Ship undergoes nongravitational acceleration in hyperbolic orbit

[MrSystems]

I have noticed that my heliocentric orbit on a transfer burn from LKO never looks quite like the planned maneuver node, and I have to do a correction (sometimes a massive one) after leaving Kerbin's SOI. I think it's a problem with KSP 1.6.1 and not with any of the mods I have installed. I think, further, it is a problem that can be confused for "warping too fast through the SOI change" and is most noticeable when changing SOIs but has nothing at all to do with changing SOIs.

Steps to Reproduce:

• Put a ship in low kerbin orbit.
• Burn to escape velocity.
• Go to the map screen and make note of where the ship is supposed to end up in Kerbol orbit
• Hit F5 to quicksave
• Open the saved file, and make note of the orbital parameters for the ship
• Wait a few in-game minutes (no need to warp)
• Hit F5 to quicksave
• Open the saved file, and notice the orbital parameters for the ship have changed
• Go to the map screen and make note of new, different orbital parameters in heliocentric orbit
• Wait or warp to but not past Kerbin's SOI, and repeat the above three steps

Problem Detail

I followed the above steps with my last launch, which was to achieve an apoapsis relative to Kerbol of ~831Gm. Immediately after the burn was completed I noted the orbital parameters in the save file, and I did so periodically later.  No warping happened between the first three columns, and all data is from within Kerbin's SOI. This is what I found:

	Immediately after	2 minutes after	5 more minutes	warping +5 hours	warping +40 min
MET	4,357	4,499	4,777	22,881	25,478
SMA	-232,942.2	-232,942.2	-233,004.5	-233,004.6	-233,004.6
ECC	4.6721	4.6721	4.6715	4.6715	4.6715
INC	11.37787102	11.37787089	11.37787088	11.37787104	11.37787104
LPE	180.4062	180.4062	180.4072	180.4072	180.4072
LAN	78.186933	78.186931	78.186930	78.186926	78.186926
MNA	5.20	9.85	312.32	355.70	355.70
EPH	426,124,386	426,124,664	426,142,769	426,145,365	426,145,365
v at SOI	3,904.455	3,904.455	3,903.936	3,903.935	3,903.935

The first 7 rows came directly out of the save file. MET= mission elapsed tIme (in seconds), SMA = semi-major axis, ECC = eccentricity, INC = inclination, LPE = argument of periapsis, LAN = longitude of ascending node, MNA = mean anomaly at epoch, EPH = epoch.  'v at SOI' is my calculation, using ROOT(mu*(2/SOI - 1/SMA)), of the residual Kerbin-relative velocity at the edge of the SOI, which directly relates to where the craft actually ends up after it leaves the SOI. The discrepancy of 0.52 m/s resulted in a 6 gigameter shift relative to my target (Plock).

What can be seen is:

• At the full 17-specific digit level used in the save file (not reproduced here) the final two columns are precisely identical in all respects, but none of the others match in any respect.
• Changes in MNA and EPH between the first four columns mean KSP was updating the ship's orbit each time (ship not "on rails").
• No changes in any variable between the last two columns mean that the ship went "on rails" at some point
• Most but not all of the change happened in the first 7 minutes after the burn was completed, while the craft was under ~500km altitude

From this data I conclude 1) that the KSP engine doesn't actually put orbiting ships on rails until some time after their thrust is cut off or until some altitude above Kerbin, and 2) the game is not correctly calculating orbital motion when the craft is not on rails. 

An additional supporting data point is that, during launches, Kerbal Engineer Redux indicates slight changes in my apoapsis (on the order of a few meters) after I've left the atmosphere on ascent.

I've even had problems getting to the Mun and Minmus from LKO, where the moon-relative periapsis at altitude ~2,000,000m is much different from what the conic sections indicated at the end of the burn from LKO.  One could perhaps blame one of my mods, such as PreciseNode, for mucking around with the conic sections, but what this data seems to show is that imprecise transfers are not due to imprecise conic sections or to "warping too fast through the edge of the SOI," but rather to imprecise tracking of ships near Kerbin. Some distinguished professors interpret unexpected nongravitational acceleration as proof of alien intervention in the solar system.

Because the "How To Get Support" thread asked nicely, here's my log, but there's nothing of interest there.