Is it possible to have a non-escape orbit that is equidistant to two celestial bodies (for example, Earth and Mars) at all times? If possible, how much does it cost to keep an object (which is much smaller than both of the large bodies) in such a trajectory?
Detailed in response to comments:
As @BMF says, all points that are equidistant to two distinct given points is a plane perpendicular to the line segment connecting them passing through its midpoint. However, there is a peculiar orbit in that medial plane such that you make a near-right angle between lines of sight to said bodies. That orbit enables a 3-axis stabilised satellite to have its antenna assembly and solar (panel and sail) assembly in the same side and at the same time enabling very tightly focussed (narrower than arc-second) communication beams, greatly simplifying the satellite design. Which is the initial motive of asking this question.