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Posted By: Qray Dec 17, 2004 - 10:14 pm

I need some help (HEY! I HEARD THAT! ;-])

A friend and I were discussing the following scenerio at work...

There is this spaceship traveling through space. It maintains a constantly increasing acceleration. Going faster and faster in relation to the universe.

Now the question is, will gravity continue to increase onboard the ship or will it increase to a certain point and hold there?

I maintain that since the acceleration is not constant, but ever increasing (even though it's increasing at a constant rate,) gravity will also increase.

My friend maintains that since it is the ship is increasing acceleration at a constant rate, gravity will eventually increase to a certain point and then stay there. Not increasing anymore.

Neither of us care who is right, but we DO want to know which it is (knowledge is key and all that rot)

Anybody know of a good formula for finding the solution?

TIA.

(Q)

Posted By: Talon Sinnah Dec 18, 2004 - 12:35 am

Nope none here. Call me when you do because I want to see how fast my fist is going when I hit the poor idiot who sat down and had nothing better to do then think of some fool formula for gravity and spaceships.

Posted By: redshift Dec 18, 2004 - 12:35 am

First thing: I can’t give you any formulas, because I suck at math. I can explain it in nonmathematical terms, though. I’m going to repeat some things you probably already know, but I’m just doing it to try and be complete.

The trick is that the issue isn’t speed (meaning, the ultimate speed you want to travel at), it’s the rate of acceleration (how quickly you get to that ultimate speed).

Let’s imagine we have a starship that can travel at 90% the speed of light. According to physics as we understand it (without any kind of “gravity generators” or whatnot), the ship wouldn’t be laid out like the Enterprise (or even the space shuttle!), where forward is “ahead” of you, if your’s facing the front of the ship. Instead, forward would be “up”, above your head, and the engines would be directly below your feet. Imagine the Empire State Building, with rocket engines on the bottom. Even once it left Earth’s gravitational pull, if the ship was accelerating at the right rate, the building’s layout would still make sense - the floor would still feel like the floor.

This is why acceleration is important. If you accelerate at the right rate, the inertia affecting the crew will feel like normal Earth gravity: 1g. If you accelerate at a slower rate, objects and people will feel “lighter” as if they were on the Moon (less than 1g). Accelerate faster, and everything will seem to weigh more (say, 2g, for example). You can see this for yourself in a car. From a stop, floor it until you hit 60 mph. You’ll be pressed against the seat. Stop, and be much lighter on the gas pedal this time. You’ll still get to 60 mph, but you won’t feel it. It will take longer, though.

The exact same principle applies in space. In fact, it’s one of the biggest problems we’ll have to deal with if we ever want manned interplanetary travel. Getting to 90% lightspeed is possible (we’ll assume), but you have to accelerate at a rate slow enough not to squash the crew. And since 90% lightspeed is so incredibly fast, it takes a very, very long time to get to that speed - and once you get close to where you’re going, you have to slow down just as carefully. An abrupt stop will kill everyone just as surely as a fast start will. To get to a nearby star, we’re talking many months of gradual acceleration, then finally some travel time at the ship’s top speed, and then many more months of gradual deceleration. A lot of time is “wasted” that way.

With an unmanned probe, the situation isn’t as bad. The thing can be designed to withstand forces that are many times stronger than normal Earth gravity. There’s nothing you can do to reinforce people’s internal organs, though.

Ironically, the way you pose your question, you’re both right.

“I maintain that since the acceleration is not constant, but ever increasing (even though it's increasing at a constant rate,) gravity will also increase.”

If you eliminate the part you’ve got in parentheses, you’re right. If you accelerate at a faster and faster rate, gravity will increase. The rate of acceleration needs to remain constant, if you want the ship’s apparent gravity to remain constant. The ship’s increasing total speed doesn’t matter - it’s all about how quickly you get to that speed. Think about the car example again. Zooming to 60 pushes you against the seat, but once you’re at 60, the pressure is gone and you feel almost as if you’re sitting still. You can also get to 60 more slowly, and hardly notice the acceleration at all.

“My friend maintains that since it is the ship is increasing acceleration at a constant rate, gravity will eventually increase to a certain point and then stay there. Not increasing anymore.”

Bingo. From a dead stop, in zero-gravity space, there will be a gradual increase in apparent gravity until the ship reaches it’s ideal acceleration rate. Handled correctly, the ship can go from a few hundred miles per hour up to 90% lightspeed, but still feel the same to the crew.

Confused yet? If you are, please post again, because I’m going to bed.

Posted By: Magus Dec 18, 2004 - 06:53 am

Hmmmm.... in answer to your post, Qray, I don't know. But my sister's home. AS she is studying to be an areonautical engineer I'm sure she can give a much better answer then myself. I'll ask her.

Posted By: redshift Dec 18, 2004 - 08:21 am

Wow. Every once in a while, I have my geek license renewed. Looks like I'm good for at least one more year.

I spent the night at the bars with my friends, came home after 2:30 AM, took a look at the boards and said "Hey, neat, somebody's got a question about space travel." So I stayed up writing a rambling, repetitive response that should have been a lot shorter and more accurate. Or better yet, not posted at all, since it doesn't really answer the question.

There will be no more drunken posts from redshift. Nope.

Talon, I live in North Carolina, and I've got a stopwatch. Let's wait until after Christmas for your experiment, though, because I don't want to have to explain my broken nose to the family.

Cheers!

Posted By: Magus Dec 18, 2004 - 12:44 pm

I asked my sister. Since the ship is flying in reltionship to the universe's expansion gravity will remain relative.

In other words it would not change.

Posted By: Qray Dec 18, 2004 - 06:07 pm

Thanks for the information guys. Very informative and useful indeed. But what I was really looking for was a mathmatical formula.

(Q)

Posted By: Magus Dec 19, 2004 - 09:24 am

Oh.

I'm sorry that I can't help you with that.

Posted By: Nomad Dec 19, 2004 - 06:42 pm

I say that you will have constant increasing gravity in relation to contant incrating accelleration. THere has got to be a simple formula involving the rate of gravity versus acceleration over time. Makes me want to find my old physics book. Havent thought of this stuff since I was majoring in aerospace engineering back in college.

Posted By: Aldan Dec 20, 2004 - 05:31 am

Just be sure to include the supposed constant of the speed of light, since acceleration is supposedly stopped there, unless some other unnatural force acts upon it. Oh, or a black hole sucks the object/person in.

Posted By: Qray Dec 20, 2004 - 08:50 pm

I would think there would be a simple formula too, Nomad. I even dugup my old college physics book, even though it's aviation orientated, it doesn't have an answer for me.

Thanks for the heads-up, Aldan, but in this scenerio, I'm assuming traveling well under the speed of light and in an area of space well away from any signifcant mass that would exert a gravitational force.

(Q)

Posted By: MerleZ Dec 21, 2004 - 07:19 am

Hmmm, been a long time since High School Physics, buddy.

First, let me tell you to ask your question at this site: ask the experts.

Now, I can't give you the formula, but maybe they can. Conceptually, since you're not getting close to the weird things that are supposed to happen when you approach light speed, I think that the force would continue to increase until you reach close to light speed. The point of acceleration increasing is that acceleration=force, so if acceleration increases, that means force increases, since they are the same thing. Force will continue to increase as long as acceleration increases. Maybe your friend is confusing the notion that at some point acceleration can no longer increase, which is not part of your particular construct.

Posted By: redshift Dec 21, 2004 - 07:26 am

Okay - this might be useful, and it's got two major plusses. (1) I haven't been drinking this time, and (2) I didn't write it, I just found it.

http://en.wikipedia.org/wiki/Acceleration

If this article doesn't have what you're looking for, it provides the basics you'll need to build on, and links to several other sources which should be helpful.

Posted By: Aldan Dec 21, 2004 - 07:43 pm

A mathematical formula that will say whether constantly increasing acceleration will mean constantly increasing gravitational force? I doubt that there is one. To me, it's much more of a logic problem. If you are in the car that redshift was speaking of, and you slowly increase how far down you press the gas pedal, in this hypothetical situation, you would keep on increasing the force pressing you back into your seat. It would be a bit more noticeable in space, due to the acceleration being the only noticeable source of gravity, but you could find that out in a car legally, if you can get on the autobahn, or illegally on any long straight stretch of road (and by long I mean 10 miles long or so. You would have to be sure to not press too slowly however, or you won't notice the difference easily enough, due to the Earth's gravity's effect on you. However, basically, what I'm saying is that it's something that could pretty easily be proven, up until you reached the speed of light. However, as you approach that speed, the relativistic effects start to occur, which throw a very complex mathematical stumbling block in the way...
Now, some of what I said may be incorrect, due to the fact that I haven't seen a physics book in years, and so may be forgetting something.

Posted By: Qray Dec 22, 2004 - 07:10 am

Thanks for all the help, guys.

I finally got an answer from a prof at Strathclyde University through the MadSci Network.

It's true that there was a simple formula. I was thinking it all wrong in thinking it was a gravity problem and looking for a formula that way when it's actually a force acceleration problem.

The acceleration felt onboard the spaceship (artificial gravity) will always equal the acceleration of the spaceship (the ship's increase in acceleration.) This is independent of the velocity of the ship (velocity and acceleration being two different things).

The formula comes from that funster Newton. That kookie kid realised that force is proportional to the rate of change of momentum.

F = m * a

Where "F" is the force (in this case...artificial gravity,) "m" the mass and "a" the acceleration. Force will rise if the mass falls and/or the acceleration rises.

So, in my original question...if there is a spaceship traveling through space at a constantly increasing rate of acceleration, the gravity felt onbaord the ship would also continue to increase, just so long as the accleration increases.

Thanks again everyone for the help.

Posted By: Nomad Dec 22, 2004 - 06:33 pm

Isnt that what I said? I was an aero space major after all!

Posted By: Magus Dec 22, 2004 - 06:36 pm

An engineer, eh? I have a riddle for you. Let's see if you can solve it.

sin X / cos X = tan

Posted By: Qray Dec 22, 2004 - 08:12 pm

Yup, Nomad, that's what you said...sans the formula ;-])

Posted By: Nomad Dec 28, 2004 - 08:52 am

X