With the Helios Star System, what does it exactly mean by 'Everything to do with astrophysics'?
By that I mean everything I have calculated about the planets and stars of the Helios System, from a physics (this branch being called astrophysics) angle.
All the things I’ve calculated for all are:
Radii/Diameters
Luminosity of the star aka Helios
Hill Sphere (the closest an object can orbit without being pulled in by the larger objects gravitational pull)
Mass
Gravity
Average surface temperature + Core temperature of Helios
Orbit radius (distance from star)
Orbital period (length of year)
Orbital speed (how fast it moves along its orbit)
Bond Albedo (how much light is reflected by the surface)
Average density of the planets
Water % on surface (for most)
Surface Area & Atmospheric Pressure for half
So most of the sciency stuff to do with the Helios system I’ve got covered.
When it comes to more people oriented and culture stuff, the countries that exist there I’ve got pretty much nothing- so that’s what I mean by ‘everything to do with astrophysics.’
This is a quick post, queued up before my vacation. All there is to it is a quick visualization of a handful of stations in a constellation and their respective hill spheres
From furthest to closest to the asteroid:
One of my standard station styles, a hollowed out sphere sized to rotate at 1 rpm. With shielding it should mass something like 30 Megatons, giving it a hill sphere just under 5000 in radius at 250 km from the asteroid’s center of mass. That’s large enough that there’s a small region around the sphere capable of supporting stable orbits.
An old classic, a pair of 1 rpm O’Neil style cylinders complete with glass floors taking up a third of the surface and reflectors to let the sunlight in. (What isn’t shown is the very necessary structure linking the two cylinders to prevent them from tumbling due to their inherent instability and killing everyone inside.) They each mass 88 megatons and at 200 km from the asteroid center they have hill spheres just under 5500 meters in radius. The small change in distance from the asteroid isn’t quite enough to make up for the more than doubling in mass.
Another of my stations, a 1/2 rpm hollow cylinder with a near-solid core to keep it stable despite having a length of pi times the radius. It masses roughly as much as both O’Neil cylinders put together but has a hill sphere just over 4900 meters, which isn’t even large enough to contain its full length.
And a 1 rpm Stanford Torus, with a hill sphere of approximately 1300 km thanks to its orbit keeping it 100 km away from the asteroid.
Visualizing the hill spheres gives me a general sense of how important the gravity of each station is to the system as a whole. If the station’s spheres of influence ever came close to each other, or worse touched, I could be confident that they’d screw up each other’s orbits in a fairly short timescale. As it is, although I'd need to build and run a simulation to be sure, I suspect that as I’ve drawn the system stationkeeping for anything but the rotavator would be a much much smaller and less important expense than ordinary maintenance.
In my fake advice column, the letter writers and the columnist talk about ‘constellations’ sometimes. What they’re referring to in that setting are groups of gravitationally linked habitats and asteroids that form their own scaled down solar systems of worlds where communication is instantaneous and transportation is possible in minutes or hours rather than weeks or months. It’s probably past time for me to actually give my very limited audience something to visualize.
So let's get back to Hill Spheres and build ourselves a constellation of space-station cities.
Step 1: Choose an Asteroid
This one that I just made up out of nowhere is an S-type with an average diameter of 10 km. It has a volume of 524,000,000,000 cubic meters, a density of 2700 kg/cubic meter, and a total mass of 1,415,000,000,000,000 kg. That gives it a surface gravity of 0.0038 m/s2, or roughly 1/2600 of Earth's gravity.
Step 2: Figure out the size of the Asteroid's Hill Sphere
Our asteroid is an Earth trojan, which puts it roughly 150,000,000,000 meters from the Sun, which masses roughly 2,000,000,000,000,000,000,000,000,000,000 kg. And altogether that gives it a hill sphere roughly 1,337,000 meters in radius. And a zone capable of comfortably supporting stable orbits of 445,000 meters.
Step 3: Build a shipping hub. If we're going to be doing asteroid mining, we're going to want a way to bring in heavy equipment and send out refined ores. Ideally, we'll want a structure that can send and receive shipments from either Mars or Venus orbits using banked momentum. That means we're looking at a velocity change of roughly 2.6 kilometers per second to transfer to Venus and 3 kilometers per second to transfer to Mars.
Unfortunately, we can’t do this with materials we can currently manufacture in bulk while maintaining a decent safety factor. What we can do is get halfway there, and even if we limit our payload acceleration to two gravities we can do that with a rotating Kevlar tether 115 km in radius*, which might as well have a comfortable Earth-gravity habitat with a radius of 57.5 km to bulk up the station and keep it more stable as it picks up and drops off payloads. The full rotavator doesn't need to be inside the stable zone of the asteroid's hill sphere, so long as the center of mass is.
So now we have an asteroid and a port city. We’re ready to start building a nation. But that’s next time’s post.
* I made a simple but serious error here originally, the maximum total velocity change that the rotavator can apply to a payload is 3 km per second but that’s catching a payload travelling 1.5 kps slower than the rotavator’s orbit and tossing it at 1.5 kps faster than its own orbit, not adding or subtracting 3 kps to a payload travelling at the rotavator’s own velocity- which is what would be needed to send a payload clear to Venus or Mars. -7/18/19
I decided to finally visualize an idea I talked about... huh I guess it was two and a half years ago. It’s a simple idea. Everything with mass warps space-time. That’s what we call gravity. Big enough things, that are far enough away from other big things, warp space around themselves enough more than everything else in the area that it’s possible for other things to orbit them. And, as it turns out, the sort of space stations I like playing around with are generally big enough as long as they aren’t in something like a low earth orbit.
The good thing about that is that it lets the people running the station park things in orbit around the station without needing to maintain a physical connection or to spend propellant keeping them in place. In this case, we’ve got a 2 kilometer diameter spherical station with inverted end caps that has a propellant depot/docking facility orbiting around its equator. Travel between the dock and the station is possible using simple mechanical catapults to send payloads into transfer orbits between the surface of the station and the docking facility. And this way, any accidents or other major safety incidents at the dock are a comfortable distance away from the station.
Here’s a closer view of the depot, with its sunshade and propellant tanks visible:
I had a follow-up question to the guy who asked if Earth had two moons. First, Thundaar references are always cool! Two, what if the moon had a moon? When the moons lined up with the Earth like an eclipse (it's still called an eclipse in this situation, right?) would the tides be stronger?
It’s entirely possible for our Moon to have a moon of it’s own. We have several artificial moons (we call them satellites) in orbit round our Moon, and a natural moon would behave the same way.
For a quick proof, the Earth can be considered a moon of the Sun, and the Moon is a moon of the Earth. You can continue this even farther by giving the Moon a moon, and maybe even give that moon a moon of it’s own.Of course, that gets crowded really quickly.
However, you couldn’t just put a rock in orbit around our Moon and have it be stable unless it’s within certain parameters. Nature has a way of keeping thing tidy.In a past column, I talked about the Hill Sphere. Today, I’m want to talk about another limit - the Roche Limit, and how the two work together.
The Roche Limit is a limit that nature sets on where your moon can go. While the Hill Sphere determines the furthest from your body that a moon can orbit without being pulled away, the Roche Limit shows the closest the moon can orbit without the moon being torn apart by gravitational stress.
A moon will only have a stable orbit if its orbits is between the Hill Sphere and the Roche Limit. These limits apply to every planet or moon - Earth, our Moon, or any other planet. The distances from the planet to the Roche Limit or Hill Sphere are affected by the distance a planet orbits its Sun (or a moon orbits its planet), how big the planet and moon are, and what the moon is made of.
If a moon comes closer that the Roche Limit to its planet, the gravitational difference between what the the moon feels on the side closest to the planet and what it feels on the side away from the planet will cause the moon to be pulled apart. The denser the material the moon is made of, the closer the moon can orbit. A moon made of metals takes more force to tear it apart than a moon made of cream cheese.
Artificial satellites are made of aluminum and titanium and very strong materials like that. They are much much stronger than rock or ice, so the Roche Limit for them is really really close to their planet. Effectively, if the satellite is artificial, don’t even worry about the Roche Limit of the planet/body it’s orbiting. The artificial satellite won’t be pulled apart.
So, lets assume that we want to place a moon around our Moon, and have it in a stable orbit. Lets also assume that this moon is made from about the same stuff that our Moon is made of - rocks, metals, and stuff like that.
Plugging numbers into the equations, we get these results:Moon’s Hill Sphere (dH): about 60,000 km from the center of the Moon. That’s about one sixth the distance from the Earth to the Moon. if the Moon’s moon orbited farther than that from the Moon, the Earth’s gravity would eventually pull it away into an orbit around the Earth.
Moon’s Roche Limit (dR): about 4000 km from the center of the Moon. The Moon’s moon would have to orbit above this distance or the Moon would tear it apart.The Moon’s moon would add it’s gravitational strength to the Moon’s, and would result in larger tides on the Earth. How much larger depends on the mass of this smaller moon. However, chances are the Moon’s moon would be much smaller than the Moon, and the effect wouldn’t be that big.And, yes, if the orbit of the Moon’s moon carried it in front of or behind the Moon as viewed from Earth, there would be eclipses,What would it look like if the Moon’s moon fell within the Roche limit and was torn apart? It would form a ring around the Moon - a ring made of much smaller pieces of the smaller moon,We have an example of that in our own system. Saturn’s rings were probably party made by a number of small moons that wandered too close and were torn apart.
Poor moons, but it’s given us one heck of a beautiful sight.
Building Constellations: Hill Spheres and Artificial Satellites
A couple weeks ago, I wrote a post on Hill Spheres, the regions around objects in space where it’s possible for those objects to maintain a satellite. I want to go back and take a quick look at what that means for constructions in space and why we might want to have them orbiting each other instead of either keeping them separate or physically attaching them to each other.
I’m going to look at four examples: a Stanford Torus orbiting Earth at the same distance as the Moon, a Stanford Torus orbiting the Sun at the same distance as Earth, a 1 km metallic asteroid orbiting the Sun at the same distance as Earth, and a Stanford torus orbiting the asteroid from the third example.
Case 1
So we have a Stanford Torus, a wheel-shaped rotating city in space with a radius of 830 meters and mass of about 10 billion kilograms, 95% of which is radiation shielding. It’s home to around 10,000 people, and it’s in its originally proposed location of the Earth-Moon L5 Lagrange point.
At that location, the Torus has a Hill Sphere of just under three kilometers in radius (assuming, like a good pretend physicist, that the torus is actually a solid sphere). It can support small stable satellites at up to half that distance from itself, or out to just under twice its own radius. These satellites will slowly drift around the torus, taking just over five and a half days to complete a single orbit.
What can we do with that? Why would we bother?
Imagine running a telescope attached to the Stanford Torus. You’re trying to watch a specific part of the sky, but the entire time, you have to deal with the Torus’s 1 rpm rotation and every vibration and tremor. If the telescope is separate, it doesn’t need to worry about either of those factors. And if it’s orbiting the Torus at just a few hundred meters, travel to and from the Torus for maintenance is simple and easy, and there’s no appreciable communications lag for control.
Or imagine you’re assembling or maintaining spacecraft. For the most part, gravity’s an annoyance, and on the Torus moving around significant masses of raw materials could cause stability problems and might need careful scheduling. If your dry dock is orbiting the Torus, you can be close to your workforce while maintaining complete control and autonomy over your own facility.
Or, let’s say that we actually care about safety. We can support a fuel storage and refueling station while keeping it far enough from the station that in a disaster, an explosion that would have split our city in two if it happened inside or in contact with the city will spread and dissipate so that it only causes a brief shudder.
Case 2
We have the same Torus, but now it’s orbiting the Sun instead of Earth. The major difference for the Torus is that relative to the Sun, its Hill Sphere is close to eighteen kilometers. And the difference that makes is that now it’s easy for two or more Tori to orbit each other. And at same time a lone torus, or a pair of them, can support more and more stable satellites.
Case 3
Now we have a 1 km diameter metallic asteroid in the same orbit as Case 2, with a mass of about 2.6 trillion tons. This has a Hill Sphere of over 1000 kilometers, allowing it to host other, smaller asteroids and space stations at a distance of up to something like 570 kilometers. Mining operations on such an asteroid could sort bulk materials and launch them to be caught and processed by specialized orbiting refineries. With an orbital velocity of only 0.5 meters per second at the location of the farthest stable orbits, there’d be only a trivial energy cost in moving the material, and the launching could be handled by hydraulic catapult systems rather than having to rely on mass drivers.
These bulky payloads could take weeks to reach their destinations, but in a hurry passengers could make the same trips in hours without major fuel costs.
Or, alternatively, a 1 km asteroid could support a station anchoring a rotovator allowing it to accept traffic from, and launch traffic to, destinations throughout the solar system without a significant need for fuel.
Case 4
Now one of our Stanford Tori is orbiting our asteroid from Case 3. If we keep it 570 kilometers from the asteroid, the torus itself will maintain a six kilometer Hill Sphere. That’s large enough that our torus can host an orbiting drydock large enough to construct entire cities using the materials from the parent asteroid.
Taken together, it’s easy to see that by remembering that it isn’t just planets and moons that have gravity we can open whole worlds of options for how to live and move in space.
