Jupiter's Gravity Well in the rotation reference frame of its orbit.
U = -k/r - ω² r
ω = angular rotation rate of Jupiter about the Sun

Expanded View of the above plot to show the curvature in the Gravity Potential and the location of the edge of the Sphere of Influence. R_SoI = d&radic[M_Jup/3M_Sun]
R_SoI = 0.355 AU
Also note the curvature in the Potential of the rotating frame, with a maximum at Jupiter, this is essentially a tidal force.

The hyperbolic orbit within the Sphere of Influence of Jupiter.

• a = -0.014 AU
• E = +31.2 MJ/kg
• b = 0.023 AU
• e = 1.96
• r_perijove = 1.95x10⁶ km
• Deflection = 61.3°

The Flyby of Jupiter as seen in the Solar System Reference Frame
This is the part within the Sphere of Influence of Jupiter. Movement is from lower right to upper right.