How Big Would A Planet Have To Be To Have Earth's Gravity?

[SAZAR]

I had this nice cute idea about a small inhabitable planet that is, say, 1km around equator (that's about 320m in diameter).

Is it possible that such planet has gravity the strength of the Earth's gravity? (or, to rephrase the question, from what matter should that 320m diameter planet be made of (it's nucleus (so there is fertile land on top)) in order to have Earth's gravity)



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(I guess something must "hold down" the atmosphere thick as the one on the Earth (hmm... and what atmosphere would it be (what about rain, thunderstroms etc?)))

(also: what rotation speed must it be in order for it to have the Earth temperature range (same distance from our Sun as the Earth))

OR!:

To rephrase the first question even more: what diameter a planet must have in order to have Earth's gravity strength if its nucleus is made of material (known to us) with greatest gravity potential (non-radioactive material mind you). So: " diameter = ? "

 

[berkeman]

Living on the outside of the 1km sphere seems like it would have many problems, especially with the depth of the atmosphere. Maybe you should invert the topology, and live inside a 1km cylinder that is spinning to give you gravity. Like in this book:

http://en.wikipedia.org/wiki/Rendezvous_with_Rama

 

[SAZAR]

Living on the outside of the 1km sphere seems like it would have many problems, especially with the depth of the atmosphere. Maybe you should invert the topology, and live inside a 1km cylinder that is spinning to give you gravity. Like in this book:

http://en.wikipedia.org/wiki/Rendezvous_with_Rama

Yeah, I've had that idea too (only regarding a ball with a source of light in it's center). I guess only zone around equator would be inhabitable. (I remember seeing such thing in StarTrek too..)

...But this with small regular planet has its point in itself, so the question still stands.

(Why would depth of the atmosphere be a problem (planet would have enough gravity strength just like Earth))

 

[DaveC426913]

You could do it with a fictional form of artifical gravity, but gravity-from-mass on such a small body will give you lots of problems with a gravitational gradient i.e. g will be noticeably stronger at your feet than at your head.

 

[SAZAR]

How come?

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Phhhh... Let's make it simple... If entire planet is solid ball made of Bismuth how wide would that ball be if it's gravity is equal to Earth's gravity?...

 

[marcus]

How come?

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you can forget ordinary materials (even if solid gold, the ball would not have enough mass. bismuth. depleted uranium. all too light)

there would be one obvious way to do it, which is to get a black hole of the right mass, and carefully enclose it, and put it at the center of your planetino

the rest could be made of anything-----plastic, old TV sets, whateveryou say you want the radius to be R = 160 meters
suppose the height of somebody is 1.6 meters
if the man's feet are at 160 and his head at 161.6 meters
then his HEAD IS ONE PERCENT HIGHER
and that means that GRAVITY IS TWO PERCENT WEAKER at his head than at his feet.

I do not think that this would necessarily be noticed in everyday walking around.

If you lay down on ground your weight would only be about 1 percent more than it was when you were standing.

So I disagree with what DaveC said about noticing it. but there would be a gradient.

What berkeman says about ATMOSPHERE THINNESS is right.
gravity falls off as square of distance, so 160 meters up (total 320 from center) it would be only ONE QUARTER as strong

as you go out it would quickly get too weak to hold on to the air
so your atmosphere would not be very deep
so it would not have enough mass to give you comfortable pressure.

 

[DaveC426913]

Let's see, according to Wiki, Bismuth at room temp has a density of <10g/cm^3. Earth has a density of ~5g/cm^3. So, a bismuth planet excluding any heating/pressure factors (which is a BIG exclusion) would only need to be a little more than half the volume of Earth. That would be a sphere around 9400km in diameter, or about 75% of the diameter of the Earth.

 

[DaveC426913]

and that means that GRAVITY IS TWO PERCENT WEAKER at his head than at his feet.

I do not think that this would necessarily be noticed in everyday walking around.

If you lay down on ground your weight would only be about 1 percent more than it was when you were standing.

So I disagree with what DaveC said about noticing it. but there would be a gradient.

I guess that depends on whether you want to do anything more than standing up and lying down.

How much would you weigh on the second floor of a building? It would be pretty frustrating to eat your lunch everyday and miss your mouth and bonk yourself in the nose because you ate on the second floor today and haven't adjusted to the change in weight.

Escape velocity would drop very rapidly with altitude. I don't know how rapidly, but you can see how this might be very bad if you miscalculated. More to thje point, you might need x velocity to get off the ground at all, but that same velocity at 100 feet would put you in orbit - or worse.

And the first kid that digs a hole in his backyard might never be seen again...

 

[berkeman]

How much would you weigh on the second floor of a building? It would be pretty frustrating to eat your lunch everyday and miss your mouth and bonk yourself in the nose because you ate on the second floor today and haven't adjusted to the change in weight.

:rofl: Pffftttt! :rofl:

You just made me spit my coffee at my computer monitor! Luckily, though, I was working in my basement office, so I only sprayed the keyboard.

 

[SAZAR]

Interesting...
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(now when we're already at gravity-fun, imagine playing basketball in some hall on the Moon... actually - how high/far could a person jump there?)

 

[DaveC426913]

actually - how high/far could a person jump there?)

Six times that of Earth. From a standing jump, straight up, you could clear maybe 18 feet.

In fact...

Moon x6
Mercury x 2.65
Venus x 1.10
Earth x 1
Mars x 2.64
Jupiter x 0.39
Saturn x 0.94
Uranus x 1.10
Neptune x 0.88
Pluto x 13.2
Sun x 0.04

(shamelessly yoinked from http://ltp-education.gsfc.nasa.gov/Gravity.doc" )

 

[SAZAR]

Mars is nice.

 

[tony873004]

And the first kid that digs a hole in his backyard might never be seen again...

But gravity would get weaker in the hole.

Actually, the kid would never be able to dig the hole. Imagine how much a toy shovelfull of dirt would weigh if it were dense enough that a 320 meter diameter world had the same g as Earth.

 

[berkeman]

But gravity would get weaker in the hole.

Not in the scenario that we were discussing, where there is a black hole in the center and separate dirt as a crust. If it were all uniform super-heavy matter of some unknown kind, then yes, gravity would be less as you descend down into that matter.

 

[DaveC426913]

Fast fact:
A planet made of Osmium or Iridium (the 2 densest elements on the periodic table) - that had the same surface g as Earth, would be 1/4 the volume of the Earth and 7560km in diameter - about 15% larger than Mars. *(again, discounting compression and pressure effects)

(If I have done my calcs right)

 

[SAZAR]

*(again, discounting compression and pressure effects)

But, that changes results greatly... or not?

 

[SAZAR]

Mass (density) equals gravity.

Does this mean that if you would dig a tunnel deep enough toward the center of THE EARTH (and solve the heat problem...) at some point you would have the weakest gravity toward down, because now mass of the Earth all around (and up) compensates regular downright gravity?

And, then - how does this affect material at the center of the Earth - I mean - there is mass all around and it PULLS (not push) from center outward? Zero gravity??

And so, gravity (pressure on material etc.) is storngest at some point between center and surface of the Earth?

(Do tell what's wrong with this way of thinking?)

Or... is gravity something that is not exacly directly related to mass, but rather a phenomenon that occurs on contact between mass and vacuum - a phenomenon that implies that mass takes up space, so space (vacuum) creates a "pressure" against mass because it "seeks ways" to rush-pour into mass but it can't so everything near enough that huge mass is affected by that rushing "pressure"? (if we assume that space is a vast mass of free primary quantum particles just like ocean mass is a vast mass of water)

(so there are no actual "gravitons" or what you-may-call-it)

So it also just SEEMS that masses actually interact in terms of gravity "field" - it JUST seeeeeeems because two masses are instad attracted by vacuum between them??

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Or is gravity a surface tension of matter on great scale (elastic intermolecular forces)

(Sheesh...)

 

[DaveC426913]

g is strongest at the surface of the Earth, where gravity from the entire mass of the Earth is pulling in one direction.

g is zero (that is, net zero) at the centre of the Earth, where the gravity from equal amounts of mass in all directions cancels out.

Gravity drops off linearly from the surface to the centre, where there is more mass below you than above you. In fact, it's a surprisingly simple relationship. If you are 1000 miles from the centre of the Earth, the g you will feel is equivalent to standing on a sphere that is 1000 miles in radius. Everything else - i.e. the hollow shell volume outside that sphere of 1000 mile radius - cancels out, resulting in no net gravitational force.


There are quite a few threads about this in this forum and elsewhere on the web.