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"A matter of Gravity" world design questions


gewing

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I am working up a world. My initial thought was that it would be somewhat less dense than the Earth, with a smaller metal core. It would be significantly larger than the earth though, and have a somewhat stronger gravity field.

 

I was intriqued by the idea of having it, due to shape or rotational speed, have a lower gravity near the equator, as it would allow even more variability in the species I want to design.

 

According to the math from "Star Hero", it is very difficult to achieve significant decrease in gravity due to rotation. I couldn't get any significant decrease...

 

 

Does anyone have "A matter of Gravity" and know how they explained it there? IIRC it was heavily pear shaped or something like that...

 

 

The basic planet was going to be metal poor, btw, but there are impact craters where iron/nickel meteors hit in the far past, so iron is somewhat available.

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Re: "A matter of Gravity" world design questions

 

If I'm thinking of the right story, the reduction in gravity near the equator was due to the planet having an ABSURDLY high rotation rate.

 

Note that due to conservation of angular momentum, it makes much more sense for a dense but small planet to be spinning fast than it does for a large, low-density planet.

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Re: "A matter of Gravity" world design questions

 

If I'm thinking of the right story, the reduction in gravity near the equator was due to the planet having an ABSURDLY high rotation rate.

 

Note that due to conservation of angular momentum, it makes much more sense for a dense but small planet to be spinning fast than it does for a large, low-density planet.

 

 

If I was doing the math right, you would need a rotation of something like one hour to get much more than maybe 10% reduction in gravity.

 

Maybe I am missing something. I am REALLY disgusted with myself, I seem to have fried the brain cells that held most of my Algebra and geometry knowledge. :mad:

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Re: "A matter of Gravity" world design questions

 

Fortunately, I still have some notes on world-building. Here's the formula I saw:

 

A planet's gravity is the ratio of the planet's density to earth's density, multiplied by the radius of the planet.

 

The earth's density is 5.5 grams per cubic centimeter.

 

Let me look around for the website. It's very good.

 

Edit: Here it is.

 

http://curriculum.calstatela.edu/courses/builders/

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Re: "A matter of Gravity" world design questions

 

In Hal Clement's "Mission of Gravity", the rotational period of the planet was 20 minutes or so. At the equator, the gravity was tolerable by humans ... a couple of gees, I think. At the poles it was more like a hundred gees.

 

I'll see if I can find and dig out my copy, but I remember those details. I'll also push some numbers around and see what I can work out.

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Re: "A matter of Gravity" world design questions

 

In Hal Clement's "Mission of Gravity"' date=' the rotational period of the planet was 20 minutes or so. At the equator, the gravity was tolerable by humans ... a couple of gees, I think. At the poles it was more like a hundred gees.[/quote']Um, wouldn't such a high rotation speed make it impossible to get near the poles? The closer who get to the axis of rotation, the greater the force acting at right-angles to it - if you tried to walk from the equator to the pole, at some point you'd be flung from the surface by the rotation. Of course, you'd be flung near-horizontally, not vertically, so it's likely that you'd return to the planet at some point closer to the start of your journey, although slightly to the East or West depending on whether you were headed South or North....

 

Also, such a planet will have massive and constant windstorms due to the Coriolis effect.

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Re: "A matter of Gravity" world design questions

 

In Hal Clement's "Mission of Gravity", the rotational period of the planet was 20 minutes or so. At the equator, the gravity was tolerable by humans ... a couple of gees, I think. At the poles it was more like a hundred gees.

 

I'll see if I can find and dig out my copy, but I remember those details. I'll also push some numbers around and see what I can work out.

 

 

that was the book, no wonder i couldn't find reference too it.

 

 

I didn't remember the 20minute days.

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Re: "A matter of Gravity" world design questions

 

Um, wouldn't such a high rotation speed make it impossible to get near the poles? The closer who get to the axis of rotation, the greater the force acting at right-angles to it - if you tried to walk from the equator to the pole, at some point you'd be flung from the surface by the rotation. Of course, you'd be flung near-horizontally, not vertically, so it's likely that you'd return to the planet at some point closer to the start of your journey, although slightly to the East or West depending on whether you were headed South or North....

 

Also, such a planet will have massive and constant windstorms due to the Coriolis effect.

Well, without going into spoilers, some of those effects are in the book. I still haven't found my copy ... it's in a box somewhere ... :ugly:

 

Clement's Mission of Gravity was written over 50 years ago, and is definitely among the "hardest" of hard sci-fi, appealing to a rock-bottom minimum of unknown (and that's unknown to the author at the time!) tech. Even the tank (the armored, armed tractor) that the only human on the planet drove in his brief time on the surface was armed with a projectile weapon (yup, a cannon), not an energy weapon: lasers hadn't been invented at the time the story was written!

 

Mesklin (the world in the story) was rather flattened, very rapidly rotating, hydrogen atmosphere, solid surface, but with substantial liquid oceans (I think they were hydrocarbons, but I'm not positive that was spelled out). I forget which star it orbits (that's mentioned in the text; it's one of the putative astrometric binaries mentioned back then, stars that seemed to have nonluminous companions, most of which weren't believed at the time and I think have been refuted since then). The native Mesklinites seem to be arthropods, and maybe 6-8 inches long, and have a nearly inborn aversion to being under anything -- which makes a great deal of sense for something that lives in 50 gees or so most of the time.

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Re: "A matter of Gravity" world design questions

 

Mesklin (the world in the story) was rather flattened' date=' very rapidly rotating, hydrogen atmosphere, solid surface, but with substantial liquid oceans (I think they were hydrocarbons, but I'm not positive that was spelled out). I forget which star it orbits (that's mentioned in the text; it's one of the putative astrometric binaries mentioned back then, stars that seemed to have nonluminous companions, most of which weren't believed at the time and I think have been refuted since then).[/quote']

Mesklin was around 61 Cygni, which is as you said, an early discovered astrometic binary.

 

In other Hal Clement novels set in the same universe he mentions Dhrann at Lalande 21185, Tenebra at Altair and Dromm at Eta Cassiopeae.

 

Agreed that Hal Clement novels are among the hardest of the hard science SF novels.

 

There was a hard to swallow planet in Charles Sheffield's BETWEEN THE STROKES OF NIGHT that spun so fast that objects near the equator were more or less in free fall.

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Re: "A matter of Gravity" world design questions

 

For some weird reason this thread made me think of an anime SF cartoon where a max security prison is built on a high gravity planetoid. No idea what the animation was. I'm pretty sure I was late-night bottlefeeding Mark 1 at the time it was airing on cable.

 

Any suggestions?

 

It has also triggered reminisecences of 'Big Planet' by Jack Vance. Something of an old SF classic. IIRC that planet is Earth-like but much much bigger, with little or no heavier elements (e.g. metals) as an explanation for the Earth-standard gravity. I think it was one of the bases for the world of Tekumel. Hazy memory - a feature of old age apparently :P

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Re: "A matter of Gravity" world design questions

 

In other Hal Clement novels set in the same universe he mentions Dhrann at Lalande 21185, Tenebra at Altair and Dromm at Eta Cassiopeae.

 

Agreed that Hal Clement novels are among the hardest of the hard science SF novels.

Star Light was set on Dhrann. A great story of communications breakdown between two sides that don't really trust each other and are compounded by an awkward (20-30 minutes, IIRC) light-travel time delay, and how catastrophically wrong things can go in such a situation when physical phenomena rise up and start doing unforeseen things to your secret plots.

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Re: "A matter of Gravity" world design questions

 

For some weird reason this thread made me think of an anime SF cartoon where a max security prison is built on a high gravity planetoid. No idea what the animation was. I'm pretty sure I was late-night bottlefeeding Mark 1 at the time it was airing on cable.

 

I believe the show you're thinking of is Outlaw Star, an excellent Japanese animation series. If you like "space opera" at all, you'd do well to watch this one.

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Re: "A matter of Gravity" world design questions

 

I am working up a world. My initial thought was that it would be somewhat less dense than the Earth, with a smaller metal core. It would be significantly larger than the earth though, and have a somewhat stronger gravity field.

 

I was intriqued by the idea of having it, due to shape or rotational speed, have a lower gravity near the equator, as it would allow even more variability in the species I want to design.

 

According to the math from "Star Hero", it is very difficult to achieve significant decrease in gravity due to rotation. I couldn't get any significant decrease...

 

 

Does anyone have "A matter of Gravity" and know how they explained it there? IIRC it was heavily pear shaped or something like that...

 

 

The basic planet was going to be metal poor, btw, but there are impact craters where iron/nickel meteors hit in the far past, so iron is somewhat available.

 

 

As pointed out, the novel is Mission of Gravity by Hal Clement. It's one of the classics of science fiction.

 

The gravity at the poles is about 700 times that of Earth, at the equator it is about 3 times that of Earth. None of the land is very much about sea level, and is fairly rapidly eroded, leading to significant shifts in coastlines (there's also the effect of seasons raising and lowering the sea level by a good bit). The seas are methane, and there's ammonia "snow". Mesklin is much larger than Earth. Mesklin's equatorial radius is about double its polar radius; that is, it's about half as "tall" as it is "wide". Mesklin's day is about 1/80 an Earth day, or about 18 minutes.

 

Mesklin has at least two moons. It also has a ring.

 

The Meslinites are ~40cm long, ~5cm in diameter, and built something like centipedes.

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Re: "A matter of Gravity" world design questions

 

As pointed out' date=' the novel is [i']Mission of Gravity[/i] by Hal Clement. It's one of the classics of science fiction.

 

The gravity at the poles is about 700 times that of Earth, at the equator it is about 3 times that of Earth. None of the land is very much about sea level, and is fairly rapidly eroded, leading to significant shifts in coastlines (there's also the effect of seasons raising and lowering the sea level by a good bit). The seas are methane, and there's ammonia "snow". Mesklin is much larger than Earth. Mesklin's equatorial radius is about double its polar radius; that is, it's about half as "tall" as it is "wide". Mesklin's day is about 1/80 an Earth day, or about 18 minutes.

 

Mesklin has at least two moons. It also has a ring.

 

The Meslinites are ~40cm long, ~5cm in diameter, and built something like centipedes.

 

 

I think I read it about 28 years ago. :)

 

I was thinking about a planet that ranged simply from about one G up to 2.5 or so at the poles. I need to go back to the math, but things are a little stressful right now...

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Um' date=' wouldn't such a high rotation speed make it impossible to get near the poles? The closer who get to the axis of rotation, the greater the force acting at right-angles to it - if you tried to walk from the equator to the pole, at some point you'd be flung from the surface by the rotation.[/quote']

Just the opposite. The cetrifugal "force" increases with increasing rate of rotation, and with increasing distance from the center.

 

Call the rate of rotation "w" (measured in radians/second) and the distance from the axis, measured parallel to the plane of the equator "R". the acceleration due to the centrifugal effect is = w^2 * R

 

That's why on Mesklin, where someone standing on the equator is twice as far from the center as he would be at the poles, the force of gravity he feels is not 1/4 (inverse square law), but < 1/200.

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Re: "A matter of Gravity" world design questions

 

I think I read it about 28 years ago. :)

 

I was thinking about a planet that ranged simply from about one G up to 2.5 or so at the poles. I need to go back to the math, but things are a little stressful right now...

Hmmm...

 

Let's suppose the planet is only 0.9 as dense as Earth. To have 2.5 g at the poles the polar radius must be 2.778 times Earth's, or 17,717 km. If the equatorial radius is 1.3x the polar (which is fairly steep), the gravity drops to about 1.48 g due to distance.

 

Thus, we need a centrifugal acceleration of about 4.7 m/s, to bring the net effect down to 1 g. At 23032100 meters, that needs only .000451744 radians/second, or a day of just under 3:52. Not unreasonable at all.

 

I'll be glad to run the numbers for you if you want to start from different assumptions. :D

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Hmmm...

 

Let's suppose the planet is only 0.9 as dense as Earth. To have 2.5 g at the poles the polar radius must be 2.778 times Earth's, or 17,717 km. If the equatorial radius is 1.3x the polar (which is fairly steep), the gravity drops to about 1.48 g due to distance.

 

Thus, we need a centrifugal acceleration of about 4.7 m/s, to bring the net effect down to 1 g. At 23032100 meters, that needs only .000451744 radians/second, or a day of just under 3:52. Not unreasonable at all.

 

I'll be glad to run the numbers for you if you want to start from different assumptions. :D

 

 

 

The brain cells I killed drinking a few years ago must have been the specific Algebra ones. :(

 

to is that 3 hours 52 minutes, or 3 minutes 52 seconds. One is more tolerable... :)

 

heck, 1.5-2 gs down to one or so would be fine... I just want the ogres to be really scary. :eg: and the dwarves, well lets just say they are stronger than the elves. :D:eg:

 

When I tried to work it out I couldn't get results I was happy with.

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Re: "A matter of Gravity" world design questions

 

The brain cells I killed drinking a few years ago must have been the specific Algebra ones. :(

 

to is that 3 hours 52 minutes, or 3 minutes 52 seconds. One is more tolerable... :)

Sorry. 3 hours 52 minutes. More exactly, 3 hours 51 minutes 49 seconds.

 

heck, 1.5-2 gs down to one or so would be fine... I just want the ogres to be really scary. :eg: and the dwarves, well lets just say they are stronger than the elves. :D:eg:

 

When I tried to work it out I couldn't get results I was happy with.

OK. 2 times Earth's gravity at the poles, with density 0.9 that of Earth, is a polar radius of 14173 km. If the equatorial radius is 1.3 the polar, that's 18425 km.

 

Working the numbers like my other example, gets 0.00031389 rad/sec, or a period of 5:33:37. A bit slower---in fact, about enough to raise the question whether the planet would be as flattened as I assumed above.

 

Say the ratio or radii is 1.2. The polar radius stays the same, the equatorial is 17008 km. We get a rotational rate of 0.000473368 rad/sec, or a period of 3:41:13, which may be too much for 1.2.

 

OK, try 1.25. 17716 km, and 4:26:05. That sounds about right, I think.

 

Alright. Your planet's radius varies from 17716 km at the equator to 14173 km at the poles, the surface gravity is 2 that of Earth at the poles, and equal to Earth's at the equator. The planet rotates in just over 4 hours 26 minutes (Earth time). Oh, and the surface area is about 6.7 times that of Earth.

 

If that doesn't suit, I can try running some other numbers. :)

 

BTW, if you want I can work up the escape velocity from the surface, both polar and equatorial.

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Re: "A matter of Gravity" world design questions

 

Just the opposite. The cetrifugal "force" increases with increasing rate of rotation' date=' and with increasing distance from the center.[/quote']See? This is why you don't want me designing worlds.

 

I knew there was something wrong with that statement as I was writing it, because I was picturing an oblate spheroid at the same time and couldn't reconcile that image with what I was writing, which would result in a torus.

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Re: "A matter of Gravity" world design questions

 

Sorry. 3 hours 52 minutes. More exactly, 3 hours 51 minutes 49 seconds.

 

 

OK. 2 times Earth's gravity at the poles, with density 0.9 that of Earth, is a polar radius of 14173 km. If the equatorial radius is 1.3 the polar, that's 18425 km.

 

Working the numbers like my other example, gets 0.00031389 rad/sec, or a period of 5:33:37. A bit slower---in fact, about enough to raise the question whether the planet would be as flattened as I assumed above.

 

Say the ratio or radii is 1.2. The polar radius stays the same, the equatorial is 17008 km. We get a rotational rate of 0.000473368 rad/sec, or a period of 3:41:13, which may be too much for 1.2.

 

OK, try 1.25. 17716 km, and 4:26:05. That sounds about right, I think.

 

Alright. Your planet's radius varies from 17716 km at the equator to 14173 km at the poles, the surface gravity is 2 that of Earth at the poles, and equal to Earth's at the equator. The planet rotates in just over 4 hours 26 minutes (Earth time). Oh, and the surface area is about 6.7 times that of Earth.

 

If that doesn't suit, I can try running some other numbers. :)

 

BTW, if you want I can work up the escape velocity from the surface, both polar and equatorial.

 

 

escape velocities would be great! THANKS.

 

imagine what the marine carnivorous life forms in the polar regions are like. :eg:

 

I wonder what the gravity gradient would do to weather patterns?

 

oh the potentials...

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Re: "A matter of Gravity" world design questions

 

escape velocities would be great! THANKS.

There's going to be a bit of a problem with escape velocities, unfortunately. And not only escape velocity...

 

Earlier today I remembered Hal Clement had written an essay, "Whirligig World," about how he designed Mesklin. I went looking for it on the Internet, but it seems it hasn't been published there. However, I found a good deal of info from the essay has been repeated in a wikipedia article (http://en.wikipedia.org/wiki/Mesklin).

 

One quote from there is disturbing:

Clement then attempted to calculate the polar gravity' date=' but this was surprisingly difficult. He admits, "To be perfectly frank, I don't know the exact value of the polar gravity; the planet is so oblate that the usual rule of spheres... would not even be a good approximation..." "Whirligig World" reports his initial calculations of the pole gravity to be 655G, the paper jacket of Heavy Planet reports the pole gravity as 700g, and a later program created by Clement computed it as 275g.[/quote']

 

Now, Mesklin is ~2.5 times as "wide" as it is "tall," and I was assuming a 1.25 multiplier, so perhaps the problem Hal Clement faced aren't present, or can be handwaved away. Still, I did assume the polar gravity could be found by assuming the total mass of the planet as a point-source at the center. If a 1:1.25 ratio is enough to make that assumption invalid, then I can't tell you what the gravity at the poles of the planet I "built" would be.

 

And this relates to the escape velocity: if I assume I can treat the mass as a point-source at the center, it's easy to figure out, if I can't, then I don't know how to find the answer.

 

Well, perhaps not. The wikipedia article cited makes it seem that Mr. Clement found the gravity at the equator of Mesklin by assuming a point-source, so I think it highly likely I can find escape velocity with the same assumption. Thus...

 

The escape velocity at the equator is 26.4 km/sec (on Earth it's about 11.2 km/sec); note that the centrifugal effect is only 2.74 m/sec so it won't help much. OTOH, the speed of a point on the equator is ~1.1 km/sec so it'll help even though it's sideways.

 

Now for the poles. If we assume a point-source mass (as if we were dealing with a sphere), the escape velocity would be about 29.5 km/sec. No help from centrifugal effect nor rotation.

 

Going to be a pain getting off or onto the planet, that's for sure. :snicker:

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Re: "A matter of Gravity" world design questions

 

I got to meet and have breakfast with Hal Clement about 6-7 years ago a a science fiction convention. I found out he was a retired high school science teacher. He was very pleasent and friendly. I think he was about 79-80 years old at the time and still going to 19-20 science fiction conventions a year. I have enjoyed all of his books.

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