# Trivial lower bounds for single point mass delta-v problems?

Given two arbitrary elliptic orbits around an ideal single point mass, there will always exist a transfer with the minimal $$\Delta v$$ required.

It's easy to find an upper bound for this ideal transfer:

$$\Delta v = \sqrt{\frac{2\mu}{r_{P1}}} - v_{P1} + \sqrt{\frac{2\mu}{r_{P2}}} - v_{P2}$$

This is a general bi-elliptical transfer, and it's sometimes not possible to do better than that.

It sets a maximum $$\Delta v$$ required for arbitrary transfers. Are there any trivial lower bounds for the minimal $$\Delta v$$ required?

• I'm no expert, but I would've thought the minimum delta V transfer around a non-gravitationally complex single mass in many cases would be your namesake. – Ingolifs Sep 26 '19 at 17:38
• Only for planar, circular orbits. – SE - stop firing the good guys Sep 26 '19 at 17:54
• You could, perhaps, calculate all possible transfers at a specified interval then iterate through them using an algorithm to decide which is most efficient. That's kind of a cop-out though, I'm sure there's a mathematical way to do it. – Magic Octopus Urn Sep 27 '19 at 5:29