Increadibly large, hollow artificial planet

[nexium]

Let us a construct a hypothetical artificial planet out of unobtainium between Mars and Venus in a circular orbit radius = one AU. Since the inner planets will likely collide long term, we will make them moons of the incredibly large planet. The radius is one million KM, so it is larger than the sun, but about the mass of Neptune as it is hollow.<br /> Would it produce a total eclipse of the sun occasionally as viewed from Jupiter' moons. My guess is an impressive transit. What would the surface gravity be? Some claim a hollow (thin wall) sphere produces no gravity anywhere inside. I don't believe that. I would guess the gravity on the inner surface is about 1/2 the gravity on the outer surface You may assume a sphere wall thickness of unobtainium that is compatable with the properties of common glass, except a billion times stronger than glass. Will that give a generous safety factor if pressurized with 98% oxygen at 4 psi = pounds per square inch, less in some parts of the interior? Would the mass of the atmosphere inside exceed the mass of the unobtainium shell? If so, the atmosphere would shift the pressure and gravity gradients inside the sphere radically? What is the maximum air temperature inside the sphere, assuming 10% transparency of the entire EM spectrum, 10% reflection and 80% absorbion in the unobtaium? Wild guesses and redesign ideas appreciated. Neil

 

[tony873004]

If it's larger than the Sun, it would certainly produce a total eclipse rather than a transit. Why would something larger and closer appear smaller?<br /><br />This thing is so large that its surface gravity would be very weak, ~ 1/1435 Earth's surface gravity.<br /><br />Anywhere inside a hollow sphere, you would be weightless. I'm not sure how the 4psi of atmosphere would change this.

 

[heyo]

I guess it being hollow changes all this, but I thought that the gravitational attraction of an object was to it's center of gravity or center of mass, therefore if you were on the outside, you'd be getting pulled towards the center of the hollow sphere, and if you were inside, you would fall towards the center, and the ocilate back and forth until you slowed down from drag from the 4psi atmosphere and settled at the center.<br /><br />But I guess another way to look at it would be... well, I think of gravity as the typical "bowling ball on a mattress" model to depect an objects bending of space, minus the extra dimension of course. (that image works well for me) So maybe the hollow planet would be more analagous to a "metal hoola hoop on a mattress" - minus the extra dimention of course, where the edges would have some gravity but there's a "hill" in the middle where you'd be weightless if you were far enough from the edge.<br /><br />Heyo

 

[vogon13]

Suspect your 4 psi atmosphere will gravitationally collapse into a very bizarre star like object that will fuse oxygen into heavier elements until it reaches iron, then it will explode, dramatically. Hard to place this object on HR diagram due to its odd composition, but suspect it will be a dangerously brilliant and short lived star like thing. Interesting to study from a safe distance.<br /><br /><br /><br />Cola that has gone flat can be poured into the toilet bowl.<br />Heloise <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[Leovinus]

No, if you're inside, you're weightless. I remember that from my early college physics classes. <div class="Discussion_UserSignature"> </div>

 

[nexium]

Hi tony: Incredible is about 800 times the diameter of the moon, but Jupiter's moons are more than 1000 times farther from Incredible than Moon is from Earth. I think the total eclipse shadow diameter is directly proportional, but perhaps not. <br /> I had guessed the gravity would be very weak, especially when a very rough wall thickness calculation came out about 1/2 millimeter. Neil

 

[tony873004]

The surface gravity for any object can be computed with<br />g = GM/r<br />where G is the gravitational constant (6.67 * 10^-11) and mass is the mass of your object in kilograms, and r is your distance from the center.<br />On Earth's surface, you are 6,378,000 meters from its center. And Earth's mass is 5.97 * 10^24. If you plug these numbers into the formula, you get 9.81 meters / second^2, the value that is commonly accepted. Your object has a radius of 1,000,000,000 meters, and a mass of 1.0247E+26 kilograms. Just plug it in to the formula for surface gravity.<br /><br /><br />angular size = (diameter / (2*pi*distance))*360<br />You can plug in the Sun's distance and diameter to get its angular size, as well as your planet's diameter and distance to get its angular size. But no matter how you space your objects, if your planet is closer Jupiter's moons than the Sun, and is larger than the Sun, then it must appear larger and be able to cast a full umbra out to infinity.<br /><br />Steve is right. Your planet could not possibly hold the other inner planets in orbit around itself. If it were the size of Neptune, you might be able to hold 2 of 3 planets, but being larger than the Sun, your planet occupies most of its sphere of influence and will not be able to hold anything in orbit in a prograde direction. However, it can temporarily hold objects in close retrograde orbits.

 

[nexium]

Hi stevehw33: Thank you for the input. Such engineering feats are very improbable in this century but almost this spectacular perhaps someday. Suppose we put the smaller moon of Mars in circular solar orbit at one AU= The distance Earth is from the Sun. We orbit a trillion tiny segments of a sphere about 990,000 kilometers from that former moon. We can now assemble the segments so they form what will be the equator of the incredibly large planet. The last few pieces will increase the radius to one million kilometers which will make the ring slightly over speed. Minor station keeping will be needed to keep the ring centered while we add more segments from the stockpiles orbiting slightly closer to what used to be the small moon of Mars. When the sphere is completed we can dismantal the former moon of Mars for raw materials. We can then add some oxygen to the inside. Move Mercury and Venus closer to the sun. Put the larger moon of Mars in circular orbit about 10,000 kilometers above the surface of Incredible: The Earth's moon, about 500,000 kilometers above the surface of Incredible, Mars a million kilometers above the surface of incredible and Earth 2 million kilometers above the surface of incredible. Incredible needs to have how much more mass than Neptune to make this reasonably stable? Perfect stability is not needed as we can do minor station keeping very long term. Neil

 

[Leovinus]

Tell me again why anybody would want to do this? <div class="Discussion_UserSignature"> </div>

 

[5stone10]

How does this differ from a Dyson Sphere ?<br /><br />They don't even acknowledge Dyson -- /> Eder had this response ... "As far as I know, I invented the bubbleworld idea in response to a dinner discussion at one of the Princeton Space manufacturing conferences." <br /><br />But -- /> " ... third type of Dyson sphere called a Dyson bubble ... composed of statites that hover motionless relative to the englobed sun using light pressure ... has such low mass requirements that it could potentially be built from the material contained in a single small moon or large asteroid."

 

[nexium]

Thank you eburacum: I agree it has many simularities to a Dyson sphere except the Dyson sphere needs to be much larger and/or deal with incredibly high temperatures. A very advanced civilization would likely build a much smaller sphere which could not hold moons except with considerable station keeping before they would attempt one this large. A step up from this size would be a sort of Dyson sphere enclosing a gas giant planet such as Neptune. All our gas giant planets produce some internal heat which would be trapped inside the sphere. If the sphere absorbed 80% of the long wave infrared radiation from the planet, the unobtainium would get quite warm and thus send infrared radiation to the cloud tops of the gas giant. The cloud tops would be warmed, slowly for perhaps ten million years. Would any one care to guess how warm our 4 gas giants would be inside a green house sphere? Neil

 

[nexium]

Hi tony: Using your formula, I got g = 10 million for Earth and 6 million for Incredible. That Neptune has 17 times the mass of Earth seems reasonable. Working the problem in kilograms and meters seems reasonable. I think the denominator should be r squared which gives 10 meters per sec per sec for Earth which is close and 0.006 which is about 9 times the gravity you got on page one for Incredible. <br /> If my arithmetic is correct; Earth's gravity at The Moon's orbit is 0.0001 Earth's surface gravity, so it appears that Increadible could hold on to a one earth mass moon orbiting a few thousand miles above the surface of Incredible, perhaps 6 moons with a modest amount of station keeping. Neil

 

[tony873004]

oops, you're right. r^2. <img src="/images/icons/smile.gif" /> <br />(1/1435) * 9.81 = 0.00683623693379791<br />we got the same answer if I truncate instead of round.<br /><br />The problem with Incredible holding any moons is its sphere of influence. <br /><br />r = a * (m/(3M))^(1/3)<br /><br />r is the hill radius, m is Incredible's mass, M is Sun's mass, a is the Sun / Incredible distance in meters.<br /><br />r = 3.8 million kilometers. The planet's radius takes up 1 million kilometers, which leaves you with 2.8 million kilometers of altitude to play with. And this assumes retrograde, chaotic orbits. That's not much room for 3 planets to orbit.<br />

 

[5stone10]

Sounds like 'hair-splitting' to me in order to get credit for something that isn't really radically different !

 

[nexium]

Hi Leovinus: Trillions of gentically modified humans could live inside such a sphere in spaciousness rarely known on Earth. Amittedly I don't have clue how we could feed that many people. If we can build such a planet; odds are good we have some major advances in food science.<br /> 2 We can also harnass moderate amounts of energy from the difference between inside and outside temperature, but likely not enough energy for a trillion people. 3 Building this planet is a step toward building a Dyson sphere. It is prudent to practice medium scale before going for bigger engineering projects. Neil

 

[le3119]

I've thought about an artificial terrestrial world, roughly Earth-sized with a surface gravity of 1.0, located further out between Jupiter and Saturn. A ring of nuclear fusion lamps would keep the world warm enough to permit liquid water and an Earthlike atmosphere. A magnetic field would be generated by rotating several rings located further out to create a solenoidal "dynamo" EM field to deflect cosmic rays. The outer crust could be divided into several layers, allowing billions of inhabitants. The issue is where do we get the material to form such a world without disrupting the existing planets, especially the inner ones we depend upon?

 

[ehs40]

this sounds like a cool idea but why dont we colonize a real planet befor we build a planet. besides it would be easier to live on something that is already there

 

[nexium]

We could gut Venus for materials. It is unlikely that Venus will ever have life other than in the upper atmosphere. There would only be enough mass for about 0.8 g at the surface, but 0.8 g is likely enough to keep humans healthy. Neil

 

[valareos]

attracted to the center of a hollow planet?<br /><br />Dont think so. Reemmber, you are dealing with 5+ dimentional space here. NOT a simple 4D space.<br /><br />If you were at the dead center of the earth (and could survive) you would NOT be weightless, you will have a negative weight. Why? the mass AROUND you has a gravitational pull, pullign you in all directions at once. THere is a whole lot more mass above you than below you at that point.<br /><br />Edit: "below meaning towards the center"<br /><br />a hollow sphere then... you are attracted to the center of mass, indeed, but in the hollow sphere, the "center of mass" would actually be a 2d sphere in the middle of the mass making up the hollow sphere. This means a person inside the sphere would be attracted to the edge, NOT the center, allowing one to walk on the inside edge of the sphere.<br /><br />making a sky the other side of the world

 

[josh1943]

in reply to above. wouldnt you be attracted in all directions at the same time the same amount therefor not move. even if you ddid move out of the center as soon as you did wouldnt that mean theres more mass on one side then the other then pull you back towards the center.

 

[valareos]

for a solid planet, yes. but you are being pulled from all directions at once in the center (a scale will show negative) try to move out a bit, and you are pulled back to the center of mass.<br /><br />on a hollow planet, the center of mass isnt the center of the sphere

 

[formulaterp]

Valareos,<br /><br />I am confused. <br /><br />What do you mean by the center of mass being a 2d sphere? What exactly is a 2d sphere anyway?<br /><br />How would a scale "show negative"?<br /><br />Inside a hollow sphere of uniform density and ignoring the gravitational effect of anything outside the sphere, you would be weightless. At all points within the sphere. In the center, slightly off center, along the interior surface. Weightless.

 

[najab]

><i>What exactly is a 2d sphere anyway?</i><p>Here you go:</p>

 

[nexium]

Text books for at least a century, teach that there is no gravity anywhere inside a hollow sphere in free fall. Perhaps they assume zero wall thickness or some other unreal condition. Some of us think there would be a small gravity outward, near the inner surface. <br /> If you insist on zero gravity, what would it be like to climb though a hole from the outside to the inside of a hollow sphere in free fall? Perhaps horizontal gravity to the closest surface at the half way point; then very weak gravity approximately outward as you moved onto the inner surface falling to approximately zero as you moved away from the hole on the inner surface?<br /> 2d likely = two dimention, but I can't guess how that relates to this topic. Neil

 

[valareos]

First clarification.<br /><br />The measured gravity at the center of a solid planet would show negative. Why? because there is more mass "above" (away from center of mass) than there is "below" (towards center of mass) this means you will be pulled by a gravitational force AWAY from the center of mass, in all directions at once (and since it is gravity pullign you towards the center of mass, negative gravity pulls you away, even though, technically in this example, it is the exact same force! its like how a neutron is its own antimatter)<br /><br />2d sphere...<br /><br />This relates to a hollow planet. A solid planet would have a center of mass as a point. on a hollow planet, the center of mass can be described as approximately halfway from where you are currently standing to the end of the mass, meaing that a person either on the outside or inside would trace out teh center of mass as a sphere. whos radius is large enough to coincide with the mid point of the mass as calculated from any one spot.<br /><br />This may be a sphere.. but it isnt a 3d sphere.. it would have a 0 thickness. take a piece of paper, roll it so the ends meet. The paper is still a representation of 2 dimentional space, that has been warped in 3 dimentions so the ends meet. The stick man on the paper will still see himself on a flat world of the paper, cause his perception is warped as well.<br /><br />that is what I mean by a 2d sphere... a two dimentional object warped in 3 dimentions due to an outside source, yet is still a 2 dimetional object