Gravity on the surface of Gliese 581 d

[horseshoe7]

Possibly habitable planet Gliese 581 d is said to be (at a minimum) 7x the mass of the Earth... but what would the gravity be at the surface of Gliese 581 d?

7x the mass does not mean 7x the Gravity at the surface.

Gravitational force is directly proportional to mass and inversely proportional to the square of the distance.

On a SUPER EARTH like Gliese 581 d, the planet surface will be farther from the center of mass (given a similar composition of elements to the Earth and/or a similar density of the composition)... now, the distance (radius) would grow in relationship to the Volume(which grows due to the increased mass of the object), according to the formula (check my work folks - I'm an Engineer, but haven't had to do much "real math" in some time):

r = cube root of (3/4*V*pi)

So, gravity is inversely proportional to the square of distance, but distance(radius) is proportional to the cube root of Volume(~proportional to mass), so it does seem that, when calculating gravity of a 7x more massive Super Earth (vs. Earth), then the Super Earth would only have 7x - (square root of 7 or 2.65) or 4.35x more gravity than Earth... again, check my work folks - but, I believe my premise stands true in any event - 7x the mass does not equal 7x the gravity.

However, if my calculations are correct, my 200lb body would feel like about 867lbs on the surface of Gliese 581 d... even if I went on a crash diet to get to ~150lbs, I'd STILL weigh about 650 pounds there!... maybe we need to "continue the seach" for more suitable habitable planets? ... hopefully, there is a more Earth-sized planet Gliese 581 f that is right in the middle of the habitable zone of the Gliese 581 system?

 

[willem2]

The radius is indeed proportional to the cube root of the mass so if r = r_earth * M^(1/3) then
g will be g_earth * M / (M^(1/3))^2 = g_earth*M^(1/3) and everyone will be 1.91 times heavier.
This weight wouldn't be very crippling, you should still be able to walk for an hour or so.
If gliese 581d has the same composition as Earth it would be compressed a bit more however

 

[eachus]

Good work, but there are several other factors at play. Since the escape velocity from Gliese 581d will be higher than Earth, I would expect it to hold on to more light elements over its lifetime. This would result in a lower average density, and thus a lower gravity. The lower intrinsic brightness of Gliese 581 would mean less energetic radiation, and a weaker stellar wind, both of which would also contribute to higher retention of volitiles.

Finally there is the issue of where in the circumstellar disk 581 d came from. In theory this could result in a higher density, but in practice I think it would result in a lower density. (More of the total mass of a smaller disk than in the solar system ending up in Gliese 581d.)

Net, net, the gravity at the surface may be lower than on Earth, but there is a much higher probability of a water world and/or an atmosphere thicker than Venus. I don't know if it will be possible anytime soon to measure the diameter, rotation rate, and atmospheric constituents of Gliese 581b, c, and d using radio interferometry, but it would be fun to try. ;-)

 

[Rasalhague]

[...] and everyone will be 1.91 times heavier.
This weight wouldn't be very crippling, you should still be able to walk for an hour or so.

Like being stuck in an elevator going up for an hour; a bit stronger than that. Googling hypergravity produces a lot of links to casual news items about Malcolm Cohen doing a 22 hour study of human tolerance to this sort of weight (using a centrifuge); does anyone know of any links to serious pages discussing the results of this or similar studies? The most detailed description I found was this report in Wired magazine of one volunteer's personal experience. It begins with an acute test of the acute effects of much higher acceleration, then describes an extended test at 1.25g. It ends with him passing out, and he learns later that his heart stopped for a few seconds. Another volunteer threw up, but that might have been an effect of the rotation.

http://www.wired.com/wired/archive/11.03/7g.html

Before fainting, he mentions yawning and feeling "sleepy and cold". Chronic hypergravity tests on rats, mice, dogs and monkeys (between 1.25g and 2.5g) have shown an effect on circadian rhythms: decreased locomotor activity (perhaps indicating drowsiness) and a drop in core body temperature, a "centrifuge-induced hypothermic response".

http://jap.physiology.org/cgi/content/full/95/3/1266

 

[Matterwave]

I think the planet would tend to be more dense, since there is more material crushing down on it (more pressure -> lower volume). I'm not sure the specific effects though...

 

[Grozny]

The radius is indeed proportional to the cube root of the mass so if r = r_earth * M^(1/3) then
g will be g_earth * M / (M^(1/3))^2 = g_earth*M^(1/3) and everyone will be 1.91 times heavier.
This weight wouldn't be very crippling, you should still be able to walk for an hour or so.
If gliese 581d has the same composition as Earth it would be compressed a bit more however

If there is multicellular life there, the land animals would be very squat, heavily muscled tank-like critters with big flat feet - six legs may be the norm instead of four. Or it may be that the multicellular life of Gliese 581 d (if there is such life) is all in the oceans; that it just takes too much energy to move about on dry land.

Is it possible to escape from Gliese 581 d with a LOX/methane rocket? This fuel produces 299 kilos of thrust per kilo of propellant at sea level here on Earth. But I do not know how its specific impulse is affected by the greater air pressure on Gliese 581 d. And, even assuming that the air pressure is the same, I got bogged down in the math trying to determine how large of a rocket would be needed to get into orbit.

Could someone help me with this problem?

 

[qraal]

If there is multicellular life there, the land animals would be very squat, heavily muscled tank-like critters with big flat feet - six legs may be the norm instead of four. Or it may be that the multicellular life of Gliese 581 d (if there is such life) is all in the oceans; that it just takes too much energy to move about on dry land.

Firstly the mass is x7 Earth, not the gravity. Plenty of people get around with the equivalent of 50-100% more mass than average, so it's not unreasonable to expect merely more muscular versions of skeletal architectures we know and love. What you described is merely one possibility not a necessity.

Is it possible to escape from Gliese 581 d with a LOX/methane rocket? This fuel produces 299 kilos of thrust per kilo of propellant at sea level here on Earth. But I do not know how its specific impulse is affected by the greater air pressure on Gliese 581 d. And, even assuming that the air pressure is the same, I got bogged down in the math trying to determine how large of a rocket would be needed to get into orbit.

Could someone help me with this problem?

Orbital velocity is straight forward, but gravity and atmospheric drag losses aren't so easy. What level of detail do you want? What surface gravity did you settle on?

 

[qraal]

Assuming Earth-like composition (an uncompressed density of 4.08 g/cc) then a Super-Earth between 1 and 10 Earth masses has a radius of roughly...

R = R*.(M)^0.27 ...where R* is Earth radius. This equation takes into account compression.

An Ice Planet, that's half water and half silicate/iron (i.e. Earth), has a similar equation

R = 1.26.R*.(M)^0.275

...thus about half the density at the same mass. The indexes are only rough - over a range of super-Earth masses they can go from 0.28-0.26, while between 0.05-0.5 Earths it's roughly 0.3. Below about 0.05 and there's very little compression increase of density. For very high masses there's a maximum radius of about 4 Earth radii, above which the core becomes degenerate and the radius shrinks with mass.

So a 7 Earth mass, Earth-like planet has a radius of about 1.7 Earths and a surface gravity of 2.44 gee. Pretty high, but not ridiculous. An Ice Planet would have a radius of 2.1 Earths and 1.55 gee surface gravity. I call it an Ice Planet, but it's likely to be covered in an Ocean, but deeper than 100-200 km that ocean will freeze into a high-pressure phase of water, probably Ice VII. It can remain frozen at hundreds of degrees and higher pressure phases probably exist able to remain "solid" even when glowing hot. The cores of Neptune and Uranus might be wrapped in the stuff.

 

[Grozny]

Firstly the mass is x7 Earth, not the gravity. Plenty of people get around with the equivalent of 50-100% more mass than average, so it's not unreasonable to expect merely more muscular versions of skeletal architectures we know and love. What you described is merely one possibility not a necessity.

Orbital velocity is straight forward, but gravity and atmospheric drag losses aren't so easy. What level of detail do you want? What surface gravity did you settle on?

My own back-of-the-envelope estimates were for gravity of about three times that of Earth. But I was assuming more compression than you guys are.

I was a bit surprised by willem2's estimate of 1.91. You say 2.44. It sounds like nobody is really sure until we learn more about the composition of the planet. It is also possible that the pressure at the center of Gliese 581 d is far greater than anything we can do in experiments and we just don't know how much rock compresses under such pressure.

Basically, I am planning to write a fiction story about us visiting there. I will, of course, have to invent some sort of "warp drive" to get us there. But, other than that, I want the story to accurately reflect current technology. Specifically, could a LOX/methane rocket, which seems like a good choice because we could obtain the methane there, get us back into orbit?

I'm going to have the story be from the point of view of an anthroplogist who is sent along. I thought it would make for conflict among the crew if the non-scientists learned, only after arriving on the surface, that the scientists were going to boost the power of their rocket with flourine, which creates poisonous gas and will kill all the natives that the anthropologists have befriended.

Would flourine be necessary?

p.s. You are right - a six-foot-tall man should weigh about 190 pounds, yet 380-pound fatties manage to survive. But they have back and foot problems and are greatly helped by cars and electric scooters. I don't think that anybody in primative societies weigh that much.

 

[DaveC426913]

Basically, I am planning to write a fiction story about us visiting there. I will, of course, have to invent some sort of "warp drive" to get us there.

Not really. If you could create a propulsion system that could accelerate 1 g continuously, you would spend almost all your trip at near light speed. At that speed, it would only take 6 years of ship time to get there. Of course, 22 1/2 years would pass on Earth. When they got back, they'd be 12 years older but Earth would be 45 years older.

Here's a primer on Gliese 581c:
http://www.davesbrain.ca/science/gliese/index.html
(When I wrote this, 581c was the Good Planet, not 581d)

 

[qraal]

My own back-of-the-envelope estimates were for gravity of about three times that of Earth. But I was assuming more compression than you guys are.

I was a bit surprised by willem2's estimate of 1.91. You say 2.44. It sounds like nobody is really sure until we learn more about the composition of the planet. It is also possible that the pressure at the center of Gliese 581 d is far greater than anything we can do in experiments and we just don't know how much rock compresses under such pressure.

Hmmm. I'm not sure that's altogether true. But planets can be made of different stuff - more iron would allow for a denser planet. Earth's iron core is only 33%, but Mercury's is near 66% of the planet's mass. That would "shrink" the planet sufficiently.

Basically, I am planning to write a fiction story about us visiting there. I will, of course, have to invent some sort of "warp drive" to get us there. But, other than that, I want the story to accurately reflect current technology. Specifically, could a LOX/methane rocket, which seems like a good choice because we could obtain the methane there, get us back into orbit?

I'm going to have the story be from the point of view of an anthroplogist who is sent along. I thought it would make for conflict among the crew if the non-scientists learned, only after arriving on the surface, that the scientists were going to boost the power of their rocket with flourine, which creates poisonous gas and will kill all the natives that the anthropologists have befriended.

Would flourine be necessary?

I think that scenario is a bit extreme - and kind of sounds familiar - but the only near-term propulsion system that could reach orbit on such a planet is a nuclear thermal rocket. The orbital and escape velocity are double Earth's and chemical rockets just barely manage Earth. Having to reach 15 km/s just to hit orbit will need nuclear engines. That would very definitely cause issues for the natives

p.s. You are right - a six-foot-tall man should weigh about 190 pounds, yet 380-pound fatties manage to survive. But they have back and foot problems and are greatly helped by cars and electric scooters. I don't think that anybody in primative societies weigh that much.

Muscles and bone can do more than we give them credit for - it's the joints that fail too soon. On such a world a stronger kind of connective tissue would allow muscles to work at full strength. Hexapods sound logical on a high gee planet, but I'm not convinced. But it's your story, so write away! Just get your invented biology right so it's convincing enough.

 

[qraal]

Not really. If you could create a propulsion system that could accelerate 1 g continuously, you would spend almost all your trip at near light speed. At that speed, it would only take 6 years of ship time to get there. Of course, 22 1/2 years would pass on Earth. When they got back, they'd be 12 years older but Earth would be 45 years older.

Here's a primer on Gliese 581c:
http://www.davesbrain.ca/science/gliese/index.html
(When I wrote this, 581c was the Good Planet, not 581d)

If the planet has 3 gee surface conditions maybe the ship should accelerate at 3 gee so everyone can adapt? In which case the tau is more like ~2 years each way. If they cruise for part of the journey then the adaptation can be made gradual via a centrifuge habitat rotating faster over time. Perhaps they cruise at tau = 10, which at 3 gee is achieved in 0.97 years and 2.9 ly distance. Then they cruise over 14 ly before braking over the remaining 3 ly. Total tau time is 3.35 years. If they accelerate to cruising speed at 1 gee the distance is 8.7 ly and 2.9 years tau, then cruise for 0.84 years and brake at 3 gee. Total tau 4.71 years.

 

[Grozny]

I think that scenario is a bit extreme - and kind of sounds familiar - but the only near-term propulsion system that could reach orbit on such a planet is a nuclear thermal rocket. The orbital and escape velocity are double Earth's and chemical rockets just barely manage Earth. Having to reach 15 km/s just to hit orbit will need nuclear engines. That would very definitely cause issues for the natives.

Why does it sound familiar? I'm not very familiar with science fiction (I've written fiction before, but not science fiction) and it would be lame if my story duplicated some classic author's story.

Nuclear propulsion will not work for my story because they would know about that before landing - and even an anthropologist can guess that this is going to be hard on the natives.

The addition of flourine has to be an expedient measure which is taken so they can lift unexpectantly heavy cargo into orbit. Thus, the moral dilemma is whether or not to add the additional cargo if it means killing all the natives who have made a religious pilgrimage to the rocket, which they think is from the gods.

I picked Gliese 581 d largely because it's in the news these days, but I can use a made-up planet too. What gravity should it be for LOX/methane to just barely get them into orbit, but require FLOX for any additional cargo?

Would LOX/hydrogen be a better choice? I picked methane because I thought it could be manufactured on the surface; also liquid hydrogen requires heavy, bulky tanks. But the use of methane is not essential to my story. Frankly, it is hard to visualize how they're going to get any big rocket, regardless of fuel type, down to the surface without crashing it, even assuming that they can transport it all they way across interstellar space in the first place.

Having the natives all be hexapods is not essential to my story. If everybody is agreed that this is only necessary for planets with far greater gravity than chemical rockets can escape from, then I can drop the hexapod bit; though I kind of like the part I've already written about the scary hexadons who eat the friendly natives and, later, get in a pitched battle with the Marines.

At what gravity level do you think birds will fail to get airborne? I was going to have none at all, though perhaps I can have gliders that leap from cliffs, but are incapable of taking off from level ground.

Incidentally, the unexpectedly heavy cargo is diamonds. I am assuming that the additional gravity makes the formation of diamonds more common than they are here on Earth, where they must be formed far under ground and then brought to the surface, either through very deep mining shafts or where great upheavals of the Earth took place.

Is this true? Is greater carbon content and more gravity likely to result in a planet with diamonds strewn about on the surface?

I want this story to be as accurate as possible - not like Stephen King's science fiction that has even amateur scientists like myself rolling their eyes. King is a fine writer when he sticks to supernatural topics, but he has a high school level knowledge of science. I don't want people saying the same thing about me.

 

[DaveC426913]

At what gravity level do you think birds will fail to get airborne? I was going to have none at all, though perhaps I can have gliders that leap from cliffs, but are incapable of taking off from level ground.

What it would do is limit the size of flyers. Smaller creatures will have an easier time of flying than larger creatures. The cost to fly would be too much. Insects would do OK, but things larger than, say, hummingbirds would have too much mass to surface area.

But smaller mass means more primitive functioning, metabolically and intelligence-wise.

The Earth equivalent is insects.

Of course, if the atmo is significantly denser, that's different again.

 

[qraal]

Why does it sound familiar? I'm not very familiar with science fiction (I've written fiction before, but not science fiction) and it would be lame if my story duplicated some classic author's story.

I was thinking of "Avatar" actually, but trouble with the natives comes in many forms in SF. It's an old, old SF trope. Doesn't mean it can't be made interesting.

Nuclear propulsion will not work for my story because they would know about that before landing - and even an anthropologist can guess that this is going to be hard on the natives.

Nukes come in many forms and can have unexpected complications. A larger than Earth planet will most likely need some kind of gas-core engine to relaunch and will be tricky to land because of the steeper atmospheric gradient in the first place. No current technology would be sufficient for a 3 gee planet, but low efficiency gas-core rockets have been built in the past, so they're a near-term technology if needed.

Alternatively the landing vehicle might be a fusion pulse rocket. That'd require a large stand-off distance for safety, but not necessarily produce a lot of residual radiation - unlike the gas-core rocket. However the deuterium propellant does produce tritium when fused and that might be unusually toxic to the natives - a fact the crew wouldn't know in advance without detailed physiological studies. It really would be an "us or them" tension point if the ship couldn't leave for fear of poisoning the locals.

The addition of flourine has to be an expedient measure which is taken so they can lift unexpectantly heavy cargo into orbit. Thus, the moral dilemma is whether or not to add the additional cargo if it means killing all the natives who have made a religious pilgrimage to the rocket, which they think is from the gods.

Problem with fluorine is that it is a very rare element compared to hydrogen, oxygen or carbon. No one would land if they had to rely on finding a supply of fluorine. As for unexpectedly heavy cargo... seems a bit forced IMO.

I picked Gliese 581 d largely because it's in the news these days, but I can use a made-up planet too.

Wait a bit longer and a real planet around Alpha Centauri might be found in the New Year. A lot of people think there'll be an announcement this year.

What gravity should it be for LOX/methane to just barely get them into orbit, but require FLOX for any additional cargo?

Would LOX/hydrogen be a better choice? I picked methane because I thought it could be manufactured on the surface; also liquid hydrogen requires heavy, bulky tanks. But the use of methane is not essential to my story. Frankly, it is hard to visualize how they're going to get any big rocket, regardless of fuel type, down to the surface without crashing it, even assuming that they can transport it all they way across interstellar space in the first place.

I agree. It seems an odd combination. Perhaps they can make stabilised polymeric nitrogen, which packs a lot of energy into propellant without being nuclear. An ideal decomposition of polymeric nitrogen into N2 should produce an exhaust velocity of about 8.2 km/s and the propellant would be easy to extract. But, of course, it's non-toxic.

Incidentally, the unexpectedly heavy cargo is diamonds. I am assuming that the additional gravity makes the formation of diamonds more common than they are here on Earth, where they must be formed far under ground and then brought to the surface, either through very deep mining shafts or where great upheavals of the Earth took place.

Is this true? Is greater carbon content and more gravity likely to result in a planet with diamonds strewn about on the surface?

Diamonds form very deep in the Earth and get brought to the surface explosively via volcanic pipes. On a planet with greater gravity the depth will be shallower, but the energy needed will be the same - but a bigger planet should have more volcanic activity. So there might be diamonds strewn about.

I want this story to be as accurate as possible - not like Stephen King's science fiction that has even amateur scientists like myself rolling their eyes. King is a fine writer when he sticks to supernatural topics, but he has a high school level knowledge of science. I don't want people saying the same thing about me.

A laudable goal.

 

[qraal]

Here's a primer on Gliese 581c:
http://www.davesbrain.ca/science/gliese/index.html
(When I wrote this, 581c was the Good Planet, not 581d)

Hey Dave, you quote 25 parsecs as 107.5 ly, but it's only 81.55 ly. The Gliese Catalogue also has a few named stars further away than 25 pc.

 

[DaveC426913]

Hey Dave, you quote 25 parsecs as 107.5 ly, but it's only 81.55 ly. The Gliese Catalogue also has a few named stars further away than 25 pc.

Really? I'll look into that. Thanks.

 

[Grozny]

So a 7 Earth mass, Earth-like planet has a radius of about 1.7 Earths and a surface gravity of 2.44 gee.

Okay, I decided to go with 2.44 gee surface gravity and a nuclear powered rocket. I will just have the anthropologist assume that it was going to be LOX/Hydrogen because that was what the space shuttle used when it lifted her into Earth orbit. She's not a very technical person and could conceivably be oblivious to what type of propulsion they will use.

I will study up on gas core and fusion pulse systems and get back to you if I have any questions.

Fusion pulse sounds best for my story because an unexpected problem the humans face is crowd control due to the natives making pilgrimages to the rocket. Not expecting this, we might have reasonably assumed that we could chase them away and so the use of the fusion pulse rocket was not, during the planning stage, totally inconsiderate of the natives.

Is anything on a fusion pulse rocket inflamable or are any parts of it vulnerable to projectile weapons? Part of my story is that the natives are in the habit of carrying flamethrowers for self defense against hexadons. I had the humans forbid flamethrowers from the area, which left the natives totally dependent on the Marines to defend them from hexadons. But this only makes sense in the context of a chemical rocket.

If necessary, I can edit out the flamethrowers and give the natives some type of projectile weapon (possibly a recoilless rifle), but that's only an issue for the humans if the fusion pulse system is vulnerable to projectiles. However, I would like to keep the flamethrowers because they are more in keeping with the native's technology level. They are similar to where we were during the industrial revolution (steam powerered factories, paddleboats, etc.)

During the industrial revolution we did not know enough about metalurgy to make high-pressure firearms and had not invented smokeless powder yet either. But if a hexadon can fight through ATGW, then it is unrealistic to think that black powder weapons could do it any damage. Flamethrowers seem like a more effective weapon given the native's technology level.

Diamonds form very deep in the Earth and get brought to the surface explosively via volcanic pipes. On a planet with greater gravity the depth will be shallower, but the energy needed will be the same - but a bigger planet should have more volcanic activity. So there might be diamonds strewn about.

I describe small diamonds strewn about on the ground. But I also describe an open pit diamond mine where the natives use a large steam-engine-powered machine to split the diamonds into long sharp shards. They surround their villages with stakes made of diamond shards to keep the hexadons out.

Is this realistic? I describe the hexadons as being 20 feet tall and tough enough to shake of ATGW hits, so these shards would have to be at least two or three feet long. And there must be enough to put hundreds of stakes around a village. Could there be that many and that large of diamonds near the surface?

 

[molinaro]

Of course, if the atmo is significantly denser, that's different again.

And it is far denser. I see comments of this planet often making the incorrect assumption that it is in the Goldilocks zone of it's star. It is not. It can have liquid water on it's surface only because of it's very dense atmosphere making that a possibility at it's surface.

 

[mugaliens]

Okay, I decided to go with 2.44 gee surface gravity and a nuclear powered rocket.

Good assumption, as we're barely able to lift off the surface of our own 1.0 gee planet with any appreciable cargo using chemical means!