# Simple gravity question

Discussion in 'Trek Tech' started by The Borgified Corpse, Mar 9, 2010.

1. ### The Borgified CorpseAdmiralAdmiral

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I'm collaborating with some other writers on a sci-fi webseries. It's set on a heavy gravity prison planet. My question is, how heavy can the gravity get before a normal, Earth-bred human is rendered incapable of functioning normally?

One draft mentions that the planet is 7 times the size of Earth. If we're talking 7 times Earth's mass, thus 7 times its gravity, that sounds rediculous to me. Am I wrong?

2. ### psCargileLieutenant CommanderRed Shirt

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You are right.

Seven gees is exceptionally high. A 200 lb person would weigh 1400 lbs. Even at 2 g that's 400 lbs. I would think that if you aren't able to support twice (or more) your weight for a long period of time, you'll be incapacitated rather quick. The heart is going to have a hard time pumping blood. The best analogy is what combat pilots can endure. Do a search for that for better explanations than what I can give.

Is there a reason why the prison planet needs to be a high gravity world? If it were just to make it exotic, I'd drop the whole notion. But if you need it, anything over 1 to 2 gees will be suitably uncomfortable until a person acclimates. 3 gees might be pushing it. At 7 to 9 gees, its not so much a prison planet as a means of execution.

3. ### The Borgified CorpseAdmiralAdmiral

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^Honestly, I think they're just trying to make it exotic. Certainly, making the gravity slightly heavier would add to the hostile nature of the planet. But I'm thinking 1.25 gees would probably be sufficient. 2 gees is probably as far as I would go. Any further and it would also start interfering with some of the cool martial arts fighting & such.

I'm just trying to make it a scant more plausible. The central conceit of the series is such strange fantasy to begin with, we probably don't want to compound it with crap science.

4. ### The Borgified CorpseAdmiralAdmiral

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BTW, the dialogue in the draft merely says the planet is 7 times the "size" of Earth. I suppose that could be referring to something else, like surface area, not mass. What's the likelihood of a planet with an Earth-like mass but 7 times the surface area?

5. ### Chaos DescendingVice AdmiralAdmiral

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Earth-like mass but 7 times the surface area would mean a planet with a much greater radius, and therefore a much lower surface gravity.

Also, in regards to original post, 7 times the mass would not equate to 7 times the gravity unless the volume (and therefore the radius) of the planet was exactly the same as Earth. The force of gravity is proportional to the mass but inversely proportional to the square of the radius.

6. ### DeksRear AdmiralRear Admiral

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How much of a time frame would be needed for a Human to adapt from a 1 G environment to 3 G for example?
If/And once the individual in question adapts ... can you then try to put the 3G adapted human into a 4, or 5 G environment and see if they can adapt with sufficient amount of time?

7. ### Chaos DescendingVice AdmiralAdmiral

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I don't know that a human being could EVER adjust to a 3g+ environment. A 200 pound man would have to get used to weighing 600 pounds. I just don't think that our knees, back, etc. are designed to withstand that sort of load.

8. ### Ronald HeldRear AdmiralRear Admiral

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Why don't you be vague about the planetary physcial parameters and just state what the acceleration is in gees.

9. ### TheCrowAdmiralAdmiral

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Just a note, this thread would be better in science and technology than trektech. With that out of the way.

Don't forget about how a high gravity world is going to effect your martial arts. You would see very few throws, jumping manuevers, high kicks, etc. Most of it would be grapples, sweeps, etc.

10. ### The Borgified CorpseAdmiralAdmiral

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OK, so, because I'm not always a math whiz, what would be the approximate surface gravity of a planet of Earth-like density with 7 times Earth's mass & 7 times Earth's volume?

11. ### TheCrowAdmiralAdmiral

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I am probably wrong, but I am guessing 1g.

12. ### T'GirlVice AdmiralAdmiral

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If the world had seven times the volume of Earth the diameter would be 32,970 miles, with a total surface area of 3,414,976,873.7 sq. miles, that's 17.34 times the area of Earth. If this world had Earth's mass the gravity at sea level would be 0.5665 gee.

If the world had Earth's density the gravity would be 2.87 gees.

Last edited: Mar 10, 2010
13. ### SpyOneCommanderRed Shirt

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The effect of high gravity on people for extended times is largely guesswork: we haven't spent a lot of time having test subjects living in centrifuges to see what happens.
IIRC, 1970s scifi had human colonies on worlds up to 2.5g on a regular basis. By the late 80s, scifi games were predicting that above 1.2g would interfere with your ability to sleep.

In the 1970s, scientists at the University of California at Davis raised some chickens in centrifuges specifically to see if the predictions were accurate. After living in 2.5g for months, chickens were 3 times stronger, had low body fat, had improved endurance, and their hearts were moving much greater volumes of blood.

I also should point out that a world much larger and more massive than the Earth will probably also be denser than the Earth: the gravity and the weight of the rock and stuff that makes up the planet will be squishing the stuff at the center much more than the Earth does. So a planet as described above (seven times the volume of Earth, at least as dense as Earth) would likely be even denser than Earth, and thus have higher gravity.

14. ### psCargileLieutenant CommanderRed Shirt

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Borgified Corpse (neat name LOL) I have a calculating spreadsheet at home (at work as I post) that I created for determining planetary attributes based on size and mass. This is something I made for my own fiction and creating solar systems in Celestria. I can email this to you if you want.

Does a planet with 7 times the amount of mass as Earth have 7 times the pull of gravity, no matter it's radius? Let's find out:

g= G*(m1/r^2) where by G is the gravitational constant 6.6742x10^-11, m1 is the mass of the Earth in kilograms, 5.9736X10^24, and r is the Earth's radius in meters, 6.37101X10^6.

For 1g that equals 9.822 meters per second per second acceleration.

7 times the Earth's mass is 4.18152x10^25, which gives, 68.757. Divide that by 9.822 and you get 7.

7 times the Earth mass and 7 times the Earth radius gives 1.403 m pers s squared, or .143 g. This would be a planet a lot less dense than Earth.

7 times the mass of the Earth and 2.4 times the radius would give you 1.21 g.

http://en.wikipedia.org/wiki/Earth's_gravity for the formula. Plug that into a spreadsheet and play.

15. ### ChristopherWriterAdmiral

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Mar 15, 2001
It depends on the density. The density of a planet can vary widely depending on its composition. Looking at my worldbuilding spreadsheet:

A pure silicate world with no significant metals and a mass of 7 M(Earth) would have a radius of 1.81, a density of 1.18, and a surface gravity of 2.14, all relative to Earth. A 7-Earth-mass world with an Earthlike composition (an iron core making up about 32.5% of its mass) would have a radius of 1.68, a density of 1.48, and a gravity of 2.48. A 7-Earth-mass world with a Mercury-like composition (iron core making up 70% of its mass) would have a radius of 1.49, a density of 2.12, and a gravity of 3.15. These are idealized cases, especially the first one, but they should give you ideas of the range of possibilities.

Or let's say you make it an ice planet with the composition of some of Saturn's moons, about 50% ice and 50% rock and metal. In that case, at 7 Earth masses, the radius would be about 2.33 of Earth's, the density only about 56% of Earth's, and the gravity only 1.29 gees. (Well, actually what I have in the spreadsheet is about 53% rock and metal and 47% ice by mass, but you get the idea.)

As for the ability to perform in high gravity, it would be extremely difficult at first, but if you trained properly and avoided injury, you could get strong enough to cope with it, just like any other kind of physical training. However, if you did strain or injure yourself early on, it might be hard to heal properly and the effects could be crippling. Also, in the long term it would put more strain on the circulatory system, but again, I think that's a question of training. I've read stories postulating that people on high-gee worlds had more heart failures and shorter lives, but I'm not so sure that's accurate. The heart is a muscle, so the more use it gets, the stronger it gets (again, assuming excessive strain and injury are avoided). So I'd think that, as with the rest of your muscles, it's a question of whether you train it properly, whether you get to start out slow and build up your strength and endurance. However, if you're suddenly dropped into a prison planet with 2-3 times your accustomed gravity and have to start fighting or struggling right away, that's more likely to lead to overstrain and injury and make it difficult to function. Although if you're already very physically fit to begin with, your chances would be better. (Needless to say, your cardiovascular fitness could be negatively impacted by factors in the prison environment such as stress or tobacco and drug use. Clean living is your best bet, but if you lived clean, why would be on a prison planet?)

Of course, all this is assuming normal, unaugmented humans. If you bring genetic and technological enhancements into the mix, all bets are off. People sent to live on high-gee worlds could have their joints reinforced or replaced with superior artificial versions, could possibly have their muscles augmented by nanofiber cables that contract with much greater force than human muscle, could have their heart and organs similarly augmented, etc. Or they could just wear the kind of strength-enhancing armature that's already being developed for military and medical uses.

16. ### STRFleet CaptainFleet Captain

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Human beings can withstand, for short periods, 4-6G of acceleration without training or mechanical assistance. For prolonged periods? I don't think anyone knows. It probably isn't more than 2G. It doesn't matter how good of shape you are, you're not carrying ~200 pounds of extra weight around all the time without problems. US soldiers, fully loaded, carry ~75 pounds of gear max, meaning the the practical limit might be as low as 1.25-1.5G.