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The Aziz

How small the >orbitable< body can be?

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That question came to my head today and I'm extremely curious.
In stock game the smallest body we can get around is Gilly, but that's still huge when compared to bodies from various planet packs. Hale from OPM or Nuu from forgotten Trans-Keptunian.

But its radius is still 4000m. While the biggest asteroids are smaller than a 100m across, and of course they act like parts, not like celestial bodies.
So, the question is, again, how small in-game body can be? Is there a limit? How heavy would it be? Is there a way to determine it? There are more questions than I can articulate, so let the possible answers be more than simble "yes x m y kg"

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Well now I want a moon that's like 100m in diameter but with Kerbin's surface gravity.

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In semi-stock I think you can run the body arbitrarily small using the rescale mods.

the principa mod... I think may have a different answer. But, I'm not sure what it might be.

Of course that is for very strict definitions of orbit.

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If only there existed someone to explain science to KSP players...  That said, I'm not sure how you would go about googling this one:

https://www.youtube.com/watch?v=Bt54lfOFsDs&amp;list=PLYu7z3I8tdEn2m_lLL3Vn7BDwkvMLo_hl&amp;index=112&amp;t=0s [for some reason embedding the video embeds the wrong one].

The catch here is that you need the object far enough from any other mass so that its sphere of influence is large enough to allow an orbit (you also need Squad to bother allowing a sphere of influence that large when most players will be more interested in how they are orbiting Kerbol).  I'd recommend installing Principia if you want to play with such low power orbits.

1 hour ago, Geonovast said:

Well now I want a moon that's like 100m in diameter but with Kerbin's surface gravity.

http://google.com/toy-solar-system-mods/

Note that they have dire warnings about not being compatible with 1.0.5, so you might have to pull an ancient copy (from the souposphere era) to be able to use it.  I'd expect a jet-powered car to be able to get a kerbal going fast enough to get into orbit using a jetpack (you might even manage on a jetpack powered go-cart, the problem is you can't liftoff in a one-g gravity).

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I messed about with Kopernicus a bit a few years ago. I didn't get very far but I did make a tiny planet with a diameter radius of 500 meters. I made it have next to no gravity (Hyperediting in gave me a hyperbolic trajectory with several million years to go). I'd assume I could make it smaller if I wanted, but I really just wanted to mess around in a Star Wars-like spacemosphere and the planet was just there because it had to be.

Prüph -

 

Edited by Fireheart318
Changed time of video start. Also, for those who are wondering, that weird word is pronounced like "proof". It is proof. I'm just in a weird mood today.

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1 hour ago, wumpus said:

Note that they have dire warnings about not being compatible with 1.0.5, so you might have to pull an ancient copy (from the souposphere era) to be able to use it.  I'd expect a jet-powered car to be able to get a kerbal going fast enough to get into orbit using a jetpack (you might even manage on a jetpack powered go-cart, the problem is you can't liftoff in a one-g gravity).

If the planet is small enough, then jumping + jetpack will get you past the distance where the jetpack has >1 TWR.

If the planet is small enough, then running eastwards could get you the required orbital velocity and the jetpack merely has to circularize.

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@The Aziz:

In the game, a gravitational body (meaning that it is orbitable, as you put it) has to have a sphere of influence.  Mathematically, the sphere of influence is dependent on the semi-major axis of the body's orbit about the sun (or whatever its primary, in the case of moons and exoplanet packs) and on the mass ratio between the primary and its satellite.

That means that the closer a body is to the sun, the smaller its sphere of influence is--or alternatively, the more massive it must be to maintain a sphere of influence of a given size.

This works in reverse:  the farther out a body is, the smaller it can be and still have a sizeable sphere of influence.

Therefore, the limit is almost certainly a factor of the game engine, though I do not rule out the possibility that the devs coded a limit in order to limit bugs in the calculations.  Also note that there is no reason why planet size and planet mass need be related:  one could imagine a low-density body of sufficiently low mass that its sphere of influence only extends to one metre above the terrain.  I don't know what would happen if you tried to code a planet of such low density that its surface extended outside of its sphere of influence--I suspect it would involve new and interesting forms of Kraken.

The short version is that your question is open-ended and the answer depends largely on where your planet is with respect to the sun.

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10 minutes ago, Zhetaan said:

Therefore, the limit is almost certainly a factor of the game engine, though I do not rule out the possibility that the devs coded a limit in order to limit bugs in the calculations.  Also note that there is no reason why planet size and planet mass need be related:  one could imagine a low-density body of sufficiently low mass that its sphere of influence only extends to one metre above the terrain.

Then goes another question. Is body density a variable? I can imagine that gravity is constant and its pull changes along with mass of chosen body (or maybe I choose wrong words, I'm not too familiar with these definitions in another languages) but, taking this from the other side, one could make a body with density greater than average neutron star (and, as side efect, their CPU would explode). I can only imagine that density is hardcoded and everything is made from the same Kerbinium.

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2 hours ago, suicidejunkie said:

If the planet is small enough, then jumping + jetpack will get you past the distance where the jetpack has >1 TWR.

If the planet is small enough, then running eastwards could get you the required orbital velocity and the jetpack merely has to circularize.

The requested planet has "Kerbin's surface gravity", so the stock kerbal jetpack doesn't have a TWR >1.  I really don't know if "toy solar system's" Kerbin requires more than 600m/s delta-v to get into orbit, but that seems low (Earth is 9,000 1/10th with the same surface gravity (Kerbin) is 3,000, presumably 1/100th with same surface gravity >600 m/s).

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2 hours ago, The Aziz said:

Then goes another question. Is body density a variable? I can imagine that gravity is constant and its pull changes along with mass of chosen body (or maybe I choose wrong words, I'm not too familiar with these definitions in another languages) but, taking this from the other side, one could make a body with density greater than average neutron star (and, as side efect, their CPU would explode). I can only imagine that density is hardcoded and everything is made from the same Kerbinium.

Density is not a variable in and of itself, because KSP models gravity as being generated by point-masses with no real volume.  In the technical sense, density is not coded at all.  This is why, for example, you can clip through the terrain (with certain bugs:  pre-v1.0 claw could do this, as could submarines from the same period) and find yourself under the world's hollow shell while you descend into nothingness.  Gravity in KSP obeys the inverse-square law, so it's not constant--it changes with both the mass and the distance from that mass.  Instead, the terrain distance from the gravitational centre of the planet is the constant, and it gives you the appearance of density from the planetary radius.

Remember that in the code, gravity emanates from a point source (so, in theory, you already have your collapsing neutron star) and the sphere of influence is determined entirely by the strength of that gravity (determined by the mass, which is a variable), its interaction with the gravity of whatever that point source orbits (determined by the relative masses), and the semi-major axis of their orbit.  The semi-major axis is relevant because the distance between gravitational sources, in obedience to the inverse square law, affects the interaction.

Planetary volume is completely unrelated and consists only of a thin shell of terrain that essentially levitates suspended at a fixed distance from that point source:  the distance (and the volume derived from it) are arbitrary.  The effect is that the terrain holds your vessel at a fixed distance from the gravitational source, which fixes the radius and thus puts an upper limit on the strength of that gravity as you feel it on the surface.  My point in my earlier post is that because planetary radius and planetary mass are unrelated, there's nothing really stopping you from having a planet whose gravity is so low and whose radius is so large that its sphere of influence extends to just above the surface, making most surface activities impossible.

There was an old planet pack called the Sentar Expansion that dealt with something a little similar to this idea:  in it was a moon named Inaccessible which had a surface rotation in excess of the orbital velocity at that altitude (actually, in excess of the escape velocity), which meant that most landings saw ships either destroyed or flung out of the sphere of influence.  Never mind that in reality, a body rotating faster than its own escape velocity would--almost by definition--fly apart.  The solution, if you're interested, was to land at the poles, because the tangential velocity of rotation was lower there.  But the point is that the terrain in this case had absolutely nothing to do with the local gravity, which is why the moon didn't destroy itself as it otherwise would have.

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2 hours ago, wumpus said:

The requested planet has "Kerbin's surface gravity"

The OP said nothing of the sort.

 

I imagine you can make the body as small as you want, as long as the SOI has a larger radius than the radius to the surface of the body.

To calculate the SOI: semiMajorAxis * Pow((bodyMass / parentMass), 0.4);

where the semiMajorAxis is the semi major axis of the orbit ellipse between the body and the parent body. bodyMass is the mass of the body you're trying to make, and the parentMass is the mass of the body you're putting it (the body) in orbit around.

So it's going to depend on how massy the body you're putting it in orbit around as well.

Edited by se5a

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A body with a surface gravity of 9.8 m/s (1 G) and a radius of 1 meter would have a gravity of 0.25 G at 2 meters. So if your kerbal could jump 1 meter high, then then the kerbal's RCS pack would only need a TWR of 0.25. Also if your kerbal could jump 1 meter high on Kerbin, on this super dense 1 m radius body, the kerbal would be able to jump much higher because the pull on the kerbal would decrease so fast as it gets higher

AFAIK, with kopernicus, there is no limit to how small you can make the planet, although I would expect bugs to appear when it gets too small (ie, you get too close to having a singularity)

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On 9/4/2018 at 3:46 PM, wumpus said:

The requested planet has "Kerbin's surface gravity", so the stock kerbal jetpack doesn't have a TWR >1.  I really don't know if "toy solar system's" Kerbin requires more than 600m/s delta-v to get into orbit, but that seems low (Earth is 9,000 1/10th with the same surface gravity (Kerbin) is 3,000, presumably 1/100th with same surface gravity >600 m/s).

The jetpack does not have TWR >1, but the Kerbal's *legs* do!

See:

On 9/5/2018 at 3:13 AM, KerikBalm said:

A body with a surface gravity of 9.8 m/s (1 G) and a radius of 1 meter would have a gravity of 0.25 G at 2 meters. So if your kerbal could jump 1 meter high, then then the kerbal's RCS pack would only need a TWR of 0.25. Also if your kerbal could jump 1 meter high on Kerbin, on this super dense 1 m radius body, the kerbal would be able to jump much higher because the pull on the kerbal would decrease so fast as it gets higher

AFAIK, with kopernicus, there is no limit to how small you can make the planet, although I would expect bugs to appear when it gets too small (ie, you get too close to having a singularity)

 

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The smallest is around 1 kilometer. You can theoretically get smaller, but the game won't say that it's under one km under the properties tab. I'm not 100% sure though.

Edited by Adstriduum

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