Sphere of influence

[MetricKerbalist]

Hi KSP colleagues,

I would please like to think out loud for a moment about this amazing and highly educational game of Kerbal Space Program.  I am still new to it, so I have much to work out.  I want to make sure that I understand something correctly.

According to the Kerbal Space Program wiki, the distance from the center of Kerbin to Mun is 12'000'000 metres.  Moreover, Kerbin's sphere of influence is 84'159'286 metres, whereas Mun's sphere of influence is 2'429'559 metres.

Therefore, Mun and indeed Mun's entire sphere of influence lie entirely within Kerbin's sphere of influence.

And next I am going to quote a statement from Wikipedia:

Kerbal Space Program "simulates trajectories and orbits using patched conic approximation instead of a full n-body simulation."

Thus, when we analyze Mun's influence on a nearby spacecraft, are the following statements correct:

• We only have to consider Mun itself along with Mun's sphere of influence.
• We do not have to take into account Kerbin's sphere of influence.
• In the real world, Mun -- as well as Kerbin -- would affect a spacecraft in Mun's vicinity.  In the real world, this would exemplify a 2-body problem.  Indeed, we could also consider the influence of Kerbol, and thereby have a 3-body problem.
• However, the physics of KSP are such that within Kerbin's sphere of influence lies a hole -- that is, a discontinuity.  That discontinuity is Mun's sphere of influence.

Do I understand things correctly?

Thank you.

Stanley

[RCgothic]

Yes, the physics of KSP include discontinuities. When a spacecraft moves from one sphere of influence to another (defined by a simple radius on a per body basis) it experiences a sudden switch.

In real life there is no discontinuity and things like libration points exist where the forces cancel out. Orbits are no longer pure ellipses when you consider n bodies either. This would be extremely resource intensive to calculate for a dynamic situation such as a game.

Patched conics is a good approximation for performance reasons, but it is not fully realistic.

Edited June 24, 2021 by RCgothic

[Geonovast]

Moved to Gameplay questions as it's about KSP and not real planets

[18Watt]

Yes, vessels on KSP will only be affected by a single celestial body at any given time.   Traveling from Kerbin to Mun, your vessel will either be affected by Kerbin’s gravity OR by Mun’s gravity, but never both.   At the moment your vessel transitions into Mun’s sphere of influence (SOI) it no longer considers Kerbin’s gravity at all.

In real life you could say that Mun itself is affected by Kerbin’s gravity, so your ship would be too.   However, in KSP the orbits of Celestial Bodies are locked.

[MetricKerbalist]

Hi @RCgothic and @18Watt,

Good.  Thank you for addressing my questions and confirming my understanding.  Mind you, please, I am not criticizing KSP at all for modifying physics.  I just needed to get all this straight in my mind.

Hi @Geonovast,

I didn't mean to post my question in the wrong place.  Thank you for moving it.

Stanley

[Zhetaan]

42 minutes ago, MetricKerbalist said:

Thus, when we analyze Mun's influence on a nearby spacecraft, are the following statements correct:

• We only have to consider Mun itself along with Mun's sphere of influence.
• We do not have to take into account Kerbin's sphere of influence.

Correct for a vessel that is inside the Mun's sphere, yes.  For a vessel just outside the sphere, then you accout for Kerbin's sphere and ignore the Mun entirely.  It's all one or all the other.

44 minutes ago, MetricKerbalist said:

• In the real world, Mun -- as well as Kerbin -- would affect a spacecraft in Mun's vicinity.  In the real world, this would exemplify a 2-body problem.  Indeed, we could also consider the influence of Kerbol, and thereby have a 3-body problem.

You're actually down a body.  The two bodies in the 2-body problem can be two massive bodies, or they can be a massive body and a negligible-mass body.  The difference pertains to whether the mass difference is enough for you to effectively treat one body as being at rest.  At a certain mass threshold, that approximation no longer holds.  Also, in the real world, you'd have to consider not just the gravitational influence of the sun, but also the radiation pressure, drag from any wisps of atmosphere, the effect of uneven mass distribution throughout the celestial bodies, precession occurring because of relativity, the possible influence of Jool (I never have gotten a good answer about Jool-driven perturbations of a realistic Kerbin system orbit--probably because the Kerbin system isn't completely stable in realistic physics), and other factors.

53 minutes ago, MetricKerbalist said:

• However, the physics of KSP are such that within Kerbin's sphere of influence lies a hole -- that is, a discontinuity.  That discontinuity is Mun's sphere of influence.

It's less a hole and more a piecewise-smooth function with derivatives equated at the boundaries to effect an equally-smooth kinetic energy handoff at the transition within the limits of the fact that the velocity vector is changing direction.  In less technical terms, it's a discontinuity in the strictest sense, but it is deliberately engineered to slot into the space in as smooth and unobtrusive a way as possible (while also allowing for the fact that there's a massive body there, obviously).

1 hour ago, MetricKerbalist said:

Do I understand things correctly?

You've got the right idea.  However, I would point out that, like most things KSP, there's a mod for that.  It's called Principia and simulates n-body physics.

[MetricKerbalist]

7 minutes ago, Zhetaan said:

You've got the right idea.  However, I would point out that, like most things KSP, there's a mod for that.  It's called Principia and simulates n-body physics.

Hi @Zhetaan,

First, thank you for the added scientific information.

Second, thanks for telling me about the mod.  Believe me, however, I have my hands full with the stock program before I so much as consider adding mods.  Still, I and, I am sure, other KSP colleagues are glad to know about Principia.

Stanley