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It's physically impossible unless the asteroid is huge like Gilly is.
https://forum.kerbalspaceprogram.com/index.php?/topic/162200-wip131-14x-151-161-principia%E2%80%94version-f%C3%A1ry-released-2019-05-04%E2%80%94n-body-and-extended-body-gravitation-axial-tilt/
Principia is wonderful, but it does not add gravity to any of the spaceship entities in KSP. This includes the asteroids.
To the OP, KSP only models gravity on the major bodies, not the small asteroids. Thus, it's impossible to orbit them. In reality, the asteroids would generate so little gravity anyway that it would be next to impossible to do it in KSP. yes, I know, we've done it in real life, but in KSP, you'd need to have very, very small amount of thrust - maybe RCS level or lower, and due to the very very low gravitational force generated by an asteroid, your orbit would be month or years long. It could be modelled, but I don't think anyone's done it due to the fact that it wouldn't really add anything to the gameplay. You can station keep near an asteroid now anyway just by matching the asteroid's orbit.
Not only is not physically impossible, but there are already several real life missions around small asteroids.
Google bennu ( osiris-reex), or Ryugu (Hayabusa2). Those are just a couple of examples
Yeah, I figured it might not but wasn't 100% sure. It was worth mentioning anyway because if someone is looking for this level of realism (microgravity), Principia is going to come as close as you can get.
Lame...
The largest asteroids have a mass around 400t or 400,000,000 kg.
The largest asteroid have a radius of let's say 50 meters.
Using the equation, a=G*m/r^2, acceleration can be solved for to find the gravitational acceleration of a craft some distance away from the asteroid.
G is the gravitational constant at 6.67*10^-11 N*m^2/kg^2.
a = 6.67*10^-11*400,000,000/50^2 = 0.000010672 m/s^2 or 10.672 micrometers/s^2.
Assuming the space potato allows for an orbit of 50 meters, we can use the equation, T=2*pi*r^(3/2)/(G*M)^(1/2), to find the orbital period.
T = 2*3.14*50^(3/2)/(6.67*10^-11*400,000,000)^(1/2) = 13,600 seconds or 3 hours 46 minutes 40 seconds.
You can orbit an asteroid but it would be very difficult.
I never said it was easy. You said it was "physically imposible", and i showed you a couple examples to show that is not, at least in real life, for KSP it might be indeed not worth the time of a modder to make it possible like desrtfox071 says.
But if you are going to bother doing some maths to prove something and call someone "Lame", at least do them right. A ton is 1000Kg, not 1000000Kg, and you can't orbit a 50 meters radius body with a 50 meters radius orbit for obvious reasons.
I had a unit conversion error.
Thanks for catching that.
Replacing mass with 400,000 kg, keeping the 50 meters the same, gives an acceleration of 1.0672*10^-8 m/s^2 and an orbital period at 60 meters of about 565,345 seconds or 6 (Earth) days 13 hours 2 minutes 25 seconds with a circular orbit velocity of 0.02 m/s or 2 cm/s.
I was wondering why the period was so short earlier...
KSP has a hard time modeling very tiny velocity numbers and it would refuse to provide any orbital information on the Navball at that speed.
The reason why I said it would by impossible earlier was because the sphere of influence would be tiny.
Using the SOI formula of r=a(m/M)^(2/5) with r being the SOI radius, a being the semi-major axis of the asteroid, m being the mass of the asteroid and M being the mass of whatever it's orbiting.
If it's orbiting Kerbin, it would have to be a = r/(m/M)^(2/5) = 60m/(400000kg/(5.2915158*10^22kg))^(2/5) = 423,408,298 m, well outside the 84,159,286 m SOI.
Moving the space rock to orbit the sun gives 60/(400000/(1.7565459*10^28))^(2/5) = 1.06355*10^11 m or .71 Au.
Eeloo orbits between 0.45 Au and 0.76 Au, around 0.60 Au so your asteroid has to be in a stable orbit near Eeloo's Apoapsis to support a minimum circular orbit of 60 meters in radius.
Again, it's possible but just very difficult and time consuming.
I'm not sure KSP could do this accurately even with mods.
Correct me if I'm wrong but the reason you can't orbit an asteroids in KSP is they do not have a SOI programmed into them.
n-body physics would allow for anything to be orbited if it's far enough away from everything.
Asteroids would have tiny spheres of influence and given the constant SOI radii of all of the planets, spheres of influence are set in stone.
Having a constant SOI works perfectly when the eccentricity of the orbiting body is 0 but the reality is it changes depending on the object's distance from everything else so Eeloo should have a noticeably variable SOI.
An asteroid's SOI would almost always be below the surface of the asteroid unless you move it out past Eeloo.
From a technical standpoint yet. There is a wrinkle here that I haven't seen anyone really point out. Calculations for gravitational force are scaled geometrically. That means if you have X number of objects within the SOI of each other, and you switch that up to 2X, you now get 4 times the calculations. In fact, this is the main reason that KSP uses the SOI method in the first place. Additionally, if the spacecraft (asteroids count as spacecraft in KSP), each have a gravitational effect on themselves and "real" spacecraft, you now get unstable orbits, collisions, and a whole lot of extra burdensome calculations. For example, Principia, which gets rid of SOIs, but still doesn't give gravity to spacecraft, took a long time to get to the point where it wasn't a major burden on the CPU and also suffered from things like planets colliding into each other as well. Suffice it to say that there are very good reasons to not have gravitational effects from spacecraft, and honestly IMO, very limited reasons to do so (as I said in my previous post). The actual gravitational effects from asteroids in KSP would be very small, and really, consider it just a rounding truncation that super small bodies like asteroids don't have gravity.
EDIT: Jupiter ninja'd me :)
Asteroids are ship-like entities. Incidentally, running on rails is how KSP currently handles all planets/moons, etc. and any ship-like entity not "active" or within 2500m of an active ship.