, 2010
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El Cid
I've been trying to lay the groundwork for a comic set in our solar system, and was trying to do some basic calculations about what likely travel times would be to the planets using advanced propulsion systems (but not “cheater” physics like warp drives, worm holes, etc.)
See … I'd say that's where you're going wrong. “Cheater physics” is by far the more sensible option!

I can almost guarantee that no matter how long you research this and no matter how many experts you consult, as soon as your explanation appears in the comic, some bright spark is going to quote an entirely different theory at you and have all sorts of technical arguments about why your number is wrong. The worldwide wonderweb is full to bursting with people who know everything about everything and are all-too-keen to second-guess everything you do.

You're far safer to invent your own form of fictional propulsion device and then as long as the whole comic stays true to the rules you invent for it, journeys between planets can take days, weeks, months or years (Hell, they can even be instant!) and no one can argue against it. (Except maybe Ozone, obviously!)

Plus, of course, it leaves you free to use whatever time periods best suit the dramatic beats of the story. Cheater physics is vastly under-rated, in my opinion!
last edited on July 14, 2011 12:04PM
Product Placement at 5:03AM, Jan. 29, 2010
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ozoneocean
What about a nuclear reactor that heats material (gained from the asteroid belt or moon) into gaseous form that you can expel from behind your craft? There's ice of various sorts out there and you can even do that with metals…
I seriously doubt we can achieve a 1G equivalent thrust that way. But then again, what do I know?
Those were my two cents.
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This space for rent.
last edited on July 14, 2011 2:52PM
ozoneocean at 5:34AM, Jan. 29, 2010
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Product Placement
I seriously doubt we can achieve a 1G equivalent thrust that way. But then again, what do I know?
Chernobyl? ^^

———————-

–edit–
A quick net search on the topic of using nuclear reactors for space propulsion yields surprising results. It turns out it's an entirely viable method- although not with the sort of unrefined trash I mentioned. One of the possible propellants is Hydrogen, super-heating it as you suggested earlier. And also better mixtures of things like sodium and Xenon using ion engines.

Hydrogen is a very simple material which you could possibly refine from material in space… :)


—————————-

Eh, whatever.
There's a million billion ways to do something when it's imaginary. El Cid's idea for a realistic time scale based on real distance and real acceleration that would be comfortable and convenient for the human body was a very good one. That sort of premise is a great way to begin a Sci-Fi story.A nice realistic, sensible core idea without going into tedious detail or easily outmoded technological concepts.
 
last edited on July 14, 2011 2:35PM
therealtj at 6:28PM, Jan. 29, 2010
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My math may be off, but I get 1.2 days for the total trip. I used the formula:

Position(final)= VelocityInitial x Time + 1/2 x Acceleration x Time^2

First I found half the trip where you are accelerating:

1/2 x 27,300,000,000 = 1/2 x 9.8(gravity) x T^2

The Vi x T term is removed since you start at rest. Next, I multiplied both sides by two to remove the 1/2 (because I could):

27,300,000,000 = 9.8 x T^2

Divide both sides by 9.8:

2785714286 = T^2

Take the square root of both sides:

T = 52779.86 seconds

Logically, it would take just as long to decelerate the rest of the way so multiplying the number by two:

T = 105559.73 seconds

Finally, there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day so:

105559.73 * 1/60 * 1/60 * 1/24 = 1.2 days.


Edit: Found your error, Ozone.

Someone
V^2 = 0ms^2 + 2x(9.8ms^2 x 27300000000m)
You found the final velocity for the ship traveling the entire distance. This is the velocity they would travel at right before crashing into Mars. :P

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last edited on July 14, 2011 4:28PM
ozoneocean at 9:59PM, Jan. 29, 2010
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therealtj, you made a big mistake there, that distance is already HALF the distance to Mars. You're halving it again.
 
last edited on July 14, 2011 2:35PM
patrickdevine at 11:29PM, Jan. 29, 2010
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ozoneocean
Product Placement
or we could simply refuel the ship and launch it from orbit but those ideas require us to build a lunar base or send several shiploads of fuel up into orbit, respectively
Of course, which was my assumption. But once in space, you don't need the same chemical fuel you used to get there. All you need is constant stable acceleration, and there are a number of ways to achieve that.

What about a nuclear reactor that heats material (gained from the asteroid belt or moon) into gaseous form that you can expel from behind your craft? There's ice of various sorts out there and you can even do that with metals…
I'll admit that I'd use a cheater explanation for the propulsion dilemma– ion thrusters powered by solar cells like what unmanned spacecraft use. Most proposed designs for manned spaceships don't use ion thrusters because when compared to something like a rocket they're actually pretty slow. I don't know how “hard” sci-fi you're going for but if you'd be willing to say that ion thrusters can provide sufficient acceleration it would probably seem believable.
last edited on July 14, 2011 2:41PM
El Cid at 7:21AM, Jan. 30, 2010
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patrickdevine
I'll admit that I'd use a cheater explanation for the propulsion dilemma– ion thrusters powered by solar cells like what unmanned spacecraft use. Most proposed designs for manned spaceships don't use ion thrusters because when compared to something like a rocket they're actually pretty slow. I don't know how “hard” sci-fi you're going for but if you'd be willing to say that ion thrusters can provide sufficient acceleration it would probably seem believable.

Nah, actually explaining how stuff works is a rookie mistake. It opens you up to all kinds of scrutiny, not to mention it's just bad writing. How many times do characters in comics stand around discussing how an internal combustion engine works? Never, and thank God ‘cuz it would be booooring!

At any rate, the original premise is dead and I’m opting for a less-structured backstory. Knowing how to calculate this stuff should prove useful just to get a feel for what kind of travel times the characters are dealing with, but I'll try to keep all the science stuff as far in the background as possible. I'm not a scientist, and neither are most of my readers, so I'm going to focus on what I know.
last edited on July 14, 2011 12:20PM
therealtj at 7:34AM, Jan. 30, 2010
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ozoneocean
therealtj, you made a big mistake there, that distance is already HALF the distance to Mars. You're halving it again.

Whoops >_>

I guess I missed that part of your post.

“The only moral it is possible to draw from this story is that one should never throw the letter Q into a privet bush, but unfortunately there are times when it is unavoidable.”
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last edited on July 14, 2011 4:28PM
El Cid at 7:41AM, Jan. 30, 2010
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Oh and by the way, just to pick at this old scab a little bit more, I'm still getting about a two-day travel time, and so did that German physics student friend of mine at the other site. Depending on what distance I plug in I get either a 42-hour or 49-hour flight time. The discrepancy seems to be that I'm ending up with a higher final velocity than 330,000 m/s. I keep getting 731,865 m/s.

2x9.81x2.73E10 = 5.356E11
SQRT(5.356E11) = 731864.74

So I guess the right answer comes down to which is the correct vF. Of course this really isn't important now that I've gone a different direction with the story but I'm sure it's still interesting just for its own sake. Or not.
last edited on July 14, 2011 12:20PM
humorman at 9:37AM, Jan. 31, 2010
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ozoneocean
OK, Mars at its closest to us (theoretically) is 54.6 million km. Half of that is 27.3.
The equations of motion are (according to my old highschool physics book):

s = 1/2(u+v)t
s = ut + 1/2 at^2
s = vt -1/2 at^2
v = u + at
v^2 = u^2 +2as

Acceleration is:
a = (v - u) / t

v is end velocity
u is initial velocity
t is time
s is distance
^2= squared…

You know u = 0
You know a = 9.8 ms^2
You know s = 27,300,000,000 meters

Given that, it shouldn't be too tricky to work out… shouldn't it? :(

I came up with 82.97 days half way (rounded), which is 165.94 days for the full journey. But I am SHITE at algebra and physics, so I don't trust that figure for a second.

If you did this, your rocket would never leave the atmosphere, let alone the ground. Since you're trying to break from Earth's gravity, your acceleration would have to be greater than 9.8 m/s^2 (being equal to that results in a net force of 0). Also, you wouldn't be spending half your trip accelerating through space, since the majority of fuel used for thrust is used to just break through the atmosphere. In reality, all you need to do is find a way to make it into the exosphere and out of Earth's gravitational pull. Remember, space has virtually no friction, so your ship doesn't need to accelerate anymore. All you need is to pick a speed at which your craft will be moving until you reach your destination.

Take a look at this graph:


Notice after the Saturn V's final stage the acceleration drops to zero. Also, keep in mind that your rocket should be optimizing the fuel it's using to lift itself. The sudden dips and rises in the graph are the points at which the rocket detaches one of it's stages making it weigh less and allowing the remainder of fuel to launch it faster than it would otherwise.

Essentially, the time of your trip varies greatly depending on two main factors:
1. Your rocket
2. Your fuel supply

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last edited on July 14, 2011 12:51PM
ozoneocean at 1:00PM, Jan. 31, 2010
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humorman
If you did this, your rocket would never leave the atmosphere, let alone the ground. Since you're trying to break from Earth's gravity, your acceleration would have to be greater than 9.8 m/s^2 (being equal to that results in a net force of 0). Also, you wouldn't be spending half your trip accelerating through space, since the majority of fuel used for thrust is used to just break through the atmosphere. In reality, all you need to do is find a way to make it into the exosphere and out of Earth's gravitational pull. Remember, space has virtually no friction, so your ship doesn't need to accelerate anymore. All you need is to pick a speed at which your craft will be moving until you reach your destination.

Take a look at this graph:


Notice after the Saturn V's final stage the acceleration drops to zero. Also, keep in mind that your rocket should be optimizing the fuel it's using to lift itself. The sudden dips and rises in the graph are the points at which the rocket detaches one of it's stages making it weigh less and allowing the remainder of fuel to launch it faster than it would otherwise.

Essentially, the time of your trip varies greatly depending on two main factors:
1. Your rocket
2. Your fuel supply
That's broadly true, but it wasn't the question. We can basically assume that the craft in Wl Cid's question has already escaped earth's gravity well in some way. This is mostly a simple A-B situation. :)
The reason for the 9.8ms^2 acceleration isn't speed, it's for the effect on the crew. It's a roughly human scale measure to work around for a fictitious story from which you can extract a realistic time based on the maths.
 
last edited on July 14, 2011 2:35PM

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