Question: Is it possible to refill ships of fuel while they are in orbit? If yes, why isn't it convenient to do it?

A large but empty ship refilled in orbit would have an incredibly high Delta-V, I think, allowing things like asteroid capture and more 

For one thing, it would be ideal to have a ship that does not need external refueling, or if so, does not need it often, and for another, exactly what type of 'fuel' it is - but that is neither here nor there.

I believe there are various ways to refuel ships in planetary orbit. I would take inspiration from aerial refueling operations used by the military. Obviously these take place within the atmosphere of Earth, so some different rules apply (like no gravity, air drag and maybe lower speeds etc), but the fundamental physics are not dissimilar: match the speeds of the tanker and recipient, establish connection in ways that do not violate the equilibrium and then after the fuel-up safely disengage.  Delta v and velocity may not be too much of an issue (though it will still be) if you can pull off a Hohmann transfer orbit with some sort of refueling station, and of course slow down a bit and get rid of that excess velocity (if you wanted to) - maybe by gravitational assistance or ramjet scooping engine (which was proposed to be a form of propulsion, before it was found to actually slow whatever it was propelling over time).

Various modes of technology come to mind when considering 'docking' with an object to refuel (around A PLANET), such as another ship (like a 'tanker' type vessel) that has the fuel you need, or in the same vein, a robotic probe that rendezvous with the orbiting ship.Or perhaps something like a space elevator-type abbreviation called a skyhook whose purpose it is to contain fuel and 'hook' passing ships to refuel. Again, a transfer orbit is needed. This might be a relevant link in regards to refueling the ISS: https://www.quora.com/How-does-and-how-often-does-the-ISS-have-to-refuel-in-order-to-maintain-enough-fuel-to-burn-its-thrusters

Is it convenient? Very much so - especially if you rely on 'refueling' your ships rather then having VERY long lived internal generators that produce the power (although that would be more for internal stuff like computers). The only reason we don't see this in the real world is because we simply don't have that much orbital infrastructure in space. Yet. But it is quite handy if you have got the technology. I'm sure that in Space Engine there will be operations you can do to refuel your ships, although the ships in the game rely on fusion to generate the alcubierre warp drive 'exotic matter' (I might be wrong on that one, I have not played the game in a while), the required hydrogen isotopes of which can be harvested basically anywhere in the universe.

That is my money on the matter, Others may add to it or disagree - I'm sure Watsisname will probably lay the verdict on it in the end.

Epicycles are also "right" if you keep adding enough of them

I came across this nice illustration how any orbit can be described by epicycles:
[youtube]QVuU2YCwHjw[/youtube]

Epicycles are also "right" if you keep adding enough of them

I came across this nice illustration how any orbit can be described by epicycles:
[youtube]QVuU2YCwHjw[/youtube]

That's just..... strange. :shock:

Mathlogger did an excelent video recently about this and how is connected to Fourier series.

[youtube]qS4H6PEcCCA[/youtube]

At the end of Geocentrism astronomers started to add epicycles on epicycles. This nested structure worked (and works still for the complex orbital perturbations we are able to measure today since you only have to add epicycles, or add terms of the Fourier series, to fit the data), but the reality is that the epicycle approach is unfalsifiable (any curve can be described that way) so it is not a scientific hypothesis. That's were Copernicanism won. Because copernicanism relied on a disprovable idea (and also because of Occam's razor; each new epicycle is a new assumption of how things are in reality while the Heliocentric model relies just in one assumption one might say).

Epicycles are also "right" if you keep adding enough of them

I came across this nice illustration how any orbit can be described by epicycles:
[youtube]QVuU2YCwHjw[/youtube]

Wow... 

Speaking of epicycles, I created this impossibility.

Fourier's discovery has had a great impact.  All audio and video compression (and hence almost 80% of internet traffic) relies on the principle of transforming the signal to be compressed to the frequency domain, reduce the data in that domain, then transfer it back.  Just like fewer epicycles require less information at the cost of details

That's were Copernicanism won. Because copernicanism relied on a disprovable idea (and also because of Occam's razor; each new epicycle is a new assumption of how things are in reality while the Heliocentric model relies just in one assumption one might say).

We could also say the Heliocentric model (combined with Newton's laws) has a predictive power.  Assuming gravity obeys an inverse square law predicts that orbits are conic sections (so the model could predict parabolic and hyperbolic orbits, even if it was only derived from observing elliptical orbits).  The orbit of any given object can also be predicted just by knowing the position, velocity, and the attracting mass.  

Observing some weird orbit would falsify it, or suggest that something else is happening than inverse square law attraction from a single source.  It might predict there are other sources, like Le Verrier predicting the location of Neptune.  Neptune would never be predicted from epicycles.

A problem with Ptolemy's epicycles was that they lacked a good way to explain the speed changes of planets.  Then Kepler discovered that the orbits can be modelled as ellipses (of which the circle is a special case), and he could also describe the speed in his second law, which was a really beautiful insight.

It's worth noting that each improvement of the understanding of planetary motion involves a generalisation of the previous theory.  Circles are a special case of ellipses, Kepler's laws became corollaries in Newton's laws of gravitation, like Newton's laws follow from Einstein's special relativity, which in turn is a special case of general relativity.  Now we must expect general relativity to become a special case of some new theory.

I came across an interesting video. I am wondering how could I calculate the orbital period of the configuration at 3:32. I know all of these are three body orbits which are unstable, but the one I am interested in appears to be doable in Space Engine.
[youtube]8_RRZcqBEAc[/youtube]

Edit: Another unrelated question. When will hydrogen and helium become minority elements in the universe? Will it even happen at all? If I am not mistaken, oxygen and carbon would then become the most abundant elements. What kind of stars would be forming and how long would they live relative to their mass? What would their life cycle look like? What kind of planets... CO₂ gas giants with diamond cores?

Same set of questions, but more far-fetched, When will carbon and oxygen also become minority elements?

If no other processes at play in the universe prevent it, iron ought to become the most abundant element, since fission releases energy for lighter elements and fusion consumes energy for heavier elements.

I calculated that I've spent just over a week airborne over the past 12 months covering a distance of about half a light second.  Does this also mean that I've travelled half a second further into the future than if I'd remained at home, or is the maths more complicated?

It's not distance but how long you were traveling and at what speed relative to say the ground, also to some slight degree slightly faster time passage due to having every so slightly less gravity being higher up.   Time slows down in when fixed in a gravitational well.

As for dilation relative to velocity there is a good calc here.

http://dilation.1e5b.de/index.php

The amounts are minuscule. Even 100 hours straight in a plane at 900 ish Km/h is so tinny you need many many decimal places of sec in precision to see it.

I calculated that I've spent just over a week airborne over the past 12 months covering a distance of about half a light second.  Does this also mean that I've travelled half a second further into the future than if I'd remained at home, or is the maths more complicated?

Half a light second (150,000 km) over a week period (7 days) is an average speed of 248 m/s. If we assume you traveled more or less at the same speed throughout your journeys, then after a 7 day period (604,800 seconds) you have travelled 0.0000002 seconds into the future (a fifth of a microsecond). Peaks in speed might change the result a little because of the strong dependance between time dilation and speed but I think this is negligible here since your are still moving in the low speed regime.

I obtain a 0.2 seconds result when I subtract 3 zeros to the speed of light. Maybe there is the problem. 300.000 km/s is 300.000.000 m/s.

Another unrelated question. When will hydrogen and helium become minority elements in the universe? Will it even happen at all?

That's a very interesting question and I doubt there's a simple answer. My bet is on the "Hydrogen will never be second rank in the chemical abundance of the universe" and here is why;

The chemical evolution of the Universe is driven by stellar nucleosynthesis or supernova nucleosynthesis, so star related processes (Big Bang nucleosynthesis finished a long time ago and we are going to ignore here us or aliens fusing Hydrogen like mad for billions of years across the Universe). So, the question is will the stars combust enought Hydrogen and produce so many heavy elements as to change the chemical abundance of the Universe enought before the end of the stelliferous era?

This is the "astrophysics periodic table". You can see how the elements were created. The vast majority of them depend on the existence of stars.


The stelliferous era is limited by the first stars of the Universe, 155 Mry after the Big Bang, and the last star some 10¹⁴ years from now (100.000 eons from now). This means that we are at the beggining of the era at 1/10.000th of the entire period (if the stelliferous era were as long as a human life of 100 years, then we would be 3 days and 16 hours old). This might mean that there is plenty of time to fuse the vast ammounts of Hydrogen we found in the Universe.

After the Big Bang 75% of all the ordinary matter was Hydrogen (by mass, but by number it was 95%). After 13.8 Gyrs of evolution we have reached a situation were 73.9% is Hydrogen. So, 100.000 eons will suffice to get to the 50%? Let's think a bit about it. That 1.1% decrease in Hydrogen over the entire history of the Universe was performed almost entirely in the first hundred million years when the large primordial stars burned Hydrogen at furious speeds. Also the star formation rate has dropped at least an order of magnitude, since the first hundred million years and the universe is very quiet now in comparison. So the drop in Hydrogen abundance is not constant, its slowing down.

Now remember that stars are not perfect fusion engines. Fusion only happens at the core, so 10% of the mass of the star is subject to fusion. But even then not all that 10% would be fused since the core is intoxicated with heavy elements that sink into the heart of the star. Currently stars are almost entirely made of Hydrogen but the majority of this Hydrogen will last for billions of years and will survive after the death of the star itself (refueling another new-born star perhaps). Also think about all the Hydrogen lost as a diluted substance by stellar wind (protons are ionized Hydrogen atoms). Stellar winds will have a hard time to coalesce into a cloud and collapse into an other Hydrogen fusing star, those atoms can only hope to be fused if their orbit across the galaxy intersect a star froming region or are pulled by a dense object. In fact the interstellar medium of our galaxy is full of Hydrogen that has yet to be fused (most of it comes from the outer shells of exploded stars). At least 5 billion solar masses of Hydrogen (5% of the mass of the galaxy) is still lurking in the galaxy as interstellar medium (a galaxy that has been here for 11 billion years and hasn't been able to depleate all that hydrogen, try to think about all the hydrogen still present in all the stars that wont get fused any time soon).
But yeah, one could argue that in the end, after 100.000 eons our galaxy (and all the galaxies) would be able to deplete all the hydrogen inside them, slowly.

But what about outside the galaxies? Look at the Smith Cloud for example, it is a 9.800 light year sized beast containing 1 million solar masses of Hydrogen that we have been able to detect only because it is getting warm while colliding with our galaxy. Take a look to Hanny's Voorpwerp a huge hydrogen cloud, extending hundreds of thousands of light years and boasting a total mass amounting to five billion times that of the Sun. We have seen that cloud only because a nearby galaxy went into an active period and relativistic jets shooting from the central black hole probably brightened the cloud.



Clouds like this or larger might be here and there close and far to our galaxy and others, just floating in the darkness of intergalactic space since the beggining of the universe, filled with pristine Hydrogen and unable to collapse on themselves to form stars and fuse that Hydrogen because of the low densities involved and the scarce interactions with other objects.

Will stars deplete the majority of Hydrogen from our galaxy? Maybe. Do galaxies will absorb the majority of intergalactic hydrogen still present? I have a serious doubt. Inside galactic clusters between 80% and 95% of matter is located in the intracluster medium instead of the galaxies themselves (according to Wikipedia) and the chemical evolution of that sparse matter has been small so that is almost all Hydrogen and Helium. There are not only "clouds" (as Smith's cloud or Hanny's Voorpwerp) in intergalactic space but there is also the so called warm–hot intergalactic medium, a ethereal gas/plasma made basically of Hydrogen atoms and nucleai, which accounts for the 40% to 50% of the entire mass of ordinary matter in the Universe. A fraction of this gas might be pulled by galactic clusters and galaxies fuelling partially some new stars in the next trillion years, but the vast majority of it will survive without collapsing to form stars in the huge cosmological voids present today.

As matter in the universe coalesces in specific regions of space (galaxies become point-like gravitational atractors in the cosmological context) the intergalactic voids open and get larger (they even start fusing toghether), and if the hydrogen is not quickly pulled by galaxies the residuals are going to be harder and harder to pull from the voids. Newton's shell theorem (the fact that inside a hollow spherical shell there is no net gravitational attraction to any of the walls) and the Cosmological Principle (the fact that the Universe at this scale is more or less homogeneous in the distribution of matter) imply that the intergalactic medium (and particularly the gas inside intergalactic voids) is very difficult to suck. This fact combined with the expansion of the Universe will probably (in my opinion) make vast ammounts of Hydrogen unaccesible for galaxies and star formation would cease even if astronomical amounts of Hydrogen would still be present in the darkness of the Universe.

I don't think Hydrogen will ever leave the throne of the most abundant element in the Universe. But I could be wrong.

I don't know how much it would effect the outcome but M class stars are entirely convective so they will eventually fuse practically all their Hydrogen and continue as a Helium burning convective star. But one thing is the rate they fuse at is so much slower than the core fusion stars, in order of 100s of billions of years, perhaps into the trillions. They also happen to be quite common.