I'm writing about a spaceship that drops past L-5 from Mars to the sun, performs a tight Oberth maneuver (@ 10 million K from sun?), has 1.5g acceleration at perihelion, but loses thrust before finishing its maneuver and swings wide. It needs a Jupiter gravity assist to change orbital planes, and I'm thinking that orbit to Jupiter will be a long one--13 AU? 15? the ship needs to "chase" Jupiter. It needs two or three months to get to Jupiter, time for the crew to repair systems that will be needed there, damaged in the CME that knocked out their propulsion. They have limited, intermittent propulsion (1/2 time) 2-3 days after leaving closest approach; I'm thinking I should limit that to .1 or .2 g acceleration. Several weeks later they get their badly-damaged main engine (a fusion-powered VASIMR) back online; that gives them ~.1 g (?) acceleration until almost Jupiter, when they finally get their inertial-reduction coils rebuilt and can thrust at 1g.
I can do simple acceleration-time-distance etc. calculations, and when I remember to add in all of the conversions, my answers are close to those produced by online relativistic spaceship calculators--and .1 or .2 g seems plenty.. But nothing I find online tells me how to account for the "gravity tax," the need to subtract out solar escape velocity from 10 diameters out.
Anybody here know that math?