What would be the smallest plausible density of a potentially habitable rocky planet? Mean density of Earth is 5514 kg/m³. Density of aluminium, which is quite a common element, is 2700 kg/m³. I often come across Earth-sized or larger desert worlds less dense than that. What elements or compounds would a rocky planet have to be made of to have a mean density of say 2400 kg/m³ or even lower? (I find such mostly as tidally heated moons of gas giants). By rocky I mean a planet containing no volatiles like hydrogen, water and ices (methane, ammonia and others like these).

On the other end would be very dense planets of mean density above 12000 kg/m³. Am I right if I conclude that iron/nickel mixture can get compressed by the planet's mass itself?

What would be the smallest plausible density of a potentially habitable rocky planet?

According to Space Engineer, SE uses the mass-radius relationship for planets to determine how big a planet should be for a given mass and type.  Figure 4 from this paper is particularly helpful:



This basically shows what you might expect.  For a given mass, iron planets are the smallest (most dense), followed by "rocky" worlds with mixtures of iron and silicates, then planets with more water in them, and finally up to gas giants.  We can also see that as a planet's mass increases, the size increases more slowly, and eventually flattens out.  This is the compression effect you pointed out.

To make it a bit easier for us to interpret here, I used the formulas from the paper, and re-plotted for density vs. mass.  I also add a few curves for different types of planets with high carbon content (carbon monoxide, graphite with iron core, and silicon-carbide with iron core).



Now we can clearly see how the density increases due to the compression effect, or read specific values.  The lowest density iron planets would be around 9 or 10 g/cm³, while silicates can be down to about 4 g/cm³.  Mars also gives us a nice benchmark of 3.93 g/cm³ at 0.107 Earth masses.

And this is probably about as low as we can get for a "rocky" planet.  To be less dense than that, we must increase the proportion of lighter materials.  Most commonly this will be water, but carbon also works -- and that brings us to the interesting case of carbon planets.

Currently carbon planets are not specifically shown in Space Engine, though they may be added later.  They are thought to arise in systems with a high abundance of carbon relative to oxygen.  Their structure would consist of iron, carbide, graphite (maybe even diamond?) and hydrocarbons.  Depending on the mixture, a carbon planet will have a density somewhere between a silicate planet and a water planet.

So with those super-low density deserts you're finding, I'm not entirely sure what's going on.  They are too low density for a purely rocky planet.  Perhaps Space Engine is modelling the planet as a silicate-water mixture (like the dark blue dotted or dash-dotted curves in the first figure), but with no water on the surface and therefore it is classified as a desert instead of a terra, but this is just a guess.

Quite hard to understand because of my poor english, but I kind of get what he meant. Very very interesting!
I always considered "c" velocity as a consequence of space-time "friction", as much as you reach that speed, the force you need to win the space-time friction is always higher and higher. I know it's a wrong concept, but it helps imagining what keeps every object "below" that speed.

It is definitely not your English -- I think this episode is very tough conceptually and also explained too hurriedly.  But yeah, the most important takeaway message from it is that 'c' is not just the speed of light, but a fundamental limit to the speed at which any information can propagate in the universe.  It is the speed of 'causality', and it is related to the structure of space-time.

Thinking of the increasing difficulty of accelerating a mass closer to the speed of light as a 'friction' is indeed a bit wrong, though I get the appeal of it.  I normally don't want to tell people not to use a conceptual device if they feel that it helps them, but in this case I hope I can convince you to try to move away from it. The problem with it is that it can get your mind stuck with thinking about things in one frame of reference, rather than thinking about how to switch between different frames of reference, which is what relativity theory is all about!

The only part of the video I didn't understand (and it's the central one so probably the most important) is why you don't need to delete earth motion around the sun and such. I mean... Galileo's transformations are wrong, ok, but why doesn't "c" depends on reference frame?

Yes, this is the heart of the whole thing.  Let's start by thinking of the Galilean transformation.  The Galilean transformation is simple and intuitive.  Let's say you're sitting on a planet, and your friend zips by on a space ship at 0.5c.  While he passes you, he launches a probe ahead of him, which leaves his ship at 0.4c.  How fast is the probe moving relative to you?  

Intuition would suggest to simply add the numbers together.  0.5c + 0.4c = 0.9c.  And that's exactly what Galilean transformation says to do!  But it is wrong.  It has to be wrong, because it implies we could get faster than light motion by just adding slower-than-light velocities together.  Furthermore, it implies that we would observe a faster or slower speed of light, depending on how fast we are moving.  By observation, we know this is not true!  The speed of light is always the same, and you cannot reach or exceed it.

So to describe nature, we must replace the Galilean transformation with something else.  It must describe how to transform between different frames of reference and find the same speed of light in all of them -- that is, the speed of light must be invariant.  

That's where the Lorentz transformation comes in.  It has several bizarre consequences.  In order to preserve the speed of light for everyone, space and time must change depending on your motion.  Clocks tick more slowly at high speeds, and distances become shorter.  Velocities must also add together in a non-intuitive way.  

In the earlier example with your friend and the probe, you see him moving past you at 0.5c, and by symmetry he sees you moving past him at -0.5c.  He sees his probe shoot out in front of him at 0.4c.  But you see the probe moving past you at 0.75c!  Not 0.9!

The problem with describing this as friction is that it works the same way whether you're describing the motion of his probe, or if he tries describing how things are moving on your planet, or anywhere else.  There is no preferred reference frame.  Relativity describes how to describe relative motions between any frame of reference, and all frames are equally valid.  That's why you don't need to delete the motion of the Earth or anything like that.  A laboratory on the ISS orbiting Earth at a mere ~7km/s is just as good a place to do physics as one on a spaceship buzzing past at 299,000 km/s.  Physics in both works the same!  And it's just as difficult to accelerate the ISS to match speed with the speedy space ship as it is to slow the speedy spaceship down to match the ISS (assuming they are the same mass).  Indeed, the speedy space ship can argue it is at rest, and it is the ISS that's moving very fast.  Both places are equally valid places to call "at rest".

So finally, the reason we can't reach the speed of light is because the way the Lorentz transformation works only allows velocities to add together in a way that approaches c, rather than added directly as we might think.  No matter how fast you go, c is still faster, by exactly c!  This is weird but true, and for it to be true other weird things must also be true, like the relativity of time and space.



I have no idea if that all makes things more clear or less, but I do hope it helped. Relativity is a very difficult topic, and it takes everyone a while before it finally clicks.  So don't feel bad if it is still very strange!

No matter how fast you go, c is still faster, by exactly c!  This is weird but true, and for it to be true other weird things must also be true, like the relativity of time and space.

The weird part of it is that logic would say "so if I'm travelling at 0.9 c but I'm considered at rest so c is faster than my speed by c, then I'm able to accelerate trying to reach 1.9 c that for me equals 1.0 c", but no, doesn't work like that!

Still, if on your ship that goes at a speed of 0.9 c you try to measure the speed of light, you would always measure 299792458 m/s, and it doesn't depends nor by direction nor any other variable, according you measure this speed in the same way you would on earth. These two statements seems to contradict each other, that's why it's so hard to understand. 

The weird part of it is that logic would say "so if I'm travelling at 0.9 c but I'm considered at rest so c is faster than my speed by c, then I'm able to accelerate trying to reach 1.9 c that for me equals 1.0 c", but no, doesn't work like that!

That's right, what's actually happening is you're saying "I'm moving at 0.9 c relative to something (call it reference frame Wats), but I'm also at rest in my own frame (call it frame Salvo1)".  Then let's say you accelerate to 0.9 c relative to frame Salvo1.  This makes your velocity relative to frame Wats 0.9945 c, not 1.8 c!  

The way the time and space transform between these frames makes it so that, according to Wats' frame, your clocks are first ticking 2.29 times slower than his, then they tick 9.53 times slower.  Your ship and everything on it are also length contracted by these same amounts!  And this works the other way, too.  You say that time and space and Wats' frame are altered in the same way.  It's important to realize these aren't just optical illusions, but real effects with real consequences!

Still, if on your ship that goes at a speed of 0.9 c you try to measure the speed of light, you would always measure 299792458 m/s, and it doesn't depends nor by direction nor any other variable, according you measure this speed in the same way you would on earth. These two statements seems to contradict each other, that's why it's so hard to understand. 

It's weird because we live our lives at speeds which are much, much slower than c relative to our immediate surroundings, so all of our experiences are very well described by the Galilean transformations.  But if c were something like a few hundred m/s, then all this special relativity stuff would be obvious to us.  Like "duh, time slows down and lengths contract when I'm moving faster."

There was a game produced by MIT a while back called A Slower Speed of Light, which is free to download and play with, and it really helps visualize some of the weirdness of special relativistic effects (particularly the optical ones).  I highly recommend it!

FUN FACT:  Time passes more quickly by 1 nanosecond per day for every 107 meters (350 feet) of elevation that you gain (for the range of altitudes on Earth's surface).  Some will think the rotation of the Earth should also make time pass more slowly closer to the equator, but this is actually wrong since it exactly cancels the effect of the equator bulging out a bit farther from Earth's center.  So the only important change is due to altitude relative to sea level.

Your head has also experienced a few more nanoseconds of time than your feet, assuming you haven't been standing on your head most of your life.

Salvo, the trouble with relativistic speed is that we have a stubborn conception that speed requires a common time reference.  To approach relativity, I think the first idea that must be scrapped is the concept of a fixed flow of time.  When you do that, then consider the implications.

Salvo,
imagine that everything that exists in the universe is moving with light speed in space time.
The faster an object moves in space, the slower it moves in time. This means that for a photon the time stands still.
The slower the object moves in space, the faster it moves in time.
One could say that for us, which we move very slowly in space, the time passes with light-speed.

Abandoning the notion of absolute time (and space) and thinking of the consequences helps a lot.  But in my experience, one of the more difficult obstacles to people first learning relativity theory is in establishing and working with different frames of reference.  It's not something we usually think about very deeply in day-to-day life.

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Most relativity texts and courses will start out by working through physics in different reference frames using the Galilean transformation, and then point out how its predictions fail.  A deep principle of nature is that the laws of physics work the same way no matter where you are, or how fast you're moving.  You can be on a train moving at constant speed and you have no idea whether it is moving or not if you can't see outside.  A thrown ball behaves normally and so does a laser beam.  

So the motivation is to find the transformation that correctly describes how physics can work the same no matter what your speed is, and a consequence of preserving these laws is that the speed of light will be a constant, while space and time are no longer the absolute things we thought they were.

What are those whitish 'cracks' you see around the surface of the sun, notably around sunspots? They're visible optically but only near the solar limb. Spicules perhaps?

Okay, I don't know where to post this, so I will post this question here.

This is related to eclipse coming in 21st of August. But, I have something interesting. I tried somewhere in previous month to advance time in Space Engine to the date when eclipse occurs. Then I would land in the America at the spot where it should be total eclipse. As I was waiting, I saw the moon just passing by the Sun not even touching it. Actually, it wasn't even close touching it. I also tried that recently but it didn't work.

Then, I tried that in Celestia. And, it actually showed the eclipse! I wasn't expecting it to be that accurate. And it also has that eclipse finder. But I was just advancing the time.

My question is: Does orbits in Space Engine need to be updated? I get it that it is still beta and that stuff, but I think it is easier just for Moon to get it's path right. This is more of a suggestion than some question for science and astronomy, but okay.

And also: Does the Moon looks like it travels from west to east during the eclipse because it travels slower than Sun on our sky? Because a lot of people have trouble answering this question. i think I got that right. Well, that's what I would answer if someone asked me.

Does orbits in Space Engine need to be updated?

Yes, and SpaceEngineer said he would try to do it before the eclipse itself.

Does orbits in Space Engine need to be updated?

Yes, and SpaceEngineer said he would try to do it before the eclipse itself.

Okay, thanks! I was just wondering if he was thinking about orbits. It looks like he was. 

Thank you for your answers.

Lets say we had a piece of wood, about the width of a 2x4, a lightyear long somehow. Lets say it was in space, and you were in a spacesuit with some form of rocketpack, you turn it on and push the piece of would. Would the entire thing move as you push 1 end? Thatd break the speed of light though. 

Lets say we had a piece of wood, about the width of a 2x4, a lightyear long somehow. Lets say it was in space, and you were in a spacesuit with some form of rocketpack, you turn it on and push the piece of would. Would the entire thing move as you push 1 end? Thatd break the speed of light though.

No. Rigid bodies are not scalable like that.
Also, the thing that make that rod react to your push is a concatenation of cause and effect in the microscopic scale so fast that you don't percive the deformation, but not faster than the speed of light.

The stress and tension inside the rod in fact is just the push and pull excerted by the electromagnetic fields of the atoms that compose the rod. To communicate that push or pull the information from the charges of the different particles has to arrive to a certain point in space as to comunicate a change in the field. That information travels in fact at the speed of light. So no. in the best case the parturbation would traverse the rod at light speed for exactly one year (AT BEST).

But I think there is an interesting issue here appart from this. Would you say that the rod has been deformed? or is acting as a deformed body? or is totally rigid but in a very special geometry (space-time)?. With this I mean for example that if you consider the fact that simultaneity can be broken could you consider from the frame of reference of the traveling perturbation that the rod is moving as a rigid body? Wouldn't from that frame of reference all the parts of the rod moved at the same time?