Orbital Mechanics buffs Help!

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I need some help on a little exercise and I just know that one of you geeks can have the answer in less time than it takes to write this blog.

A habitable planet has been located that is 800 light years from earth. The Colonisaton ship can accelerate at 3 earth gravities. The exhaust gas velocity is about 97% of the speed of light. Facilities within the ship will hold felt gravity at 1.1 Gs. How long will it take to get there?

40 years ago, I could have done this problem with a pencil. That capability is long gone off into the ether. I suspect that there is a computer program around that can do it in about .1 seconds.

Can someone kindly give me the answer? I suspect about 1000 years.

Much peace

Khadijah

Comments

It depends..

Do you mean elapsed time on Earth, or as perceived on the space ship? Cause it's different as the ship will approach the speed of light and relativistic effects will come into play. Also remember, it needs to decelerate half the time - if the ships under constant acceleration.

Sorry, I just knew it would not be simple.

I think I mean relative ship time. One of the parameters is that the engine/fuel supply will last 1500 years. I am not a math person at all. I mean I did just barely pass Calc 1, but that course really proved to me that I was not Mechanical Engeering material.

Just guessing, I suspect that it would take 1000 to 1200 years. One of the problems is the exhaust gas velocity is only about 97% of the speed of light. So, I would expect that the faster the ship goes, the less acceleration it will get. The more I think about it, I wonder if it will get there at all.

Space is a really hostile place, and as I think of the problem, perhaps they could have built several smaller ships in the hope that at least one would get through.

Much peace

K

No answers for you, sorry

laika's picture

But it's interesting to me that I ran into this EXACT same problem in my QUINTESSENCE OF DUST, one of my very first stories here. I knew there was math that could be done to figure out how fast they'd need to be going and how far, how many earth years converted to how many ship-years given the acceleration & the relativistic time distorition; but short of hiring someone I couldn't have begun to do it.

Luckily for me, all this took place at the BEGINNING of my story, so I chose to keep it all vague, hoping none of these smart people around here would take me to task; and so far I've lucked out. Hope you find someone...
~~hugs, Veronica
.

EXERPTS, THE TEXT OF THAT PART OF MY STORY:

...a trip to quite literally the middle of nowhere---a portion of the way to Proxima Centauri---undertaken to test how well the revolutionary new propulsion system worked before a real crew was sent forth on a real trip to the stars.

Due to budget cuts it had been necessary to scale the original plans to send a four man crew way back, and there had been a minimum of science conducted. They had compiled data on particle densities in interstellar space. There was an experiment involving pine saplings, and four others dealing with quantum physics that were boxed off and that they'd been warned not to mess with. The mission's real scientific dividend would be in proving once and for all that the "theory" of relativity was nothing short of a law; as these two astronauts only eighteen months older than when they had left were welcomed home by nieces and nephews with graying hair.

So it was a lot these two spacefarers had been asked to sacrifice for such an unglamorous mission. They were basically forfeiting their whole lives, to start out all over as a pair of historical oddities. They had expected that they would arrive home to find technologies they'd never dreamed of in use, to see everyone dressed very strangely, using unfamiliar slang and listening to ugly, incomprehensible music. In short, to experience in their mid-twenties and in one fell swoop the severe culture shock that people usually go through when they're a whole lot older.

The consultation that had been arranged with a man who had woken up in 2017 after a twenty-eight year coma was especially eye opening. This was not just some dickwad shrink or behavioral theorist- the guy had been there! And after hearing his story they were prepared to face some real emotional rough spots when they got home. But even with all the environmental and political troubles mankind was facing when they left in 2022, neither astronaut was pessimistic enough to doubt that there would be anyone around to greet them on their return...

It felt weird to be weightless again. A constant rate of acceleration and then deceleration on the return leg had provided the equivalent of gravity. As they orbited the Earth they were now close enough to pick up ordinary broadcast radio---for which no fancy directional antenna was needed---but they couldn't hear a thing...

.
"The federal government will only recognize 2 genders,
as assigned at birth-" (The man in his own words:)

https://www.youtube.com/watch?v=C1lugbpMKDU

Now my curiosity is up.

I'll have to go find your story and read it. I am much more addicted to SF than anything.

Thanks

K

Time dilation and history

Of course, there's always the Law of Unintended Consequences...

I remember an A.E. van Vogt story (sorry, no title) in which three men set out on a pioneering trip to Proxima Centauri (IIRC)... and found a welcoming committee waiting for them when they got there!

What everyone had forgotten was that science doesn't stand still over the many years (Earth perceived time) that their flight took, and that in that time someone invented/discovered FTL travel, colony ships were sent out and Proxima became a bustling populated world before the original three explorers arrived!

The trip back took a day or so...

Penny

Probably...

...the best treatment of this sort of thing, imo, is Joe Haldeman's The Forever War, which features this sort of temporal displacement and the attempts of the characters to deal with it on emotional, social, and relationship levels. It also serves as a sort of reflection by Haldeman on his service in Vietnam (which sort of thing, actually, is an excellent real-world example and resource of this sort of event and its consequences). It's an excellent read, and is rightly considered one of the classics of the genre. It won the Nebula and the Hugo awards for its year. A film version is in the works by Ridley Scott, with the original David Peoples-authored script being revised by Matthew Michael Carnahan.

-Liz

Successor to the LToC

-Liz

Successor to the LToC
Formerly known as "momonoimoto"

Story

Sounds like "Far Centaurus"

The problem is underspecified

The velocity of the exhaust gas is not enough information; the real number that matters is the thrust, which you can’t compute from the exhaust velocity alone. You need to also know the mass/second being expelled (and since it’s relativistic, you’d need to know rest vs. effective mass). You’d also need to know the mass of the ship to compute the ship’s acceleration.

Is the gravity on the ship 1.1G due to the acceleration? That would be enough to compute the answer. If there’s some kind of antigravity altering the perceived acceleration, then we’re back to needing the thrust and the mass of the ship, or alternatively, the true acceleration (minus anti-gravity).

Once you have that, you compute the time required to travel 400 light-years, then double it since you have to decelerate for the second half.

Also...

...you would need to know the initial bunkerage mass of reaction material (which becomes a reduction calculation over time, decreasingly affecting acceleration), and also cargo/crew mass, as that is usually (and quite correctly) a separate datum from the actual mass of the ship, as well as atmosphere, water, and food, and you need to as well consider the means of heating the ship—if you are relying on the drive engines to provide the requisite energy, it decreases the efficiency of those drives; if you rely on other means (battery-bank/radioisotope-reactor/something else), then you either need to incorporate that into your ship design, or account for its weight separately (yet another datum). As a note, heating is >absolutely necessary<, as vacuum is not only, well, a void (negligible air and water; will remove same from a habitat unless perfectly sealed; perfect seals are impossible, so attention is instead paid to making the seals as good as possible so as to minimize lossage), it is also only a few degrees above absolute zero, and any object located in a void >rapidly< cools to nearly the same temperature—not a survivable condition. Even crew carried as cargo in some form of suspended animation, unless it involves some sort of time manipulation (in which case, the transit times are moot), still need to be kept at a >much< higher temperature, and at a fairly high environmental pressure, else the frozen tissues suffer degradation from other than the current limiting (and deal-breaking) issue of cell-rupturing ice crystals.

I can try asking among my friends, one of whom maintains the local university's physics department's computers and network. If I get any information, though, it won't be for a few days at best. Do you have time for me to ask? I've only worked with intra-system inter-planetary transits, and I >really< don't remember the math for that, even, so I'm not much help in myself to the question of inter-stellar mechanics.

That said, it seems to me that you might also need to know the vectors of both systems, both relative to a "fixed" referent, such as the galaxy, and relative to each other. At that distance, and given the large interval on which the journey would be made (again, referent to the rest of the galaxy; okay, not so big on that scale, either, but still) the possibility of missing the target due to considering it static when, in fast, it's moving fairly rapidly and potentially in very different directions would be, if you would pardon the phrase, cosmically embarrassing.

-Liz

Successor to the LToC

-Liz

Successor to the LToC
Formerly known as "momonoimoto"

online calculator

http://www.cthreepo.com/lab/math1.shtml

at 1.1G acceleration it's about 12 years ship time, 802 years earth time.

at 3G it's 5 years ship time, 801 years earth time.

that's constant acceleration over whole travel time, half the time acceleration, half the time decelleration.

to endure 3G for 5 years is quite an excercise.

Handy!

That is a very useful calculator. :-)

Space Math

Breanna Ramsey's picture

This link from Mutabilis is a good resource for the question you're asking. Since you state that there is some kind of compensator in use to keep internal gravity at a manageable level that isn't an issue, but what is an issue are consumables; fuel, food, water and atmosphere. The majority of the mass of a vessel for this type of journey would be fuel because the engine is operating constantly; the ship accelerates at 3g for half the journey and then decelerates for the other half. Food, water and life support for a trip of six years duration (the time experienced by passengers and crew) could be a serious problem, but if the vessel has a means of suspended animation this would be eliminated. You probably wouldn't want to have everyone asleep for the entire journey, however, in case something went wrong. There would probably be a fairly large crew working in rotation, with say two-thirds asleep while one third stands watch.

Scott

I cried for her.
I cried for me.
I cried for a world that wouldn’t let her be.
-- from Luna by Julie Anne Peters

http://genomorph.tglibrary.com/

Bree

The difference between fiction and reality? Fiction has to make sense.
-- Tom Clancy

http://genomorph.tglibrary.com/ (Currently broken)
http://bree-ramsey314.livejournal.com/
Twitter: @genomorph

Acceleration

That will change as the ship speeds up. The Lorenz transformations are the key, where rest mass, length and time change by a ratio called "Tau". Can't do Greek letters here, but Tau is defined as the square root of [1-(v squared/C squared)]

In this case, C is lightspeed, v the velocity of the ship. As V approaches C, Tau approaches zero. Mass of moving ship is rest mass divided by Tau, length is rest length in direction of travel times Tau, and I will leave you to work out the time dilation effect.

What that means is that if your ship starts going really fast, it won't be able to keep accelerating due to the increase in its own mass. F=ma, and all that.

Geek Letters

Puddintane's picture

Most computers and displays can handle Greek letters these days by using "escaped" "numeric entities."

tau = τ (Ampersand#964;) where Ampersand is replaced by &

Tau = Τ (Ampersand#932;) where Ampersand is replaced by &

Cheers,

Puddin'

A tender heart is an asset to an editor: it helps us be ruthless in a tactful way.
--- The Chicago Manual of Style

-

Cheers,

Puddin'

A tender heart is an asset to an editor: it helps us be ruthless in a tactful way.
--- The Chicago Manual of Style

D'oh!

I knew I was forgetting something important related to this! Yes, the principle criticism to the concept of high-C-fractional travel. Thank you!

re: the concept of rotating crew (per Scott's comment, especially): You would have about a third of your crew on actual duty at any given time >anyway< without "hibernation", just due to standard shift rotation. *being just >slightly< oblivious to what you actually intended* ~__^ Seriously, though, if you had suspended animation technology available, you likely wouldn't >need< to have a full third of your crew awake at any given time, as the majority of the crew, again, given that technology, can be composed of specialists not cross-trained in starship operation. even given the assumption that you >really< want to spend the tens of millions of dollars required to train them in the extra skill-set, there just isn't the need, as you only need a couple of people each waking duty rotation to maintain and run the ship, unless something goes wrong, in which case, you either have enough time to awaken additional help, or you are likely dead anyway and the point is somewhat moot. Additionally, it's better from a small-group psychological and sociological standpoint to have relatively few people on duty at one time, and the rest in SA and thus reducing the overall group levels of stress due to being together in a constrained space for an extended time. This particular consideration is actually one of the big ones in planning for mars missions, and is one of the big obstacles. The solution has been to select for mission crew those who show an extremely rare ability to handle just such conditions. Finding such individuals is difficult, as the quality is hard to effectively test for. It might be supposed, though, that the selection for flight operations crew for such a long, dangerous mission would very much focus on such individuals, and, in the interest of cost-effectiveness, >only< train for primary flight operations those few who need to occupy that role, and leave the rest of the crew positions to specialists who lack that quality, but who have obtained credentials and capabilities in other, less-demanding (in this sense, at least) areas.

tl;dr: You don't need to spend the money and the effort to make your whole crew capable of running flight operations, and therefore do not need to have even a full third awake at any given time. Until you reach your destination, they are best handled as very fragile cargo, leaving the professional space jockeys to handle the actual journey unhindered.

re: inertial compensators and Heisenberg compensators, and such: No! No blocks of solid platinum! No, no no! >.< Silly-"Science!" workarounds are best left out of a story unless you >NEED< to have them. They detract from the story, no matter the situation, and are only justifiable if there is no way to >avoid< inclusion and still have the story make sense. Even then, they are black boxes that are best treated as little as possible. One of the problems that Trek-science has developed in its march away from real-world physics is the fact that writers for the episodes lost sight of that fact, requiring ever-greater convolutions to incorporate the various bits into new stories, and in turn causing such a growth in complexity that the whole mess has massive >technological< inconsistencies within itself. When a new story is rendered unbelievable due to the author forgetting some detain that was really only mentioned in one story a couple of decades ago, but that is the foundation for several other technologies that were "invented" based on or even just taking advantage of it, and the new author, assuming these contravenes the former, it makes the whole situation seem more artificial and less believable than it should.

tl;dr: "Extra-tech" should be kept to a minimum, as it raises the threshold for suspension of disbelief, making the story harder to "get into".

In that vein, Khadijah, remember that most science fiction authors tend to >massively< gloss over the numbers for celestial mechanics and travel between points A and B. The reason for this is that, as has been shown, those numbers are >complicated<, and most science fiction authors, even those who have appropriate physics or mathematics degrees, don't want to write a goodly-sized novelette just to justify their numbers before getting to the actual story. Those that >do< dwell on the numbers tend, no matter whether they are considered a good author otherwise, to be called on that exact point. Witness David Weber: he's reasonably well-thought of by space opera and military SF writers and fans (with exceptions; taste is a factor in that, as are issues with other aspects of his work), but he is >routinely criticized for the really dumb errors in his math and for some technical aspects of his extrapolated physics and technology that he >over-includes<, and thus sets himself up for critique of by people who actually work in related fields, whether they themselves are right or wrong. In short, it's better if you just figure something that sounds reasonable, provides just enough of the framework that you need to hang your story from, check about that specific something if you feel particularly uncertain or if the detail would make for more than just a mcguffin, and then just write the part of the story that's actually interesting to you.

-Liz

Successor to the LToC

-Liz

Successor to the LToC
Formerly known as "momonoimoto"

indeed

i second that motion.

for example:

if you can reduce 3G acceleration down to 1.1G felt by the crew, why stop there? compensate a larger acceleration and you can be there at the end of the week, with all the simplifications that makes for crew comfort.

Wow Space calculations are very complicated!

Perhaps for the purpose of my story I should just be suitably vague as far as the math goes. This is a tale that I am feeling on an entirely emotional level. In truth, in the unlikely event that humanity survives, and we do someday have real space travel, it will have to be of the sort that allows explorers to travel thousands of times the speed of light. That means that all the relativistic laws will have to be worked around, were that even posible. It seems to me that travel in that medium could make the North Atlantic in a single mast sail boat seem like a nursery.

It is now that I realise that I am feeling quite torn up, by events in the Arab world; hoping for the best were some sort of representative government takes hold, but fearing that radicals will spread extreme thought. I do not feel very secure. Perhaps that is where this story is originating?

Thank you all for your input.

Khadijah

So like,

the ship's accelerating at 3G and the inside is 1.1G? Doesn't that mean the outside is going to get there way before the inside? What about all those poor people inside? I'm so confused...maybe I shouldn't have worn the blond wig today-the gray is much smarter about numbers and stuff :-)

Well good luck anyway!

hugs
Carla Ann

Acceleration discrepancy

Nah, that's no problem. You just have to set the inertial compensator to take up the difference!

Penny

Duke-Brannick Box

They can accelerate as much as the want as long as they have a Gravity Wave Generator: (Also referred to as a Gee Wee or Duke-Brannick Box) A large, power consumptive device that is capable of generating artificial gravity on a space craft, or canceling out gravity if already present. Don't remember who came up with the idea in the care-givers universe but you can find out and ask to borrow it.

No particular need, since it's been done many times before...

Puddintane's picture

The Dillon-Wagoner Graviton Polarity Generator, AKA Spindizzy, was "invented" by James Blish for his Cities in Flight series of SF novels.

Philip Frances Nowlan "invented" an "anti-gravity" belt in 1928, and the Skylark series by EE "Doc" Smith had inertialess drives and "fifth rays" which performed all manner of technological miracles.

Frank Herbert called his version a "Gravity Web," but one could as easily call it a Floozis.

Cheers,

Puddin'

A tender heart is an asset to an editor: it helps us be ruthless in a tactful way.
--- The Chicago Manual of Style

-

Cheers,

Puddin'

A tender heart is an asset to an editor: it helps us be ruthless in a tactful way.
--- The Chicago Manual of Style

And there are more...

More recently David Weber's got his Warshaski [sp?] sails and alpha-? bands... And wedges and such. QUite "hard" science fiction - and interesting social commentary at the same time.

What are your story parameters?

Realistically, the needs of the story should probably dictate the method and time it would take for a colony ship to get to a distant star.

800 light years is a very loooong way to go for a slower than light colony ship. I worked it out once for Sappho. NASA says that there are 385 known star objects, 16 of them Earth-like "friendly" G class stars, within 10 parsecs, or 32.6 light years, of Earth. Extrapolating from that, the number of stars within 100 light years is around 11K, 460 being G class. A sphere with a radius of 800 light years would have 5.7 million stars, and 236K G class stars.

For Sappho, the colony ships were slower than light, but used hibernation pods to retard aging. With hibernation pods, you can take pretty much as long as you like and the heck with the food supplies, and even without hibernation pods, there is something called recycling, which should work very well on a large scale. :) It doesn't take that much longer to travel 50 light years, real time, accelerating at .1 G than at 3 G, 66.7 years vs. 50.7 years. Even at a tiny .01 G (a modified ion drive, perhaps?), the trip would take only 148 years.

"Happiness is when what you think, what you say, and what you do are in harmony."

Mahatma Gandhi

"Happiness is when what you think, what you say, and what you do are in harmony."

Mahatma Gandhi

the number of stars close to our sun

the number of stars close to our sun is offset by the presence of the "local cluster". from the outside that is an "open star cluster" like the Pleiades. your interpolated numbers are therefore a bit high.
within 100 light years are "only" 1858 known stars. nevertheless, that should still be a high enough number to choose a suitable target.

my guess is that Khadijah choose a far larger distance as a plot device. 800 years travel time, 1600 years round trip, would mean a trip without return, at least in such a time that mutual assistance can be given.

Rechecked my figures

I did make a small mistake. Instead of 16 class G stars with 10 parsecs, I had a reading error. It should be 19 class G stars, which only increases the supply at greater distances. Other than that, the figures hold. The formula for the volume of a sphere is V=4/3*pi*r^3. NASA says that there are 381 stars (that they know of) within 32.6 light years (10 parsecs), and 19 of them are class G. (The vast majority of stars in this range are the very dim, and hard to detect red dwarves.)

http://www.solstation.com/stars/pc10.htm

The difference between the volume of 32.6 light years radius and 100 light years radius is a factor of about 29. Plug in the figures for a 100 ly and 800 ly radius. Of course, with a small database of 19 class G stars, the actual figures are going to be off a bit, a little more or a little less, but probably not that much.

4/3 * pi * 32.6^3 = about 145K cubic light years. 381 stars total, 19 G class stars

4/3 * pi * 100^3 = about 4,166.75K cubic light years. About 29x the volume. About 11K stars, 551 class G stars.

4/3 * pi * 800^3 = about 2,144,668.58K cubic light years. About 515 x the volume at 100 ly. 5,665K stars, 283K class G stars.

Note: Of course, the figure at 800 light years radius, is likely somewhat too high because the average depth of the Milky Way is around 1000 light years and we're in the rough middle of a spiral -- but maybe not. Wikipedia says that the real drop off in depth occurs at around 40K ly from the galactic center and Earth is around 26.4K ly from the center. Maybe the extrapolation at 100 light year radius is somewhat too high also, depending on Earth's exact location in the spiral, but the difference between your figure of 1858 known stars in a 100 ly radius and the extrapolated one of 11k is a bit too much to ignore. Consider: 381 stars within 32.6 light years, yet only 5 times the number of stars within a volume 29x greater? Hmm, looks mighty fishy to me. The discrepancy may be due to red dwarves being so numerous, yet so hard to detect.

"Happiness is when what you think, what you say, and what you do are in harmony."

Mahatma Gandhi

"Happiness is when what you think, what you say, and what you do are in harmony."

Mahatma Gandhi