Hi all! Don't know if this is the place to ask this but I'm at my wit's end. I'm doing all this for a research project.

Tldr: Giant space cable from Phobos to catapult spacecraft towards earth. Because of Phobos's orbital angle wrt the solar system plane, the spacecraft would never reach Earth. What am I missing?

Expanding:

Let's say we were to put a skyhook around the moon. Because it would dip very close to the surface, I think using a frozen orbit is mandatory if we want the skyhook to last more than a few days because of the gravitational pulls of the mascons. So that leaves us with only 4 inclinations possible for our orbit : 26 50 76 and 86°

However the moon's obliquity is at 6.7° meaning that if we wanted to catapult something on a direct trajectory towards earth we would need the skyhook to be at 6.7° inclination with regards to the moon's equator. That doesn't match any frozen orbit

This problem also arises when using phobos as an anchor point for mega Skyhooks around Mars, with phobos's inclination to the ecliptic plane being at 26°

So launching from the moon might give us a weird trajectory around the earth but if launching from Phobos, the spacecraft would completely miss the earth and just orbit the sun

What am I missing? I haven't found anyone addressing this problem in any research papers.

Edit : Made a quick Paint drawing to illustrate my point using Phobos. https://www.reddit.com/user/FenuaBreeze/comments/n3e7qk/skyhook_on_phobos_and_orbital_inclination/?utm_source=share&utm_medium=web2x&context=3 As I understand it, the spacecraft launched from the tip of the red Skyhook will miss Earth by going "under" it because of how the inclination "aims" the Skyhook