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So to ansver your question we need Ike-AP + Ike-SOI = Your-New-PE that you must not drop below in Your-Duna-Orbit.
Ike apoapsis = 3 296 000 m ( from Duna center )
Ike-SOI = 1 049 598.9 m ( from Ike center )
( source http://wiki.kerbalspaceprogram.com/wiki/Ike#cite_note-centered-1 )
So .... 3 296 000 + 1 049 599 = 4 345 599 m
Is this correct? Does it make sense?
'In orbital mechanics, the apsis technically refers to the distance measured between the centers of mass of the central and orbiting body. However, in the case of spacecraft, the family of terms are commonly used to refer to the orbital altitude of the spacecraft from the surface of the central body (assuming a constant, standard reference radius).'
(source: https://en.wikipedia.org/wiki/Apsis)
The same obviously applies to the periapsis as well then.
So this is where things get confusing - I would again argue that the Ike (planetary body) apoapsis is calculated from Dunas center of mass (as maj.solo pointed out), however the periapsis of your ship (spacecraft) is calculated from Dunas surface thus requiring you to subtract Dunas equatorial radius in order to 'convert' between both ways of calculating orbital altitudes.
Ike apoapsis = 3 296 000 m ( from Duna center )
Ike-SOI = 1 049 598.9 m ( from Ike center )
Duna equatorial radius = 320 000 m (also from KSP wiki)
3 296 000 + 1 049 599 - 320 000 = 4 025 599 m (spacecraft periapsis)
Thoughts / objections?
Only reason for that is that the altimeter on the space craft is from surface. But if you take the numbers above and set the altimeter to that you DEFINITELY will NOT get into Ike SOI,
Measuring from the center makes it easier add and subtract distances in various directions. He could recalculate
Ike_AP + Ike_SOI - Duna_Equatorial_Radius
You definitely want to set the altimeter to something higher than the theoretical minimum but that is what was asked for here ;)
4 026 000 m should be safe enough though.