# Ballistic missile typical trajectory - along which path is it supposed to travel between Russia, China and US?

Today I was puzzled when my son was holding a school globe asking me to show with my finger a trajectory of a (nuclear) ballistic missile flying from US to China and Russia and vice versa (from Russia and China to US:)))

There should be some optimal trajectories and some general limitations on possible trajectories at all.

All I could remember that in space there are no "straight line" trajectory - only ellipses with different eccentricity.

Could you provide trajectories and some general considerations what kinds of paths are prohibited and which ones are most optimal and why?

What continents / parts of ocean / major cities :) does it fly by?

But really, I know that such trajectories are very complicated and I don't have a clue.

• I find that presentation authoritative but pretty darn dense. Is it possible to add a sentence or two and just mention the key messages we can get from it? ("read this presentation" is not really an SE answer). Also I'm stuck wondering if $\theta_{bo}$ up through slide 14 is the same as $\phi_{bo}$ from 15 onward? Thanks! – uhoh Feb 21 '19 at 0:55