turin said:
By "planet", do you just mean a solid sphere?
You're right-- I didn't carefully consider the definition of a planet. Thanks for pointing this out. I should have said something along the lines of "object in space cool enough to walk on. " And for simplicity, I'd like to first assume that this object is pretty much uniform in density. But I would also like it to be spherical in nature-- much like planets. That's probably why I called it a planet in the first place-- it reminded me of mercury or something, or the moon ( I know the moon is not a planet-- it is a satellite). So in short, let us assume that this object is a sphere, cool enough and solid enough to walk on, and is uniform in density. And let's assume that this thing is not rotating, or in any kind of orbit-- for simplicities sake.
turin said:
Is that gravitational acceleration at the surface? Given that a person's average height is not much less than the size of your "planet", this is going to require a precise elevation at which g is defined. I'm assuming that you are just trying to figure out if there is a logical inconsistency for such a "planet".
Yes, g= 9.8m/s^2, at the surface of the "small planet".
turin said:
(Be careful with the word "prove"; you should at least state your assumptions.) I suppose you just want to do this nonrelativistically, so you probably used Newton's gravitation law to find M and then you found that escape velocity was less than c? I agree that this doesn't seem anywhere close to a black hole. BTW, what kind of object would you say is comparable in "size" (i.e. Schwarzschild radius) to a black hole with this mass?
Here's why I decided this thing wasn't a black hole:
"If a spherical, non rotating body with mass M has radius less than Rs, then... the body is a black hole"
Here is the equation associated with this:
Rs = 2GM/(c^2)
when I did the calculation, I found that Rs for my "small planet" was approximately 2/(c^2), which makes 2m look large! Therefore, I was able to conclude from the given definition that my "small planet" was not a black hole-- the radius of my "small planet" is too large.
To figure out the mass of my "small planet" in the first place I used the equation:
m = gr^2/(G)
, where g = 9.8m/s^2, r = 2, and G = about 6.67X10^-11
turin said:
Well, I agree with the density range, but it just depends on what you mean by "star".
What I mean by star... Well since my "small planet" falls in the density range of a neutron star and a white dwarf, and all the "cooled" metals known on Earth are about 10^7 less dense than my object, then it seems to me that if my object in fact could exist at all, it would only exist as something liquid or gaseous and certainly not a cool solid.
That is just the logic in my head. I'm running into trouble because I can't find a way to prove the logic in my head.
turin said:
Did you calculate the pressure? Have you ever seen a phase diagram with liquid or gas ON THE BOTTOM?! What mechanism do you think supplies the pressure (i.e. what conteracts the gravitational collapse)? Would you say that a white dwarf is not solid? What about a neutron star? What about some other kinds of material?
This is where I find myself "stuck." I don't even know how to even clarify my issues enough to know what I need to do to be able to calculate the pressure; All I have at my disposal that relates to pressure is the equation pv = nrt (which I know is just Ideal gas law, and may or may not be applicable to my planet at all. And even if we assume that it is, I find that the higher the temperature, the less dense the object, because of the equation d = Pm/(nRT), which goes against my logic). So I find myself in a pickle (oh, and another equation is p = df/da -- which I wouldn't even know where to begin-- I don't know anything about the force for df).
So I've found myself in a complex situation; I want to be able to say that because of the density of my object, it would be impossible for it to be solid. I just don't know how to go about proving that because I don't even know what material my planet is. But to make things a bit more simple, we could assume that it is made of the most dense element known to man, and then some how prove that this material itself would even have to be in liquid or gaseous form on my planet to match the density of my planet.
All I know is that platinum has a density of 21.4 x 10^3 -- higher than gold, lead, etc, so to make it match the density of my planet (something X 10^11), it would have to be compressed by pressure or something at the very least! And because of this, would most likely not be in solid form! I'm not convinced that platinum is the most dense element, but I am convinced that all metal elements only have a density around something X 10^3, more than over a million times less dense than that of my planet.
turin said:
Well, I would agree with your conclusion, but for a different reason. Suspend, for the moment, your disbelief about the solidity of the "planet" (because that just amounts to finding the right material). What happens when you take a step? Think center of gravity and ability to balance.
From this statement I gather that you think such a "small planet" could exist in space, and be solid, if it were made of the right material. But keep in mind, the right material would have to be manufactured naturally by the universe, not by humans. Do you think such a material exists naturally in the universe?
I also gather from "What happens when you take a step? Think center of gravity and ability to balance." that you believe we might need to crawl around the planet rather than walk. I'm really not sure of the implications of having the gravity of the Earth on such a small planet. I draw a blank when it comes to thinking about what we might actually experience physically. I certainly wouldn't object to you saying the consequences out right!
turin said:
Why? The pressure at the bottom of the ocean is immense. What do you think the temperature of the water is down there?
You know, I bet it is freezing down there. Cold air is a lot denser than hot air. I would be willing to bet that cold water compresses "nicer" than hot water (hot expands, cold shrinks). So am I thinking in opposite terms when it comes to my planet? Is the truth of the matter that my planet would have to be really really freaking cold? I would like this alternative too.
I do believe that temperatures near absolute zero can exist in space somewhere. But the possibility of a spherical object even forming under such cold conditions is highly unlikely. Things tend not to want to move at such extremely low temperatures right? Would the particles of my planet even come together if this were the case? I assume gravity works under all conditions, so they probably would. But what kind of phenomena would cause...
I never thought of the situation in which my planet was the result of beginning as a star, and then having been cooled down over long periods of time, having been the core of a super giant or something...
"As you may know, a white dwarf is the cinder of a star which used to be like the Sun. At the end of its life, such a star expels much of its atmosphere, and the nuclear fusion stops. The hot core, about the size of the Earth but much denser, becomes exposed: this is the white dwarf.
When a star has just become a white dwarf, it is hotter than 100,000 K (about 180,000 F). It then gradually cools --- after many billions of years, it can become cooler than the Sun (which is about 6,000 K). So there is no particular temperature associated with the white dwarfs. " [
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970512e.html]
Note however; this is still not cool enough to walk on right? It would probably still be glowing a little bit? Well, I guess we can compare this to walking on the moon. How hot does the moon get in the sun?
"Maximum surface temperature 123°C
Minimum surface temperature -233°C"
[
http://209.85.173.132/search?q=cach...erature+of+the+moon&hl=en&ct=clnk&cd=1&gl=us]
I would say this is a lot cooler than 6,000 k! And we all know the moon is a lot less dense than my planet!
I don't really care if I'm right or wrong. I just would like help proving the existence or non-existence of such a small "planet" that could exist naturally in the universe without human or "divine" intervention.
The whole point is, could there ever be such an object that we could walk or crawl on in which we could clearly see that we were "upside-down" as opposed to the Earth where we couldn't tell if we were upside down relative to someone else on the exact opposite side of the Earth because the Earth is too freakin' large to notice the difference.
All I know is that I've eliminated the danger of it being a black hole. Can such a dense object exist that is cool enough to walk, crawl, be on?
I don't know how to go about proving it one way or the other; that's what I am asking help for.
It would be interesting to know what the physical effects of being on such a planet would feel like; would it feel like the earth, or would it be much different?