Getting the Science Right, Part 2

Several years ago, I toyed around with writing a story about a space station. The space station was a wheel-type station very similar to the space station depicted in "2001: A Space Odyssey" except that it had more levels or "floors," if you will.

Basically, the premise of the story was that the space station was a kind of resort. The station included research facilities, but a large portion of one "wheel" was set aside for recreational activities.

The space station was large, a kilometer in diameter. Accordingly, the outermost ("lowest") level was five hundred meters from the center of rotation. The perceived "gravity" at this point was one g, or about 9.8 meters per second squared.

In development of the idea, I considered the following questions. I pose them here for entertainment value.

Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation? (Related: was the space station in "2001" rotating at an appropriate rate? Also: How fast would the space station need to rotate if it were two kilometers in diameter instead of one kilometer in diameter?)

Question 2: One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared. The purpose of such a level would be to acclimate lunar travelers to the gravity of the Moon. How far is the "lunar level" from the center of rotation?

Question 3: One of the lower levels of the space station (gravity close to one g) has a swimming pool. Sloshing water from pool is to be avoided. Should there be any modifications to the pool in order to prevent this hazard? What will the water in the pool look like? (E.g., will the surface be flat? Will water "pile up" on one side of the pool?)

Question 4: One of the lower levels of the space station has a miniature golf course. Under what conditions, if any, will a putt roll "true?"

Question 5: If a golfer holds a golf ball one meter directly over his right toe and drops it, will the ball "fall" straight down and land on his right toe? (The notion of how objects "fall" could have consequences for things such as diving into the pool, taking a shower, or going to the bathroom.)

Question 6: People on the Earth cannot "feel" the Earth rotating. Could people on the space station "feel" the station rotating?

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort?

I found that posing questions like this, and trying to answer them with scientific accuracy, could help create a more vivid description of the environment.

#3 The pool's surface will curve like the pool's "bottom"; but with a steeper slope to it I think.

Brown said:

One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared.

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Babylon 5 also featured a space station that rotated to produce artificial gravity. On the Babylon 5 station, the outermost levels (where the gravity was the strongest) were called "downbelow", and were the place where all the misfits and scumbags were relegated to. Apparently, the Low Gravity district was also the High Rent district.

Question 3: One of the lower levels of the space station (gravity close to one g) has a swimming pool. Sloshing water from pool is to be avoided. Should there be any modifications to the pool in order to prevent this hazard? What will the water in the pool look like? (E.g., will the surface be flat? Will water "pile up" on one side of the pool?)

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Curved surface. Don’t have the diving board too close to the edge! See lower for reason.

Question 4: One of the lower levels of the space station has a miniature golf course. Under what conditions, if any, will a putt roll "true?"

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I don’t see a problem here (assuming putting). Driving from a green however may introduce problems.

Question 5: If a golfer holds a golf ball one meter directly over his right toe and drops it, will the ball "fall" straight down and land on his right toe? (The notion of how objects "fall" could have consequences for things such as diving into the pool, taking a shower, or going to the bathroom.)

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Yes, any object that changes it’s ‘hight’ will follow a curved path (conservation of momentum) modified by the atmospheric drag.

Question 6: People on the Earth cannot "feel" the Earth rotating. Could people on the space station "feel" the station rotating?

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No, only if there is a change.

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort?

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how to correctly align the toilet paper on the roll, I can’t believe they still get this wrong, I mean how simple is this, it’s not like you need to be a rocket scientist or anything.

Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation?

I get 44.9 seconds/rotation, although I may have dropped a factor of a half somewhere...

(Related: was the space station in "2001" rotating at an appropriate rate? Also: How fast would the space station need to rotate if it were two kilometers in diameter instead of one kilometer in diameter?)

63 s/rev

Question 2: One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared. The purpose of such a level would be to acclimate lunar travelers to the gravity of the Moon. How far is the "lunar level" from the center of rotation?

83 m, I think.

Re: Re: Getting the Science Right, Part 2

Matabiri said:

Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation?

I get 44.9 seconds/rotation, although I may have dropped a factor of a half somewhere...

Click to expand...

This is correct. I found the answer surprising because it means that you have to rotate a pretty large space station rather fast to get one g. (Arthur C. Clarke has suggested that space stations would rotate more slowly, to give the sensation of less than one g.)

The computation goes like this: for uniform rotation (i.e., the wheel rotating at a constant radial velocity), radial acceleration (in meters per second per second) equals radius (in meters) times radial velocity (in radians per second) squared. The radial acceleration is given as 9.8 meters per second per second, and the radius is given as 500 meters. Radial velocity is easily computed as 0.14 radians per second. There are 2*pi radians in a revolution, so 0.14 radians per second = 0.14/(2*pi) = 0.0223 revolutions per second. Take the inverse, and you get about 44.9 seconds per revolution.

If the radius is 1000 meters, then you can spin the station slower to get one g, but the station still has to spin pretty fast. Again, Matabiri's answer is correct.

To find the "lunar level," use the same radial velocity (0.14 radians per second) and let radial acceleration be 1.6 meters per second squared, and solve for the radius. The lunar level is at about 82 meters from the center.

As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved?

Re: Re: Re: Getting the Science Right, Part 2

Brown said:

As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved?

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For an observer in an inertial frame, outside the station, the object would follow a straight line with the tangential velocity it initially had. Since the station floor is curved, the object will eventually hit the floor.
Since the station is rotating, the object will hit the floor behind the 'vertical' it initially belonged to.
An observer rotating with the station will see a curved path.

BTW, I obtained the same results as Matabiri and you. And I was surprised too.

Re: Re: Re: Getting the Science Right, Part 2

Brown said:

...As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved?

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Assuming the object is not at the the centre of the hub, and in the absence of any mathematical skill, is it that the apparent fall of any object would be straight down, along a line intersecting the station hub and the original position of the dropped object? I suspect it may curve, with respect to the orientation of the start of the drop, but that the increasing acceleration of gravity as it proceeds to the rim combined with any lateral acceleration component from the spin of the station at drop time results in the effect. Not sure what might happen if it were dropped from the station's centre of mass, a back hand lob? Thinking about it, you couldn't drop it from that position, could you?

I think that if you drop a object it will appear to fall straight down, when what it is actually doing is travelling at a tangent to the point at which it was released.

Remember that when you let it go it has a momentum in the direction that the space station is rotating. There is now no force acting on it, so it will simply continue in a straight line, but the floor of the space station is in it's path. I haven't done the maths, but I'm pretty sure that the time it takes for the object to reach the intersection point of floor that's in it's path is the same as the time it takes for the point that was directly below it to rotate to that same intersection point.

I think that makes sense!

wollery said:

I think that if you drop a object it will appear to fall straight down, when what it is actually doing is travelling at a tangent to the point at which it was released.

Remember that when you let it go it has a momentum in the direction that the space station is rotating. There is now no force acting on it, so it will simply continue in a straight line, but the floor of the space station is in it's path. I haven't done the maths, but I'm pretty sure that the time it takes for the object to reach the intersection point of floor that's in it's path is the same as the time it takes for the point that was directly below it to rotate to that same intersection point.

I think that makes sense!

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Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is ωt, while the angle described by the body is tan^-1(R₁/V₁t) < ωt, where ω is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path.

Brown said:

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort?

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Care would have to be taken with the atmospherics .... presence of any heavier than air gas would tend to the outer ring and suffocate people out there, whilst lighter-than-air ones would get the residents nearer the hub.

In order to get adequate air exchange for for comfort, health and climate control a massive HVAC system would need to be in place, either that or some sort of nifty micro-metereology system. Little clouds and mini thunderstorms!

Probably also need some contingency in place for the utter chaos caused by a change in angular velocity!

SGT said:

Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is ωt, while the angle described by the body is tan^-1(R₁/V₁t) < ωt, where ω is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path.

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Yeah, I did the maths last night. It was fairly obvious as soon as I drew a little cartoon sketch that I was wrong.

Oh well, there you go.

SGT said:

Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is ωt, while the angle described by the body is tan^-1(R₁/V₁t) < ωt, where ω is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path.

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Actually the angle described by the body is tan^-1(V₁t/R₁) < ωt. I inverted the sides of the triangle, but the reasonig is still valid, as wollery checked.

Re: Re: Getting the Science Right, Part 2

Benguin said:

Care would have to be taken with the atmospherics .... presence of any heavier than air gas would tend to the outer ring and suffocate people out there, whilst lighter-than-air ones would get the residents nearer the hub.

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That's actually not such a big problem, the thermal energy of the air will keep it fairly well mixed. Keep in mind that carbon dioxide is about 50% heavier than air, and it mixes pretty well down here on earth.

But what's a MAJOR issue is keeping the whole thing sealed up. The bigger your space station, the more possible places for leaks to occur. And if they occur too often, you'll spend too much time/money/energy/whatever chasing them down and hauling air up to replace what you lose. This isn't necessarily an insurmountable obstacle, but it is a big one that you'd need to spend a LOT of design and constructon effort to minimize.

Re: Re: Re: Getting the Science Right, Part 2

Ziggurat said:

That's actually not such a big problem, the thermal energy of the air will keep it fairly well mixed. Keep in mind that carbon dioxide is about 50% heavier than air, and it mixes pretty well down here on earth.

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Very true, but we do have lot's of air movement through meterological effects and more localised convection etc to keep it all mixing up. I'm sure 'brownian motion' (OK, I know, I can't remember the proper physics term!) alone isn't enough to keep us all from gasping.

If you think, it isn't far above our surface that we have some fairly active turbulence stirring the atmosphere up, kept going by vast amounts of thermal energy from the sun. Our station could get pretty stagnant without care.

But what's a MAJOR issue is keeping the whole thing sealed up. The bigger your space station, the more possible places for leaks to occur. And if they occur too often, you'll spend too much time/money/energy/whatever chasing them down and hauling air up to replace what you lose. This isn't necessarily an insurmountable obstacle, but it is a big one that you'd need to spend a LOT of design and constructon effort to minimize.

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There would be significant risks associated with breaches and, though micro-meteorite strikes would be a danger, I think the major risks comes from accidents inside. Explosions, fires, or even things falling under internal gravity present a very clear danger to the membrane.

Okay, so this is really sad, and I'm not sure I should admit to this, but......

After doing the maths to see if a dropped object followed a curved path I was wondering just how far behind the original drop point it would fall, and how it would vary with the height it was dropped from.

So I wrote a computer program to calculate it!

I know, I'm a sad geek, but the results are quite interesting, assuming a radius of 500m;
drop height; 1m, distance; 4.225 cm
drop height; 2m, distance; 11.98 cm
drop height; 10m, distance; 1.361 m
drop height; 50m, distance; 16.65 m
drop height; 100m, distance; 53.25 m
drop height; 200m, distance; 203.02 m
drop height; 300m, distance; 566.00 m
drop height; 400m, distance; 1.764 km
drop height; 490m, distance; 24.22 km (which is almost 8 times round the station!)

Well I thought it was interesting!
And besides, it distracted me from real work for 20 minutes.

One thing I've always considered about this -- The higher up you drop from, the less "sideways" velocity it will have. So, dropping from the center, (or throwing, as the center would have no perceived gravity at all), the "bottom" of the space station would continue rotating past, while the object continues in a straight line with respect to its origin.

If there is a building or a large wall at the "bottom", this will be moving at 44.9 second's rotation. Therefore, while the landing might be soft (at only the speed the object was dropped/thrown, it will very probably be smashed from the side as the rotating objects encounter it.

Imagine hanging slightly above the center of one of those carnival cyclotron spinning rides. Now throw a ball at one of the riders. You will hit the side of the little cubicle of a rider farther along the circle.

However, if you are off center, and attached to (rotating with) the ride, I can see where the mental puzzle gets a little more difficult.

It's been explained above that a dropped body will not fall along an apparently vertical path, and the observer inside the station will see the object follow a curved path. This is correct, and I was mildly surprised by this, too.

Some folks think that if you let an object go, "zero gravity takes over" and the object just floats in the air. Actually, as has been described, the object follows a straight line tangent path, which is interrupted by the floor of the station.

Some other folks also think that if you let the object go, it follows a path directly away from the center of the wheel, being pushed in that direction by "centrifugal force."

In light of the effect on falling objects, someone might want to tackle the question of whether it would be possible to "feel" the station rotating. (If they can "feel" it rotating, there is a possibility that guests will experience motion sickness.)

My computations pertaining to falling objects caused me to wonder whether it would be feasible to put a miniature golf course on a space station. Should the putting greens be flat, or curved to match the curvature of the station? Does it matter the ball is hit in the direction of rotation or perpendicular to the direction of rotation? When putted, will the ball roll "true?"

If memory serves, a miniature golf hole could be designed so that a putt rolls "true." But a hole could also be designed so that a putt would roll in odd ways, even though the putting surface looks flat. This could make for an interesting miniature golf course. You wouldn't need no stinkin' windmills to make it challenging.

Atmospheric circulation and airlock considerations have been mentioned. Here are a few other considerations that might be taken into account by a developer that wanted to create a space-based resort: mechanized transportation from one site on the station to another, without adversely affecting the spin of the station (darn that conservation of angular momentum!); evacuation plans in the event of a radiation hazard; a heavily shielded section to serve as a "lifeboat" in the event not everyone can be evacuated; development of a zero-g recreational room (you know people would want to do that!) and activities that would be permitted therein; and techniques and apparatus (such as bars, ropes, padding, etc.) for moving people safely from a zero-g environment in their spaceships docked in the hub to the outer levels of the station.

Edited to add a "dropped" word.

alfaniner said:

One thing I've always considered about this -- The higher up you drop from, the less "sideways" velocity it will have. So, dropping from the center, (or throwing, as the center would have no perceived gravity at all), the "bottom" of the space station would continue rotating past, while the object continues in a straight line with respect to its origin.

If there is a building or a large wall at the "bottom", this will be moving at 44.9 second's rotation. Therefore, while the landing might be soft (at only the speed the object was dropped/thrown, it will very probably be smashed from the side as the rotating objects encounter it.

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Great point. I considered this in connection with having a "high dive" feature above the resort pool. Basically, the diver would jump from a considerable height (and would jump in such a way that he would indeed go into the pool) and would fall fairly slowly toward the water.

Sounds like fun. But the water is eventually going to hit him harder than he thinks, and from a direction that may catch him off guard.

Brown said:

In light of the effect on falling objects, someone might want to tackle the question of whether it would be possible to "feel" the station rotating. (If they can "feel" it rotating, there is a possibility that guests will experience motion sickness.)

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Ignoring everything else in that post (although the golf idea is intriguing) motion sickness derives from changes in the direction and rate of motion, ie non-constant acceleratoins and velocities. In this space station there is only one acceleration, which I hope would be smooth, and this is directed radially inwards. I see no reason why anyone should feel motion sickness.

Unless of course they look out the side window and see the Earth and stars rotating at 0.14 rad/s!